We propose a unified framework to study policy evaluation (PE) and the associated temporal difference (TD) methods for reinforcement learning in continuous time and space. We show that PE is equivalent to maintaining the martingale condition of a process. From this perspective, we find that the mean-square TD error approximates the quadratic variation of the martingale and thus is not a suitable objective for PE. We present two methods to use the martingale characterization for designing PE algorithms. The first one minimizes a ``martingale loss function", whose solution is proved to be the best approximation of the true value function in the mean--square sense. This method interprets the classical gradient Monte-Carlo algorithm. The second method is based on a system of equations called the ``martingale orthogonality conditions" with test functions. Solving these equations in different ways recovers various classical TD algorithms, such as TD($\lambda$), LSTD, and GTD. Different choices of test functions determine in what sense the resulting solutions approximate the true value function. Moreover, we prove that any convergent time-discretized algorithm converges to its continuous-time counterpart as the mesh size goes to zero, and we provide the convergence rate. We demonstrate the theoretical results and corresponding algorithms with numerical experiments and applications.

Gradient-descent (GD) based algorithms are an indispensable tool for optimizing modern machine learning models. The paper considers distributed stochastic GD (D-SGD)--a network-based variant of GD. Distributed algorithms play an important role in large-scale machine learning problems as well as the Internet of Things (IoT) and related applications. The paper considers two main issues. First, we study convergence of D-SGD to critical points when the loss function is nonconvex and nonsmooth. We consider a broad range of nonsmooth loss functions including those of practical interest in modern deep learning. It is shown that, for each fixed initialization, D-SGD converges to critical points of the loss with probability one. Next, we consider the problem of avoiding saddle points. It is well known that classical GD avoids saddle points; however, analogous results have been absent for distributed variants of GD. For this problem, we again assume that loss functions may be nonconvex and nonsmooth, but are smooth in a neighborhood of a saddle point. It is shown that, for any fixed initialization, D-SGD avoids such saddle points with probability one. Results are proved by studying the underlying (distributed) gradient flow, using the ordinary differential equation (ODE) method of stochastic approximation.

This paper proposes a Disentangled gEnerative cAusal Representation (DEAR) learning method under appropriate supervised information. Unlike existing disentanglement methods that enforce independence of the latent variables, we consider the general case where the underlying factors of interests can be causally related. We show that previous methods with independent priors fail to disentangle causally related factors even under supervision. Motivated by this finding, we propose a new disentangled learning method called DEAR that enables causal controllable generation and causal representation learning. The key ingredient of this new formulation is to use a structural causal model (SCM) as the prior distribution for a bidirectional generative model. The prior is then trained jointly with a generator and an encoder using a suitable GAN algorithm incorporated with supervised information on the ground-truth factors and their underlying causal structure. We provide theoretical justification on the identifiability and asymptotic convergence of the proposed method. We conduct extensive experiments on both synthesized and real data sets to demonstrate the effectiveness of DEAR in causal controllable generation, and the benefits of the learned representations for downstream tasks in terms of sample efficiency and distributional robustness.

In this paper, we provide a general framework for studying multi-agent online learning problems in the presence of delays and asynchronicities. Specifically, we propose and analyze a class of adaptive dual averaging schemes in which agents only need to accumulate gradient feedback received from the whole system, without requiring any between-agent coordination. In the single-agent case, the adaptivity of the proposed method allows us to extend a range of existing results to problems with potentially unbounded delays between playing an action and receiving the corresponding feedback. In the multi-agent case, the situation is significantly more complicated because agents may not have access to a global clock to use as a reference point; to overcome this, we focus on the information that is available for producing each prediction rather than the actual delay associated with each feedback. This allows us to derive adaptive learning strategies with optimal regret bounds, even in a fully decentralized, asynchronous environment. Finally, we also analyze an “optimistic” variant of the proposed algorithm which is capable of exploiting the predictability of problems with a slower variation and leads to improved regret bounds.

Understanding the properties of neural networks trained via stochastic gradient descent (SGD) is at the heart of the theory of deep learning. In this work, we take a mean-field view, and consider a two-layer ReLU network trained via noisy-SGD for a univariate regularized regression problem. Our main result is that SGD with vanishingly small noise injected in the gradients is biased towards a simple solution: at convergence, the ReLU network implements a piecewise linear map of the inputs, and the number of knot'' points -- i.e., points where the tangent of the ReLU network estimator changes -- between two consecutive training inputs is at most three. In particular, as the number of neurons of the network grows, the SGD dynamics is captured by the solution of a gradient flow and, at convergence, the distribution of the weights approaches the unique minimizer of a related free energy, which has a Gibbs form. Our key technical contribution consists in the analysis of the estimator resulting from this minimizer: we show that its second derivative vanishes everywhere, except at some specific locations which represent theknot'' points. We also provide empirical evidence that knots at locations distinct from the data points might occur, as predicted by our theory.

Learning optimal individualized treatment rules (ITRs) has become increasingly important in the modern era of precision medicine. Many statistical and machine learning methods for learning optimal ITRs have been developed in the literature. However, most existing methods are based on data collected from traditional randomized controlled trials and thus cannot take advantage of the accumulative evidence when patients enter the trials sequentially. It is also ethically important that future patients should have a high probability to be treated optimally based on the updated knowledge so far. In this work, we propose a new design called sequentially rule-adaptive trials to learn optimal ITRs based on the contextual bandit framework, in contrast to the response-adaptive design in traditional adaptive trials. In our design, each entering patient will be allocated with a high probability to the current best treatment for this patient, which is estimated using the past data based on some machine learning algorithm (for example, outcome weighted learning in our implementation). We explore the tradeoff between training and test values of the estimated ITR in single-stage problems by proving theoretically that for a higher probability of following the estimated ITR, the training value converges to the optimal value at a faster rate, while the test value converges at a slower rate. This problem is different from traditional decision problems in the sense that the training data are generated sequentially and are dependent. We also develop a tool that combines martingale with empirical process to tackle the problem that cannot be solved by previous techniques for i.i.d. data. We show by numerical examples that without much loss of the test value, our proposed algorithm can improve the training value significantly as compared to existing methods. Finally, we use a real data study to illustrate the performance of the proposed method.

Many current applications in data science need rich model classes to adequately represent the statistics that may be driving the observations. Such rich model classes may be too complex to admit uniformly consistent estimators. In such cases, it is conventional to settle for estimators with guarantees on convergence rate where the performance can be bounded in a model-dependent way, i.e. pointwise consistent estimators. But this viewpoint has the practical drawback that estimator performance is a function of the unknown model within the model class that is being estimated. Even if an estimator is consistent, how well it is doing at any given time may not be clear, no matter what the sample size of the observations. In these cases, a line of analysis favors sample dependent guarantees. We explore this framework by studying rich model classes that may only admit pointwise consistency guarantees, yet enough information about the unknown model driving the observations needed to gauge estimator accuracy can be inferred from the sample at hand. In this paper we obtain a novel characterization of lossless compression problems over a countable alphabet in the data-derived framework in terms of what we term deceptive distributions. We also show that the ability to estimate the redundancy of compressing memoryless sources is equivalent to learning the underlying single-letter marginal in a data-derived fashion. We expect that the methodology underlying such characterizations in a data-derived estimation framework will be broadly applicable to a wide range of estimation problems, enabling a more systematic approach to data-derived guarantees.

We consider infinite-horizon discounted Markov decision problems with finite state and action spaces and study the convergence rates of the projected policy gradient method and a general class of policy mirror descent methods, all with direct parametrization in the policy space. First, we develop a theory of weak gradient-mapping dominance and use it to prove sharp sublinear convergence rate of the projected policy gradient method. Then we show that with geometrically increasing step sizes, a general class of policy mirror descent methods, including the natural policy gradient method and a projected Q-descent method, all enjoy a linear rate of convergence without relying on entropy or other strongly convex regularization. Finally, we also analyze the convergence rate of an inexact policy mirror descent method and estimate its sample complexity under a simple generative model.

Block coordinate descent (BCD) methods are widely used for large-scale numerical optimization because of their cheap iteration costs, low memory requirements, amenability to parallelization, and ability to exploit problem structure. Three main algorithmic choices influence the performance of BCD methods: the block partitioning strategy, the block selection rule, and the block update rule. In this paper we explore all three of these building blocks and propose variations for each that can significantly improve the progress made by each BCD iteration. We (i) propose new greedy block-selection strategies that guarantee more progress per iteration than the Gauss-Southwell rule; (ii) explore practical issues like how to implement the new rules when using "variable" blocks; (iii) explore the use of message-passing to compute matrix or Newton updates efficiently on huge blocks for problems with sparse dependencies between variables; and (iv) consider optimal active manifold identification, which leads to bounds on the "active-set complexity" of BCD methods and leads to superlinear convergence for certain problems with sparse solutions (and in some cases finite termination at an optimal solution). We support all of our findings with numerical results for the classic machine learning problems of least squares, logistic regression, multi-class logistic regression, label propagation, and L1-regularization.

Imposing orthogonality on the layers of neural networks is known to facilitate the learning by limiting the exploding/vanishing of the gradient; decorrelate the features; improve the robustness. This paper studies the theoretical properties of orthogonal convolutional layers. We establish necessary and sufficient conditions on the layer architecture guaranteeing the existence of an orthogonal convolutional transform. The conditions prove that orthogonal convolutional transforms exist for almost all architectures used in practice for 'circular' padding. We also exhibit limitations with 'valid' boundary conditions and 'same' boundary conditions with zero-padding. Recently, a regularization term imposing the orthogonality of convolutional layers has been proposed, and impressive empirical results have been obtained in different applications (Wang et al., 2020). The second motivation of the present paper is to specify the theory behind this. We make the link between this regularization term and orthogonality measures. In doing so, we show that this regularization strategy is stable with respect to numerical and optimization errors and that, in the presence of small errors and when the size of the signal/image is large, the convolutional layers remain close to isometric. The theoretical results are confirmed with experiments and the landscape of the regularization term is studied. Experiments on real data sets show that when orthogonality is used to enforce robustness, the parameter multiplying the regularization term can be used to tune a tradeoff between accuracy and orthogonality, for the benefit of both accuracy and robustness. Altogether, the study guarantees that the regularization proposed in Wang et al. (2020) is an efficient, flexible and stable numerical strategy to learn orthogonal convolutional layers.

Many real-world structured prediction problems need machine learning to capture data distribution and constraint reasoning to ensure structure validity. Nevertheless, constrained structured prediction is still limited in real-world applications because of the lack of tools to bridge constraint satisfaction and machine learning. In this paper, we propose COnstraint REasoning embedded Structured Prediction (Core-Sp), a scalable constraint reasoning and machine learning integrated approach for learning over structured domains. We propose to embed decision diagrams, a popular constraint reasoning tool, as a fully-differentiable module into deep neural networks for structured prediction. We also propose an iterative search algorithm to automate the searching process of the best Core-Sp structure. We evaluate Core-Sp on three applications: vehicle dispatching service planning, if-then program synthesis, and text2SQL generation. The proposed Core-Sp module demonstrates superior performance over state-of-the-art approaches in all three applications. The structures generated with Core-Sp satisfy 100% of the constraints when using exact decision diagrams. In addition, Core-Sp boosts learning performance by reducing the modeling space via constraint satisfaction.

Many important machine learning problems can be formulated as highly constrained convex optimization problems. One important example is metric constrained problems. In this paper, we show that standard optimization techniques can not be used to solve metric constrained problem. To solve such problems, we provide a general active set framework, called Project and Forget, and several variants thereof that use Bregman projections. Project and Forget is a general purpose method that can be used to solve highly constrained convex problems with many (possibly exponentially) constraints. We provide a theoretical analysis of Project and Forget and prove that our algorithms converge to the global optimal solution and have a linear rate of convergence. We demonstrate that using our method, we can solve large problem instances of general weighted correlation clustering, metric nearness, information theoretic metric learning and quadratically regularized optimal transport; in each case, out-performing the state of the art methods with respect to CPU times and problem sizes.

CleanRL is an open-source library that provides high-quality single-file implementations of Deep Reinforcement Learning (DRL) algorithms. These single-file implementations are self-contained algorithm variant files such as dqn.py, ppo.py, and ppo_atari.py that individually include all algorithm variant's implementation details. Such a paradigm significantly reduces the complexity and the lines of code (LOC) in each implemented variant, which makes them quicker and easier to understand. This paradigm gives the researchers the most fine-grained control over all aspects of the algorithm in a single file, allowing them to prototype novel features quickly. Despite having succinct implementations, CleanRL's codebase is thoroughly documented and benchmarked to ensure performance is on par with reputable sources. As a result, CleanRL produces a repository tailor-fit for two purposes: 1) understanding all implementation details of DRL algorithms and 2) quickly prototyping novel features. CleanRL's source code can be found at https://github.com/vwxyzjn/cleanrl.

Bayesian Neural Networks with Latent Variables (BNN+LVs) capture predictive uncertainty by explicitly modeling model uncertainty (via priors on network weights) and environmental stochasticity (via a latent input noise variable). In this work, we first show that BNN+LV suffers from a serious form of non-identifiability: explanatory power can be transferred between the model parameters and latent variables while fitting the data equally well. We demonstrate that as a result, in the limit of infinite data, the posterior mode over the network weights and latent variables is asymptotically biased away from the ground-truth. Due to this asymptotic bias, traditional inference methods may in practice yield parameters that generalize poorly and misestimate uncertainty. Next, we develop a novel inference procedure that explicitly mitigates the effects of likelihood non-identifiability during training and yields high-quality predictions as well as uncertainty estimates. We demonstrate that our inference method improves upon benchmark methods across a range of synthetic and real data-sets.

We introduce a flexible framework that produces high-quality almost-exact matches for causal inference. Most prior work in matching uses ad-hoc distance metrics, often leading to poor quality matches, particularly when there are irrelevant covariates. In this work, we learn an interpretable distance metric for matching, which leads to substantially higher quality matches. The learned distance metric stretches the covariate space according to each covariate's contribution to outcome prediction: this stretching means that mismatches on important covariates carry a larger penalty than mismatches on irrelevant covariates. Our ability to learn flexible distance metrics leads to matches that are interpretable and useful for the estimation of conditional average treatment effects.

We propose algorithms for approximate filtering and smoothing in high-dimensional Factorial hidden Markov models. The approximation involves discarding, in a principled way, likelihood factors according to a notion of locality in a factor graph associated with the emission distribution. This allows the exponential-in-dimension cost of exact filtering and smoothing to be avoided. We prove that the approximation accuracy, measured in a local total variation norm, is "dimension-free" in the sense that as the overall dimension of the model increases the error bounds we derive do not necessarily degrade. A key step in the analysis is to quantify the error introduced by localizing the likelihood function in a Bayes' rule update. The factorial structure of the likelihood function which we exploit arises naturally when data have known spatial or network structure. We demonstrate the new algorithms on synthetic examples and a London Underground passenger flow problem, where the factor graph is effectively given by the train network.

We introduce a new library named abess that implements a unified framework of best-subset selection for solving diverse machine learning problems, e.g., linear regression, classification, and principal component analysis. Particularly, abess certifiably gets the optimal solution within polynomial time with high probability under the linear model. Our efficient implementation allows abess to attain the solution of best-subset selection problems as fast as or even 20x faster than existing competing variable (model) selection toolboxes. Furthermore, it supports common variants like best subset of groups selection and $\ell_2$ regularized best-subset selection. The core of the library is programmed in C++. For ease of use, a Python library is designed for convenient integration with scikit-learn, and it can be installed from the Python Package Index (PyPI). In addition, a user-friendly R library is available at the Comprehensive R Archive Network (CRAN). The source code is available at: https://github.com/abess-team/abess.

We study a version of adversarial classification where an adversary is empowered to corrupt data inputs up to some distance $\varepsilon$, using tools from variational analysis. In particular, we describe necessary conditions associated with the optimal classifier subject to such an adversary. Using the necessary conditions, we derive a geometric evolution equation which can be used to track the change in classification boundaries as $\varepsilon$ varies. This evolution equation may be described as an uncoupled system of differential equations in one dimension, or as a mean curvature type equation in higher dimension. In one dimension, and under mild assumptions on the data distribution, we rigorously prove that one can use the initial value problem starting from $\varepsilon=0$, which is simply the Bayes classifier, in order to solve for the global minimizer of the adversarial problem for small values of $\varepsilon$. In higher dimensions we provide a similar result, albeit conditional to the existence of regular solutions of the initial value problem. In the process of proving our main results we obtain a result of independent interest connecting the original adversarial problem with an optimal transport problem under no assumptions on whether classes are balanced or not. Numerical examples illustrating these ideas are also presented.

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and they often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting in improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. High-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of benchmark data sets from three different databases exhibit advantages of the proposed methods.

Instrumental variable methods have been widely used to identify causal effects in the presence of unmeasured confounding. A key identification condition known as the exclusion restriction states that the instrument cannot have a direct effect on the outcome which is not mediated by the exposure in view. In the health and social sciences, such an assumption is often not credible. To address this concern, we consider identification conditions of the population average treatment effect with an invalid instrumental variable which does not satisfy the exclusion restriction, and derive the efficient influence function targeting the identifying functional under a nonparametric observed data model. We propose a novel multiply robust locally efficient estimator of the average treatment effect that is consistent in the union of multiple parametric nuisance models, as well as a multiply debiased machine learning estimator for which the nuisance parameters are estimated using generic machine learning methods, that effectively exploit various forms of linear or nonlinear structured sparsity in the nuisance parameter space. When one cannot be confident that any of these machine learners is consistent at sufficiently fast rates to ensure $\surd{n}$-consistency for the average treatment effect, we introduce new criteria for selective machine learning which leverage the multiple robustness property in order to ensure small bias. The proposed methods are illustrated through extensive simulations and a data analysis evaluating the causal effect of 401(k) participation on savings.

In this paper, we study two challenging problems in explainable AI (XAI) and data clustering. The first is how to directly design a neural network with inherent interpretability, rather than giving post-hoc explanations of a black-box model. The second is implementing discrete $k$-means with a differentiable neural network that embraces the advantages of parallel computing, online clustering, and clustering-favorable representation learning. To address these two challenges, we design a novel neural network, which is a differentiable reformulation of the vanilla $k$-means, called inTerpretable nEuraL cLustering (TELL). Our contributions are threefold. First, to the best of our knowledge, most existing XAI works focus on supervised learning paradigms. This work is one of the few XAI studies on unsupervised learning, in particular, data clustering. Second, TELL is an interpretable, or the so-called intrinsically explainable and transparent model. In contrast, most existing XAI studies resort to various means for understanding a black-box model with post-hoc explanations. Third, from the view of data clustering, TELL possesses many properties highly desired by $k$-means, including but not limited to online clustering, plug-and-play module, parallel computing, and provable convergence. Extensive experiments show that our method achieves superior performance comparing with 14 clustering approaches on three challenging data sets. The source code could be accessed at www.pengxi.me.

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.

Quantile regression is a fundamental problem in statistical learning motivated by a need to quantify uncertainty in predictions, or to model a diverse population without being overly reductive. For instance, epidemiological forecasts, cost estimates, and revenue predictions all benefit from being able to quantify the range of possible values accurately. As such, many models have been developed for this problem over many years of research in statistics, machine learning, and related fields. Rather than proposing yet another (new) algorithm for quantile regression we adopt a meta viewpoint: we investigate methods for aggregating any number of conditional quantile models, in order to improve accuracy and robustness. We consider weighted ensembles where weights may vary over not only individual models, but also over quantile levels, and feature values. All of the models we consider in this paper can be fit using modern deep learning toolkits, and hence are widely accessible (from an implementation point of view) and scalable. To improve the accuracy of the predicted quantiles (or equivalently, prediction intervals), we develop tools for ensuring that quantiles remain monotonically ordered, and apply conformal calibration methods. These can be used without any modification of the original library of base models. We also review some basic theory surrounding quantile aggregation and related scoring rules, and contribute a few new results to this literature (for example, the fact that post sorting or post isotonic regression can only improve the weighted interval score). Finally, we provide an extensive suite of empirical comparisons across 34 data sets from two different benchmark repositories.

We propose a novel framework to study asynchronous federated learning optimization with delays in gradient updates. Our theoretical framework extends the standard FedAvg aggregation scheme by introducing stochastic aggregation weights to represent the variability of the clients update time, due for example to heterogeneous hardware capabilities. Our formalism applies to the general federated setting where clients have heterogeneous datasets and perform at least one step of stochastic gradient descent (SGD). We demonstrate convergence for such a scheme and provide sufficient conditions for the related minimum to be the optimum of the federated problem. We show that our general framework applies to existing optimization schemes including centralized learning, FedAvg, asynchronous FedAvg, and FedBuff. The theory here provided allows drawing meaningful guidelines for designing a federated learning experiment in heterogeneous conditions. In particular, we develop in this work FedFix, a novel extension of FedAvg enabling efficient asynchronous federated training while preserving the convergence stability of synchronous aggregation. We empirically demonstrate our theory on a series of experiments showing that asynchronous FedAvg leads to fast convergence at the expense of stability, and we finally demonstrate the improvements of FedFix over synchronous and asynchronous FedAvg.

We bound the excess risk of interpolating deep linear networks trained using gradient flow. In a setting previously used to establish risk bounds for the minimum $\ell_2$-norm interpolant, we show that randomly initialized deep linear networks can closely approximate or even match known bounds for the minimum $\ell_2$-norm interpolant. Our analysis also reveals that interpolating deep linear models have exactly the same conditional variance as the minimum $\ell_2$-norm solution. Since the noise affects the excess risk only through the conditional variance, this implies that depth does not improve the algorithm's ability to "hide the noise". Our simulations verify that aspects of our bounds reflect typical behavior for simple data distributions. We also find that similar phenomena are seen in simulations with ReLU networks, although the situation there is more nuanced.

In this work, we study the performance of sub-gradient method (SubGM) on a natural nonconvex and nonsmooth formulation of low-rank matrix recovery with $\ell_1$-loss, where the goal is to recover a low-rank matrix from a limited number of measurements, a subset of which may be grossly corrupted with noise. We study a scenario where the rank of the true solution is unknown and over-estimated instead. The over-estimation of the rank gives rise to an over-parameterized model in which there are more degrees of freedom than needed. Such over-parameterization may lead to overfitting, or adversely affect the performance of the algorithm. We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements. In particular, we show that small initialization nullifies the effect of over-parameterization on the performance of SubGM, leading to an exponential improvement in its convergence rate. Moreover, we provide the first unifying framework for analyzing the behavior of SubGM under both outlier and Gaussian noise models, showing that SubGM converges to the true solution, even under arbitrarily large and arbitrarily dense noise values, and, perhaps surprisingly, even if the globally optimal solutions do not correspond to the ground truth. At the core of our results is a robust variant of restricted isometry property, called Sign-RIP, which controls the deviation of the sub-differential of the $\ell_1$-loss from that of an ideal, expected loss. As a byproduct of our results, we consider a subclass of robust low-rank matrix recovery with Gaussian measurements, and show that the number of required samples to guarantee the global convergence of SubGM is independent of the over-parameterized rank.

Relational databases are a successful model for data storage, and rely on query languages for information retrieval. Most of these query languages are based on relational algebra, a mathematical formalization at the core of relational models. Knowledge graphs are flexible data storage structures that allow for knowledge completion using machine learning techniques. Knowledge hypergraphs generalize knowledge graphs by allowing multi-argument relations. This work studies knowledge hypergraph completion through the lens of relational algebra and its core operations. We explore the space between relational algebra foundations and machine learning techniques for knowledge completion. We investigate whether such methods can capture high-level abstractions in terms of relational algebra operations. We propose a simple embedding-based model called Relational Algebra Embedding (ReAlE) that performs link prediction in knowledge hypergraphs. We show theoretically that ReAlE is fully expressive and can represent the relational algebra operations of renaming, projection, set union, selection, and set difference. We verify experimentally that ReAlE outperforms state-of-the-art models in knowledge hypergraph completion, and in representing each of these primitive relational algebra operations. For the latter experiment, we generate a synthetic knowledge hypergraph, for which we design an algorithm based on the Erdos-R'enyi model for generating random graphs.

We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep generative model is used to model high-dimensional data that are assumed to concentrate around some low-dimensional structure. Estimating the distribution supported on this low-dimensional structure, such as a low-dimensional manifold, is challenging due to its singularity with respect to the Lebesgue measure in the ambient space. In the considered model, a usual likelihood approach can fail to estimate the target distribution consistently due to the singularity. We prove that a novel and effective solution exists by perturbing the data with an instance noise, which leads to consistent estimation of the underlying distribution with desirable convergence rates. We also characterize the class of distributions that can be efficiently estimated via deep generative models. This class is sufficiently general to contain various structured distributions such as product distributions, classically smooth distributions and distributions supported on a low-dimensional manifold. Our analysis provides some insights on how deep generative models can avoid the curse of dimensionality for nonparametric distribution estimation. We conduct a thorough simulation study and real data analysis to empirically demonstrate that the proposed data perturbation technique improves the estimation performance significantly.

A recurrent neural network (RNN) is a widely used deep-learning network for dealing with sequential data. Imitating a dynamical system, an infinite-width RNN can approximate any open dynamical system in a compact domain. In general, deep narrow networks with bounded width and arbitrary depth are more effective than wide shallow networks with arbitrary width and bounded depth in practice; however, the universal approximation theorem for deep narrow structures has yet to be extensively studied. In this study, we prove the universality of deep narrow RNNs and show that the upper bound of the minimum width for universality can be independent of the length of the data. Specifically, we show a deep RNN with ReLU activation can approximate any continuous function or $L^p$ function with the widths $d_x+d_y+3$ and $\max\{d_x+1,d_y\}$, respectively, where the target function maps a finite sequence of vectors in $\mathbb{R}^{d_x}$ to a finite sequence of vectors in $\mathbb{R}^{d_y}$. We also compute the additional width required if the activation function is sigmoid or more. In addition, we prove the universality of other recurrent networks, such as bidirectional RNNs. Bridging a multi-layer perceptron and an RNN, our theory and technique can shed light on further research on deep RNNs.

Data driven individualized decision making problems have received a lot of attentions in recent years. In particular, decision makers aim to determine the optimal Individualized Treatment Rule (ITR) so that the expected specified outcome averaging over heterogeneous patient-specific characteristics is maximized. Many existing methods deal with binary or a moderate number of treatment arms and may not take potential treatment effect structure into account. However, the effectiveness of these methods may deteriorate when the number of treatment arms becomes large. In this article, we propose GRoup Outcome Weighted Learning (GROWL) to estimate the latent structure in the treatment space and the optimal group-structured ITRs through a single optimization. In particular, for estimating group-structured ITRs, we utilize the Reinforced Angle based Multicategory Support Vector Machines (RAMSVM) to learn group-based decision rules under the weighted angle based multi-class classification framework. Fisher consistency, the excess risk bound, and the convergence rate of the value function are established to provide a theoretical guarantee for GROWL. Extensive empirical results in simulation studies and real data analysis demonstrate that GROWL enjoys better performance than several other existing methods.

Agents that can learn to imitate behaviours observed in video -- without having direct access to internal state or action information of the observed agent -- are more suitable for learning in the natural world. However, formulating a reinforcement learning (RL) agent that facilitates this goal remains a significant challenge. We approach this challenge using contrastive training to learn a reward function by comparing an agent's behaviour with a single demonstration. We use a Siamese recurrent neural network architecture to learn rewards in space and time between motion clips while training an RL policy to minimize this distance. Through experimentation, we also find that the inclusion of multi-task data and additional image encoding losses improve the temporal consistency of the learned rewards and, as a result, significantly improve policy learning. We demonstrate our approach on simulated humanoid, dog, and raptor agents in 2D and quadruped and humanoid agents in 3D. We show that our method outperforms current state-of-the-art techniques and can learn to imitate behaviours from a single video demonstration.

Although deep learning has made great progress in recent years, the exploding economic and environmental costs of training neural networks are becoming unsustainable. To address this problem, there has been a great deal of research on algorithmically-efficient deep learning, which seeks to reduce training costs not at the hardware or implementation level, but through changes in the semantics of the training program. In this paper, we present a structured and comprehensive overview of the research in this field. First, we formalize the algorithmic speedup problem, then we use fundamental building blocks of algorithmically efficient training to develop a taxonomy. Our taxonomy highlights commonalities of seemingly disparate methods and reveals current research gaps. Next, we present evaluation best practices to enable comprehensive, fair, and reliable comparisons of speedup techniques. To further aid research and applications, we discuss common bottlenecks in the training pipeline (illustrated via experiments) and offer taxonomic mitigation strategies for them. Finally, we highlight some unsolved research challenges and present promising future directions.

We study a family of adversarial multiclass classification problems and provide equivalent reformulations in terms of: 1) a family of generalized barycenter problems introduced in the paper and 2) a family of multimarginal optimal transport problems where the number of marginals is equal to the number of classes in the original classification problem. These new theoretical results reveal a rich geometric structure of adversarial learning problems in multiclass classification and extend recent results restricted to the binary classification setting. A direct computational implication of our results is that by solving either the barycenter problem and its dual, or the MOT problem and its dual, we can recover the optimal robust classification rule and the optimal adversarial strategy for the original adversarial problem. Examples with synthetic and real data illustrate our results.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also \commHL{demonstrate the performance of} our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

A model involving Gaussian processes (GPs) is introduced to simultaneously handle multitask learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors’ estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty in both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performance when dealing with group-structured data. The model handles irregular grids of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real data sets. The overall algorithm, called MagmaClust, is publicly available as an R package.

Geo-tagged images are publicly available in large quantities, whereas labels such as object classes are rather scarce and expensive to collect. Meanwhile, contrastive learning has achieved tremendous success in various natural image and language tasks with limited labeled data. However, existing methods fail to fully leverage geospatial information, which can be paramount to distinguishing objects that are visually similar. To directly leverage the abundant geospatial information associated with images in pre-training, fine-tuning, and inference stages, we present Contrastive Spatial Pre-Training (CSP), a self-supervised learning framework for geo-tagged images. We use a dual-encoder to separately encode the images and their corresponding geo-locations, and use contrastive objectives to learn effective location representations from images, which can be transferred to downstream supervised tasks such as image classification. Experiments show that CSP can improve model performance on both iNat2018 and fMoW datasets. Especially, on iNat2018, CSP significantly boosts the model performance with 10-34% relative improvement with various labeled training data sampling ratios.

Pretraining on a large-scale corpus has become a standard method to build general language models (LMs). Adapting a model to new data distributions targeting different downstream tasks poses significant challenges. Naive fine-tuning may incur catastrophic forgetting when the over-parameterized LMs overfit the new data but fail to preserve the pretrained features. Lifelong learning (LLL) aims to enable information systems to learn from a continuous data stream across time. However, most prior work modifies the training recipe assuming a static fixed network architecture. We find that additional model capacity and proper regularization are key elements to achieving strong LLL performance. Thus, we propose Lifelong-MoE, an extensible MoE (Mixture-of-Experts) architecture that dynamically adds model capacity via adding experts with regularized pretaining. Our results show that by only introducing a limited number of extra experts while keeping the computation cost constant, our model can steadily adapt to data distribution shifts while preserving the previous knowledge. Compared to existing lifelong learning approaches, Lifelong-MoE achieves better few-shot performance on NLP tasks. More impressively, Lifelong-MoE surpasses multi-task learning on 19 downstream NLU tasks.

The wide application of pre-trained models is driving the trend of once-for-all training in one-shot neural architecture search (NAS). However, training within a huge sample space damages the performance of individual subnets and requires much computation to search for a optimal model. In this paper, we present PreNAS, a search-free NAS approach that accentuates target models in one-shot training. Specifically, the sample space is dramatically reduced in advance by a zero-cost selector, and weight-sharing one-shot training is performed on the preferred architectures to alleviate update conflicts. Extensive experiments have demonstrated that PreNAS consistently outperforms state-of-the-art one-shot NAS competitors for both Vision Transformer and convolutional architectures, and importantly, enables instant specialization with zero search cost. Our code is available at https://github.com/tinyvision/PreNAS.

Non-local interactions play a vital role in boosting performance for image restoration. However, local window Transformer has been preferred due to its efficiency for processing high-resolution images. The superiority in efficiency comes at the cost of sacrificing the ability to model non-local interactions. In this paper, we present that local window Transformer can also function as modeling non-local interactions. The counterintuitive function is based on the permutation-equivariance of self-attention. The basic principle is quite simple: by randomly shuffling the input, local self-attention also has the potential to model non-local interactions without introducing extra parameters. Our random shuffle strategy enjoys elegant theoretical guarantees in extending the local scope. The resulting Transformer dubbed ShuffleFormer is capable of processing high-resolution images efficiently while modeling non-local interactions. Extensive experiments demonstrate the effectiveness of ShuffleFormer across a variety of image restoration tasks, including image denoising, deraining, and deblurring. Code is available at https://github.com/jiexiaou/ShuffleFormer.

Modern machine learning models deployed in the wild can encounter both covariate and semantic shifts, giving rise to the problems of out-of-distribution (OOD) generalization and OOD detection respectively. While both problems have received significant research attention lately, they have been pursued independently. This may not be surprising, since the two tasks have seemingly conflicting goals. This paper provides a new unified approach that is capable of simultaneously generalizing to covariate shifts while robustly detecting semantic shifts. We propose a margin-based learning framework that exploits freely available unlabeled data in the wild that captures the environmental test-time OOD distributions under both covariate and semantic shifts. We show both empirically and theoretically that the proposed margin constraint is the key to achieving both OOD generalization and detection. Extensive experiments show the superiority of our framework, outperforming competitive baselines that specialize in either OOD generalization or OOD detection. Code is publicly available at https://github.com/deeplearning-wisc/scone.

State of the art reinforcement learning has enabled training agents on tasks of ever increasing complexity. However, the current paradigm tends to favor training agents from scratch on every new task or on collections of tasks with a view towards generalizing to novel task configurations. The former suffers from poor data efficiency while the latter is difficult when test tasks are out-of-distribution. Agents that can effectively transfer their knowledge about the world pose a potential solution to these issues. In this paper, we investigate transfer learning in the context of model-based agents. Specifically, we aim to understand where exactly environment models have an advantage and why. We find that a model-based approach outperforms controlled model-free baselines for transfer learning. Through ablations, we show that both the policy and dynamics model learnt through exploration matter for successful transfer. We demonstrate our results across three domains which vary in their requirements for transfer: in-distribution procedural (Crafter), in-distribution identical (RoboDesk), and out-of-distribution (Meta-World). Our results show that intrinsic exploration combined with environment models present a viable direction towards agents that are self-supervised and able to generalize to novel reward functions.

Despite the success of autoregressive large language models in text generation, it remains a major challenge to generate text that satisfies complex constraints: sampling from the conditional distribution ${\Pr}(\text{text} | \alpha)$ is intractable for even the simplest lexical constraints $\alpha$. To overcome this challenge, we propose to use tractable probabilistic models (TPMs) to impose lexical constraints in autoregressive text generation models, which we refer to as GeLaTo (Generating Language with Tractable Constraints). To demonstrate the effectiveness of this framework, we use distilled hidden Markov models, where we can efficiently compute ${\Pr}(\text{text} | \alpha)$, to guide autoregressive generation from GPT2. GeLaTo achieves state-of-the-art performance on challenging benchmarks for constrained text generation (e.g., CommonGen), beating various strong baselines by a large margin. Our work not only opens up new avenues for controlling large language models but also motivates the development of more expressive TPMs.

The class-wise training losses often diverge as a result of the various levels of intra-class and inter-class appearance variation, and we find that the diverging class-wise training losses cause the uncalibrated prediction with its reliability. To resolve the issue, we propose a new calibration method to synchronize the class-wise training losses. We design a new training loss to alleviate the variance of class-wise training losses by using multiple class-wise scaling factors. Since our framework can compensate the training losses of overfitted classes with those of under-fitted classes, the integrated training loss is preserved, preventing the performance drop even after the model calibration. Furthermore, our method can be easily employed in the post-hoc calibration methods, allowing us to use the pre-trained model as an initial model and reduce the additional computation for model calibration. We validate the proposed framework by employing it in the various post-hoc calibration methods, which generally improves calibration performance while preserving accuracy, and discover through the investigation that our approach performs well with unbalanced datasets and untuned hyperparameters.

Mixup, a simple data augmentation method that randomly mixes two data points via linear interpolation, has been extensively applied in various deep learning applications to gain better generalization. However, its theoretical explanation remains largely unclear. In this work, we aim to seek a fundamental understanding of the benefits of Mixup. We first show that Mixup using different linear interpolation parameters for features and labels can still achieve similar performance as standard Mixup. This indicates that the intuitive linearity explanation in Zhang et al., (2018) may not fully explain the success of Mixup. Then, we perform a theoretical study of Mixup from the feature learning perspective. We consider a feature-noise data model and show that Mixup training can effectively learn the rare features (appearing in a small fraction of data) from its mixture with the common features (appearing in a large fraction of data). In contrast, standard training can only learn the common features but fails to learn the rare features, thus suffering from bad generalization performance. Moreover, our theoretical analysis also shows that the benefits of Mixup for feature learning are mostly gained in the early training phase, based on which we propose to apply early stopping in Mixup. Experimental results verify our theoretical findings and demonstrate the effectiveness of the early-stopped Mixup training.

In contrastive learning, the choice of "view" controls the information that the representation captures and influences the performance of the model. However, leading graph contrastive learning methods generally produce views via random corruption or learning, which could lead to the loss of essential information and alteration of semantic information. An anchor view that maintains the essential information of input graphs for contrastive learning has been hardly investigated. In this paper, based on the theory of graph information bottleneck, we deduce the definition of this anchor view; put differently, the anchor view with essential information of input graph is supposed to have the minimal structural uncertainty. Furthermore, guided by structural entropy, we implement the anchor view, termed SEGA, for graph contrastive learning. We extensively validate the proposed anchor view on various benchmarks regarding graph classification under unsupervised, semi-supervised, and transfer learning and achieve significant performance boosts compared to the state-of-the-art methods.

Discovering knowledge about which types of events influence others, using datasets of event sequences without time stamps, has several practical applications. While neural sequence models are able to capture complex and potentially long-range historical dependencies, they often lack the interpretability of simpler models for event sequence dynamics. We provide a novel neural framework in such a setting - a probabilistic attention-to-influence neural model - which not only captures complex instance-wise interactions between events but also learns influencers for each event type of interest. Given event sequence data and a prior distribution on type-wise influence, we efficiently learn an approximate posterior for type-wise influence by an attention-to-influence transformation using variational inference. Our method subsequently models the conditional likelihood of sequences by sampling the above posterior to focus attention on influencing event types. We motivate our general framework and show improved performance in experiments compared to existing baselines on synthetic data as well as real-world benchmarks, for tasks involving prediction and influencing set identification.

We present CTreeOT, a convergent, differentiable algorithm for matching two trees when each tree is conditioned on some input. Such conditional tree matching is useful for light-weight, few-shot adaptation of tree prediction models without parameter fine-tuning. CTreeOT includes an alignment algorithm that extends the popular Sinkhorn algorithm for matching tree nodes while supporting constraints on tree edges. The algorithm involves alternating between matrix rescaling and message passing updates, and can be efficiently expressed as GPU tensor operations. The second part of CTreeOT is fine-grained relevance-based reweighting of nodes that makes the match scores useful for prediction tasks. We demonstrate the usefulness of CTreeOT for cross-schema adaptation of Text-to-SQL, a popular semantic parsing task. We show that compared to state-of-the-art methods, we achieve significant increase in adaptation accuracy.

We consider guiding denoising diffusion models with general differentiable loss functions in a plug-and-play fashion, enabling controllable generation without additional training. This paradigm, termed Loss-Guided Diffusion (LGD), can easily be integrated into all diffusion models and leverage various efficient samplers. Despite the benefits, the resulting guidance term is, unfortunately, an intractable integral and needs to be approximated. Existing methods compute the guidance term based on a point estimate. However, we show that such approaches have significant errors over the scale of the approximations. To address this issue, we propose a Monte Carlo method that uses multiple samples from a suitable distribution to reduce bias. Our method is effective in various synthetic and real-world settings, including image super-resolution, text or label-conditional image generation, and controllable motion synthesis. Notably, we show how our method can be applied to control a pretrained motion diffusion model to follow certain paths and avoid obstacles that are proven challenging to prior methods.

To balance quality and cost, various domain areas of science and engineering run simulations at multiple levels of sophistication. Multi-fidelity active learning aims to learn a direct mapping from input parameters to simulation outputs at the highest fidelity by actively acquiring data from multiple fidelity levels. However, existing approaches based on Gaussian processes are hardly scalable to high-dimensional data. Deep learning-based methods often impose a hierarchical structure in hidden representations, which only supports passing information from low-fidelity to high-fidelity. These approaches can lead to the undesirable propagation of errors from low-fidelity representations to high-fidelity ones. We propose a novel framework called Disentangled Multi-fidelity Deep Bayesian Active Learning (D-MFDAL), which learns the surrogate models conditioned on the distribution of functions at multiple fidelities. On benchmark tasks of learning deep surrogates of partial differential equations including heat equation, Poisson's equation and fluid simulations, our approach significantly outperforms state-of-the-art in prediction accuracy and sample efficiency.

Self-supervised learning (SSL) speech models such as wav2vec and HuBERT have demonstrated state-of-the-art performance on automatic speech recognition (ASR) and proved to be extremely useful in low label-resource settings. However, the success of SSL models has yet to transfer to utterance-level tasks such as speaker, emotion, and language recognition, which still require supervised fine-tuning of the SSL models to obtain good performance. We argue that the problem is caused by the lack of disentangled representations and an utterance-level learning objective for these tasks. Inspired by how HuBERT uses clustering to discover hidden acoustic units, we formulate a factor analysis (FA) model that uses the discovered hidden acoustic units to align the SSL features. The underlying utterance-level representations are disentangled using probabilistic inference on the aligned features. Furthermore, the variational lower bound derived from the FA model provides an utterance-level objective, allowing error gradients to be backpropagated to the Transformer layers to learn highly discriminative acoustic units. When used in conjunction with HuBERT's masked prediction training, our models outperform the current best model, WavLM, on all utterance-level non-semantic tasks on the SUPERB benchmark with only 20% of labeled data.

Self-supervised learning (SSL) learns high-quality representations from large pools of unlabeled training data. As datasets grow larger, it becomes crucial to identify the examples that contribute the most to learning such representations. This enables efficient SSL by reducing the volume of data required. Nevertheless, quantifying the value of examples for SSL has remained an open question. In this work, we address this problem for the first time, by proving that examples that contribute the most to contrastive SSL are those that have the most similar augmentations to other examples, in expectation. We provide rigorous guarantees for the generalization performance of contrastive learning on such subsets. Through extensive experiments, we show that we can safely exclude 20% of examples from CIFAR100 and 40% from STL10 and TinyImageNet, without affecting downstream task performance. In general, subsets selected by our method outperform random subsets by over 3% across these datasets. Interestingly, we also discover the subsets that contribute the most to contrastive learning are those that contribute the least to supervised learning.

Off-policy learning from multistep returns is crucial for sample-efficient reinforcement learning, but counteracting off-policy bias without exacerbating variance is challenging. Classically, off-policy bias is corrected in a per-decision manner: past temporal-difference errors are re-weighted by the instantaneous Importance Sampling (IS) ratio after each action via eligibility traces. Many off-policy algorithms rely on this mechanism, along with differing protocols for cutting the IS ratios (traces) to combat the variance of the IS estimator. Unfortunately, once a trace has been cut, the effect cannot be easily reversed. This has led to the development of credit-assignment strategies that account for multiple past experiences at a time. These trajectory-aware methods have not been extensively analyzed, and their theoretical justification remains uncertain. In this paper, we propose a multistep operator that unifies per-decision and trajectory-aware methods. We prove convergence conditions for our operator in the tabular setting, establishing the first guarantees for several existing methods as well as many new ones. Finally, we introduce Recency-Bounded Importance Sampling (RBIS), which leverages trajectory awareness to perform robustly across $\lambda$-values in an off-policy control task.

In-context learning (ICL) is a type of prompting where a transformer model operates on a sequence of (input, output) examples and performs inference on-the-fly. In this work, we formalize in-context learning as an algorithm learning problem where a transformer model implicitly constructs a hypothesis function at inference-time. We first explore the statistical aspects of this abstraction through the lens of multitask learning: We obtain generalization bounds for ICL when the input prompt is (1) a sequence of i.i.d. (input, label) pairs or (2) a trajectory arising from a dynamical system. The crux of our analysis is relating the excess risk to the stability of the algorithm implemented by the transformer. We characterize when transformer/attention architecture provably obeys the stability condition and also provide empirical verification. For generalization on unseen tasks, we identify an inductive bias phenomenon in which the transfer learning risk is governed by the task complexity and the number of MTL tasks in a highly predictable manner. Finally, we provide numerical evaluations that (1) demonstrate transformers can indeed implement near-optimal algorithms on classical regression problems with i.i.d. and dynamic data, (2) provide insights on stability, and (3) verify our theoretical predictions.

Recent studies have shown that paddings in convolutional neural networks encode absolute position information which can negatively affect the model performance for certain tasks. However, existing metrics for quantifying the strength of positional information remain unreliable and frequently lead to erroneous results. To address this issue, we propose novel metrics for measuring and visualizing the encoded positional information. We formally define the encoded information as Position-information Pattern from Padding (PPP) and conduct a series of experiments to study its properties as well as its formation. The proposed metrics measure the presence of positional information more reliably than the existing metrics based on PosENet and tests in F-Conv. We also demonstrate that for any extant (and proposed) padding schemes, PPP is primarily a learning artifact and is less dependent on the characteristics of the underlying padding schemes.

The recent integration of deep learning and pairwise similarity annotation-based constrained clustering---i.e., deep constrained clustering (DCC)---has proven effective for incorporating weak supervision into massive data clustering: Less than 1% of pair similarity annotations can often substantially enhance the clustering accuracy. However, beyond empirical successes, there is a lack of understanding of DCC. In addition, many DCC paradigms are sensitive to annotation noise, but performance-guaranteed noisy DCC methods have been largely elusive. This work first takes a deep look into a recently emerged logistic loss function of DCC, and characterizes its theoretical properties. Our result shows that the logistic DCC loss ensures the identifiability of data membership under reasonable conditions, which may shed light on its effectiveness in practice. Building upon this understanding, a new loss function based on geometric factor analysis is proposed to fend against noisy annotations. It is shown that even under unknown annotation confusions, the data membership can still be provably identified under our proposed learning criterion. The proposed approach is tested over multiple datasets to validate our claims.

Clustering (or community detection) on multilayer graphs poses several additional complications with respect to standard graphs as different layers may be characterized by different structures and types of information. One of the major challenges is to establish the extent to which each layer contributes to the cluster assignment in order to effectively take advantage of the multilayer structure and improve upon the classification obtained using the individual layers or their union. However, making an informed a-priori assessment about the clustering information content of the layers can be very complicated. In this work, we assume a semi-supervised learning setting, where the class of a small percentage of nodes is initially provided, and we propose a parameter-free Laplacian-regularized model that learns an optimal nonlinear combination of the different layers from the available input labels. The learning algorithm is based on a Frank-Wolfe optimization scheme with inexact gradient, combined with a modified Label Propagation iteration. We provide a detailed convergence analysis of the algorithm and extensive experiments on synthetic and real-world datasets, showing that the proposed method compares favourably with a variety of baselines and outperforms each individual layer when used in isolation.

Offline reinforcement learning (RL) aims to find an optimal policy for sequential decision-making using a pre-collected dataset, without further interaction with the environment. Recent theoretical progress has focused on developing sample-efficient offline RL algorithms with various relaxed assumptions on data coverage and function approximators, especially to handle the case with excessively large state-action spaces. Among them, the framework based on the linear-programming (LP) reformulation of Markov decision processes has shown promise: it enables sample-efficient offline RL with function approximation, under only partial data coverage and realizability assumptions on the function classes, with favorable computational tractability. In this work, we revisit the LP framework for offline RL, and provide a new reformulation that advances the existing results in several aspects, relaxing certain assumptions and achieving optimal statistical rates in terms of sample size. Our key enabler is to introduce proper constraints in the reformulation, instead of using any regularization as in the literature, also with careful choices of the function classes and initial state distributions. We hope our insights bring into light the use of LP formulations and the induced primal-dual minimax optimization, in offline RL.

Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image classification models due to its demonstrated benefits over empirical risk minimization with regards to generalization and robustness. In this work, we try to explain some of this success from a feature learning perspective. We focus our attention on classification problems in which each class may have multiple associated features (or $\textit{views}$) that can be used to predict the class correctly. Our main theoretical results demonstrate that, for a non-trivial class of data distributions with two features per class, training a 2-layer convolutional network using empirical risk minimization can lead to learning only one feature for almost all classes while training with a specific instantiation of Mixup succeeds in learning both features for every class. We also show empirically that these theoretical insights extend to the practical settings of image benchmarks modified to have multiple features.

Continuous monitoring with an ever-increasing number of sensors has become ubiquitous across many application domains. However, acquired time series are typically high-dimensional and difficult to interpret. Expressive deep learning (DL) models have gained popularity for dimensionality reduction, but the resulting latent space often remains difficult to interpret. In this work we propose SOM-CPC, a model that visualizes data in an organized 2D manifold, while preserving higher-dimensional information. We address a largely unexplored and challenging set of scenarios comprising high-rate time series, and show on both synthetic and real-life data (physiological data and audio recordings) that SOM-CPC outperforms strong baselines like DL-based feature extraction, followed by conventional dimensionality reduction techniques, and models that jointly optimize a DL model and a Self-Organizing Map (SOM). SOM-CPC has great potential to acquire a better understanding of latent patterns in high-rate data streams.

With recent advances in natural language processing, rationalization becomes an essential self-explaining diagram to disentangle the black box by selecting a subset of input texts to account for the major variation in prediction. Yet, existing association-based approaches on rationalization cannot identify true rationales when two or more snippets are highly inter-correlated and thus provide a similar contribution to prediction accuracy, so-called spuriousness. To address this limitation, we novelly leverage two causal desiderata, non-spuriousness and efficiency, into rationalization from the causal inference perspective. We formally define a series of probabilities of causation based on a newly proposed structural causal model of rationalization, with its theoretical identification established as the main component of learning necessary and sufficient rationales. The superior performance of the proposed causal rationalization is demonstrated on real-world review and medical datasets with extensive experiments compared to state-of-the-art methods.

Graph size generalization is hard for Message passing neural networks (MPNNs). The graph-level classification performance of MPNNs degrades across various graph sizes. Recently, theoretical studies reveal that a slow uncontrollable convergence rate w.r.t. graph size could adversely affect the size generalization. To address the uncontrollable convergence rate caused by correlations across nodes in the underlying dimensional signal-generating space, we propose to use Wasserstein barycenters as graph-level consensus to combat node-level correlations. Methodologically, we propose a Wasserstein barycenter matching (WBM) layer that represents an input graph by Wasserstein distances between its MPNN-filtered node embeddings versus some learned class-wise barycenters. Theoretically, we show that the convergence rate of an MPNN with a WBM layer is controllable and independent to the dimensionality of the signal-generating space. Thus MPNNs with WBM layers are less susceptible to slow uncontrollable convergence rate and size variations. Empirically, the WBM layer improves the size generalization over vanilla MPNNs with different backbones (e.g., GCN, GIN, and PNA) significantly on real-world graph datasets.

Recent work on neural algorithmic reasoning has investigated the reasoning capabilities of neural networks, effectively demonstrating they can learn to execute classical algorithms on unseen data coming from the train distribution. However, the performance of existing neural reasoners significantly degrades on out-of-distribution (OOD) test data, where inputs have larger sizes. In this work, we make an important observation: there are many different inputs for which an algorithm will perform certain intermediate computations identically. This insight allows us to develop data augmentation procedures that, given an algorithm's intermediate trajectory, produce inputs for which the target algorithm would have exactly the same next trajectory step. We ensure invariance in the next-step prediction across such inputs, by employing a self-supervised objective derived by our observation, formalised in a causal graph. We prove that the resulting method, which we call Hint-ReLIC, improves the OOD generalisation capabilities of the reasoner. We evaluate our method on the CLRS algorithmic reasoning benchmark, where we show up to 3x improvements on the OOD test data.

We propose Beam Tree Recursive Cell (BT-Cell) - a backpropagation-friendly framework to extend Recursive Neural Networks (RvNNs) with beam search for latent structure induction. We further extend this framework by proposing a relaxation of the hard top-$k$ operators in beam search for better propagation of gradient signals. We evaluate our proposed models in different out-of-distribution splits in both synthetic and realistic data. Our experiments show that BT-Cell achieves near-perfect performance on several challenging structure-sensitive synthetic tasks like ListOps and logical inference while maintaining comparable performance in realistic data against other RvNN-based models. Additionally, we identify a previously unknown failure case for neural models in generalization to unseen number of arguments in ListOps. The code is available at: https://github.com/JRC1995/BeamTreeRecursiveCells.

We introduce a value-based RL agent, which we call BBF, that achieves super-human performance in the Atari 100K benchmark. BBF relies on scaling the neural networks used for value estimation, as well as a number of other design choices that enable this scaling in a sample-efficient manner. We conduct extensive analyses of these design choices and provide insights for future work. We end with a discussion about updating the goalposts for sample-efficient RL research on the ALE. We make our code and data publicly available at https://github.com/google-research/google-research/tree/master/biggerbetterfaster.

Score-based generative modeling, informally referred to as diffusion models, continue to grow in popularity across several important domains and tasks. While they provide high-quality and diverse samples from empirical distributions, important questions remain on the reliability and trustworthiness of these sampling procedures for their responsible use in critical scenarios. Conformal prediction is a modern tool to construct finite-sample, distribution-free uncertainty guarantees for any black-box predictor. In this work, we focus on image-to-image regression tasks and we present a generalization of the Risk-Controlling Prediction Sets (RCPS) procedure, that we term $K$-RCPS, which allows to $(i)$ provide entrywise calibrated intervals for future samples of any diffusion model, and $(ii)$ control a certain notion of risk with respect to a ground truth image with minimal mean interval length. Differently from existing conformal risk control procedures, ours relies on a novel convex optimization approach that allows for multidimensional risk control while provably minimizing the mean interval length. We illustrate our approach on two real-world image denoising problems: on natural images of faces as well as on computed tomography (CT) scans of the abdomen, demonstrating state of the art performance.

We study variance-dependent regret bounds for Markov decision processes (MDPs). Algorithms with variance-dependent regret guarantees can automatically exploit environments with low variance (e.g., enjoying constant regret on deterministic MDPs). The existing algorithms are either variance-independent or suboptimal. We first propose two new environment norms to characterize the fine-grained variance properties of the environment. For model-based methods, we design a variant of the MVP algorithm (Zhang et al., 2021a). We apply new analysis techniques to demonstrate that this algorithm enjoys variance-dependent bounds with respect to the norms we propose. In particular, this bound is simultaneously minimax optimal for both stochastic and deterministic MDPs, the first result of its kind. We further initiate the study on model-free algorithms with variance-dependent regret bounds by designing a reference-function-based algorithm with a novel capped-doubling reference update schedule. Lastly, we also provide lower bounds to complement our upper bounds.

We study the problem of constrained efficient global optimization, where both the objective and constraints are expensive black-box functions that can be learned with Gaussian processes. We propose CONFIG (CONstrained efFIcient Global Optimization), a simple and effective algorithm to solve it. Under certain regularity assumptions, we show that our algorithm enjoys the same cumulative regret bound as that in the unconstrained case and similar cumulative constraint violation upper bounds. For commonly used Matern and Squared Exponential kernels, our bounds are sublinear and allow us to derive a convergence rate to the optimal solution of the original constrained problem. In addition, our method naturally provides a scheme to declare infeasibility when the original black-box optimization problem is infeasible. Numerical experiments on sampled instances from the Gaussian process, artificial numerical problems, and a black-box building controller tuning problem all demonstrate the competitive performance of our algorithm. Compared to the other state-of-the-art methods, our algorithm significantly improves the theoretical guarantees while achieving competitive empirical performance.

The speed of gradient descent for convex Lipschitz functions is highly dependent on the choice of learning rate. Setting the learning rate to achieve the optimal convergence rate requires knowing the distance D from the initial point to the solution set. In this work, we describe a single-loop method, with no back-tracking or line searches, which does not require knowledge of D yet asymptotically achieves the optimal rate of convergence for the complexity class of convex Lipschitz functions. Our approach is the first parameter-free method for this class without additional multiplicative log factors in the convergence rate. We present extensive experiments for SGD and Adam variants of our method, where the method automatically matches hand-tuned learning rates across more than a dozen diverse machine learning problems, including large-scale vision and language problems. Our method is practical, efficient and requires no additional function value or gradient evaluations each step. An implementation is provided in the supplementary material.

Recently Chen and Poor initiated the study of learning mixtures of linear dynamical systems. While linear dynamical systems already have wide-ranging applications in modeling time-series data, using mixture models can lead to a better fit or even a richer understanding of underlying subpopulations represented in the data. In this work we give a new approach to learning mixtures of linear dynamical systems that is based on tensor decompositions. As a result, our algorithm succeeds without strong separation conditions on the components, and can be used to compete with the Bayes optimal clustering of the trajectories. Moreover our algorithm works in the challenging partially-observed setting. Our starting point is the simple but powerful observation that the classic Ho-Kalman algorithm is a relative of modern tensor decomposition methods for learning latent variable models. This gives us a playbook for how to extend it to work with more complicated generative models.

Multiview Self-Supervised Learning (MSSL) is based on learning invariances with respect to a set of input transformations. However, invariance partially or totally removes transformation-related information from the representations, which might harm performance for specific downstream tasks that require such information. We propose 2D strUctured and EquivarianT representations (coined DUET), which are 2d representations organized in a matrix structure, and equivariant with respect to transformations acting on the input data. DUET representations maintain information about an input transformation, while remaining semantically expressive. Compared to SimCLR (Chen et al., 2020) (unstructured and invariant) and ESSL (Dangovski et al., 2022) (unstructured and equivariant), the structured and equivariant nature of DUET representations enables controlled generation with lower reconstruction error, while controllability is not possible with SimCLR or ESSL. DUET also achieves higher accuracy for several discriminative tasks, and improves transfer learning.

Out-of-distribution (OOD) detection is a critical requirement for the deployment of deep neural networks. This paper introduces the HEAT model, a new post-hoc OOD detection method estimating the density of in-distribution (ID) samples using hybrid energy-based models (EBM) in the feature space of a pre-trained backbone. HEAT complements prior density estimators of the ID density, e.g. parametric models like the Gaussian Mixture Model (GMM), to provide an accurate yet robust density estimation. A second contribution is to leverage the EBM framework to provide a unified density estimation and to compose several energy terms. Extensive experiments demonstrate the significance of the two contributions. HEAT sets new state-of-the-art OOD detection results on the CIFAR-10 / CIFAR-100 benchmark as well as on the large-scale Imagenet benchmark. The code is available at: https://github.com/MarcLafon/heatood.

Large language models excel at a wide range of complex tasks. However, enabling general inference in the real world, e.g. for robotics problems, raises the challenge of grounding. We propose embodied language models to directly incorporate real-world continuous sensor modalities into language models and thereby establish the link between words and percepts. Input to our embodied language model are multimodal sentences that interleave visual, continuous state estimation, and textual input encodings. We train these encodings end-to-end, in conjunction with a pre-trained large language model, for multiple embodied tasks including sequential robotic manipulation planning, visual question answering, and captioning. Our evaluations show that PaLM-E, a single large embodied multimodal model, can address a variety of embodied reasoning tasks, from a variety of observation modalities, on multiple embodiments, and further, exhibits positive transfer: the model benefits from diverse joint training across internet-scale language, vision, and visual-language domains. Our largest model with 562B parameters, in addition to being trained on robotics tasks, is a visual-language generalist with state-of-the-art performance on OK-VQA, and retains generalist language capabilities with increasing scale.

One of the fundamental quests of AI is to produce agents that coordinate well with humans. This problem is challenging, especially in domains that lack high quality human behavioral data, because multi-agent reinforcement learning (RL) often converges to different equilibria from the ones that humans prefer. We propose a novel framework, instructRL, that enables humans to specify what kind of strategies they expect from their AI partners through natural language instructions. We use pretrained large language models to generate a prior policy conditioned on the human instruction and use the prior to regularize the RL objective. This leads to the RL agent converging to equilibria that are aligned with human preferences. We show that instructRL converges to human-like policies that satisfy the given instructions in a proof-of-concept environment as well as the challenging Hanabi benchmark. Finally, we show that knowing the language instruction significantly boosts human-AI coordination performance in human evaluations in Hanabi.

In meta reinforcement learning (meta RL), an agent seeks a Bayes-optimal policy -- the optimal policy when facing an unknown task that is sampled from some known task distribution. Previous approaches tackled this problem by inferring a $\textit{belief}$ over task parameters, using variational inference methods. Motivated by recent successes of contrastive learning approaches in RL, such as contrastive predictive coding (CPC), we investigate whether contrastive methods can be used for learning Bayes-optimal behavior. We begin by proving that representations learned by CPC are indeed sufficient for Bayes optimality. Based on this observation, we propose a simple meta RL algorithm that uses CPC in lieu of variational belief inference. Our method, $\textit{ContraBAR}$, achieves comparable performance to state-of-the-art in domains with state-based observation and circumvents the computational toll of future observation reconstruction, enabling learning in domains with image-based observations. It can also be combined with image augmentations for domain randomization and used seamlessly in both online and offline meta RL settings.

In Federated Learning (FL), adaptive optimization is an effective approach to addressing the statistical heterogeneity issue but cannot adapt quickly to concept drifts. In this work, we propose a novel adaptive optimizer called Flash that simultaneously addresses both statistical heterogeneity and the concept drift issues. The fundamental insight is that a concept drift can be detected based on the magnitude of parameter updates that are required to fit the global model to each participating client's local data distribution. Flash uses a two-pronged approach that synergizes client-side early-stopping training to facilitate detection of concept drifts and the server-side drift-aware adaptive optimization to effectively adjust effective learning rate. We theoretically prove that Flash matches the convergence rate of state-of-the-art adaptive optimizers and further empirically evaluate the efficacy of Flash on a variety of FL benchmarks using different concept drift settings.

Gradient clipping is a popular modification to standard (stochastic) gradient descent, at every iteration limiting the gradient norm to a certain value $c >0$. It is widely used for example for stabilizing the training of deep learning models (Goodfellow et al., 2016), or for enforcing differential privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping mechanism, its convergence guarantees often require specific values of $c$ and strong noise assumptions. In this paper, we give convergence guarantees that show precise dependence on arbitrary clipping thresholds $c$ and show that our guarantees are tight with both deterministic and stochastic gradients. In particular, we show that (i) for deterministic gradient descent, the clipping threshold only affects the higher-order terms of convergence, (ii) in the stochastic setting convergence to the true optimum cannot be guaranteed under the standard noise assumption, even under arbitrary small step-sizes. We give matching upper and lower bounds for convergence of the gradient norm when running clipped SGD, and illustrate these results with experiments.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Incremental learning is a machine learning approach that involves training a model on a sequence of tasks, rather than all tasks at once. This ability to learn incrementally from a stream of tasks is crucial for many real-world applications. However, incremental learning is a challenging problem on graph-structured data, as many graph-related problems involve prediction tasks for each individual node, known as Node-wise Graph Incremental Learning (NGIL). This introduces non-independent and non-identically distributed characteristics in the sample data generation process, making it difficult to maintain the performance of the model as new tasks are added. In this paper, we focus on the inductive NGIL problem, which accounts for the evolution of graph structure (structural shift) induced by emerging tasks. We provide a formal formulation and analysis of the problem, and propose a novel regularization-based technique called Structural-Shift-Risk-Mitigation (SSRM) to mitigate the impact of the structural shift on catastrophic forgetting of the inductive NGIL problem. We show that the structural shift can lead to a shift in the input distribution for the existing tasks, and further lead to an increased risk of catastrophic forgetting. Through comprehensive empirical studies with several benchmark datasets, we demonstrate that our proposed method, Structural-Shift-Risk-Mitigation (SSRM), is flexible and easy to adapt to improve the performance of state-of-the-art GNN incremental learning frameworks in the inductive setting.

Resource-constrained perception systems such as edge computing and vision-for-robotics require vision models to be both accurate and lightweight in computation and memory usage. While knowledge distillation is a proven strategy to enhance the performance of lightweight classification models, its application to structured outputs like object detection and instance segmentation remains a complicated task, due to the variability in outputs and complex internal network modules involved in the distillation process. In this paper, we propose a simple yet surprisingly effective sequential approach to knowledge distillation that progressively transfers the knowledge of a set of teacher detectors to a given lightweight student. To distill knowledge from a highly accurate but complex teacher model, we construct a sequence of teachers to help the student gradually adapt. Our progressive strategy can be easily combined with existing detection distillation mechanisms to consistently maximize student performance in various settings. To the best of our knowledge, we are the first to successfully distill knowledge from Transformer-based teacher detectors to convolution-based students, and unprecedentedly boost the performance of ResNet-50 based RetinaNet from 36.5% to 42.0% AP and Mask R-CNN from 38.2% to 42.5% AP on the MS COCO benchmark. Code available at https://github.com/Shengcao-Cao/MTPD.

Graphs are omnipresent and GNNs are a powerful family of neural networks for learning over graphs. Despite their popularity, scaling GNNs either by deepening or widening suffers from prevalent issues of $\textit{unhealthy gradients, over-smoothening, information squashing}$, which often lead to sub-standard performance. In this work, we are interested in exploring a principled way to scale GNNs capacity without deepening or widening, which can improve its performance across multiple small and large graphs. Motivated by the recent intriguing phenomenon of model soups, which suggest that fine-tuned weights of multiple large-language pre-trained models can be merged to a better minima, we argue to exploit the fundamentals of model soups to mitigate the aforementioned issues of memory bottleneck and trainability during GNNs scaling. More specifically, we propose not to deepen or widen current GNNs, but instead present $\textbf{first data-centric perspective}$ of model soups to build powerful GNNs by dividing giant graph data to build independently and parallelly trained multiple comparatively weaker GNNs without any intermediate communication, and $\textit{combining their strength}$ using a greedy interpolation soup procedure to achieve state-of-the-art performance. Moreover, we provide a wide variety of model soup preparation techniques by leveraging state-of-the-art graph sampling and graph partitioning approaches that can handle large graph data structures. Our extensive experiments across many real-world small and large graphs, illustrate the effectiveness of our approach and point towards a promising orthogonal direction for GNN scaling. Codes are available at: https://github.com/VITA-Group/graph_ladling

Deep learning methods are highly accurate, yet their opaque decision process prevents them from earning full human trust. Concept-based models aim to address this issue by learning tasks based on a set of human-understandable concepts. However, state-of-the-art concept-based models rely on high-dimensional concept embedding representations which lack a clear semantic meaning, thus questioning the interpretability of their decision process. To overcome this limitation, we propose the Deep Concept Reasoner (DCR), the first interpretable concept-based model that builds upon concept embeddings. In DCR, neural networks do not make task predictions directly, but they build syntactic rule structures using concept embeddings. DCR then executes these rules on meaningful concept truth degrees to provide a final interpretable and semantically-consistent prediction in a differentiable manner. Our experiments show that DCR: (i) improves up to +25% w.r.t. state-of-the-art interpretable concept-based models on challenging benchmarks (ii) discovers meaningful logic rules matching known ground truths even in the absence of concept supervision during training, and (iii), facilitates the generation of counterfactual examples providing the learnt rules as guidance.

Federated Learning (FL) has been a popular approach to enable collaborative learning on multiple parties without exchanging raw data. However, the model performance of FL may degrade a lot due to non-IID data. While many FL algorithms focus on non-IID labels, FL on non-IID features has largely been overlooked. Different from typical FL approaches, the paper proposes a new learning concept called ADCOL (Adversarial Collaborative Learning) for non-IID features. Instead of adopting the widely used model-averaging scheme, ADCOL conducts training in an adversarial way: the server aims to train a discriminator to distinguish the representations of the parties, while the parties aim to generate a common representation distribution. Our experiments show that ADCOL achieves better performance than state-of-the-art FL algorithms on non-IID features.

Recent works on neural network pruning advocate that reducing the depth of the network is more effective in reducing run-time memory usage and accelerating inference latency than reducing the width of the network through channel pruning. In this regard, some recent works propose depth compression algorithms that merge convolution layers. However, the existing algorithms have a constricted search space and rely on human-engineered heuristics. In this paper, we propose a novel depth compression algorithm which targets general convolution operations. We propose a subset selection problem that replaces inefficient activation layers with identity functions and optimally merges consecutive convolution operations into shallow equivalent convolution operations for efficient end-to-end inference latency. Since the proposed subset selection problem is NP-hard, we formulate a surrogate optimization problem that can be solved exactly via two-stage dynamic programming within a few seconds. We evaluate our methods and baselines by TensorRT for a fair inference latency comparison. Our method outperforms the baseline method with higher accuracy and faster inference speed in MobileNetV2 on the ImageNet dataset. Specifically, we achieve $1.41\times$ speed-up with $0.11$%p accuracy gain in MobileNetV2-1.0 on the ImageNet.

The output distribution of a neural network (NN) over the entire input space captures the complete input-output mapping relationship, offering in- sights toward a more comprehensive NN under- standing. Exhaustive enumeration or traditional Monte Carlo methods for the entire input space can exhibit impractical sampling time, especially for high-dimensional inputs. To make such difficult sampling computationally feasible, in this paper, we propose a novel Gradient-based Wang-Landau (GWL) sampler. We first draw the connection between the output distribution of a NN and the density of states (DOS) of a physical system. Then, we renovate the classic sampler for the DOS problem, Wang-Landau algorithm, by re-placing its random proposals with gradient-based Monte Carlo proposals. This way, our GWL sampler investigates the under-explored subsets of the input space much more efficiently. Extensive experiments have verified the accuracy of the output distribution generated by GWL and also showcased several interesting findings - for example, in a binary image classification task, both CNN and ResNet mapped the majority of human unrecognizable images to very negative logit values.

Since their introduction, diffusion models have quickly become the prevailing approach to generative modeling in many domains. They can be interpreted as learning the gradients of a time-varying sequence of log-probability density functions. This interpretation has motivated classifier-based and classifier-free guidance as methods for post-hoc control of diffusion models. In this work, we build upon these ideas using the score-based interpretation of diffusion models, and explore alternative ways to condition, modify, and reuse diffusion models for tasks involving compositional generation and guidance. In particular, we investigate why certain types of composition fail using current techniques and present a number of solutions. We conclude that the sampler (not the model) is responsible for this failure and propose new samplers, inspired by MCMC, which enable successful compositional generation. Further, we propose an energy-based parameterization of diffusion models which enables the use of new compositional operators and more sophisticated, Metropolis-corrected samplers. Intriguingly we find these samplers lead to notable improvements in compositional generation across a wide variety of problems such as classifier-guided ImageNet modeling and compositional text-to-image generation.

Activity difference based learning algorithms---such as contrastive Hebbian learning and equilibrium propagation---have been proposed as biologically plausible alternatives to error back-propagation. However, on traditional digital chips these algorithms suffer from having to solve a costly inference problem twice, making these approaches more than two orders of magnitude slower than back-propagation. In the analog realm equilibrium propagation may be promising for fast and energy efficient learning, but states still need to be inferred and stored twice. Inspired by lifted neural networks and compartmental neuron models we propose a simple energy based compartmental neuron model, termed dual propagation, in which each neuron is a dyad with two intrinsic states. At inference time these intrinsic states encode the error/activity duality through their difference and their mean respectively. The advantage of this method is that only a single inference phase is needed and that inference can be solved in layerwise closed-form. Experimentally we show on common computer vision datasets, including Imagenet32x32, that dual propagation performs equivalently to back-propagation both in terms of accuracy and runtime.

We provide an efficient implementation of the backpropagation algorithm, specialized to the case where the weights of the neural network being trained are sparse. Our algorithm is general, as it applies to arbitrary (unstructured) sparsity and common layer types (e.g., convolutional or linear). We provide a fast vectorized implementation on commodity CPUs, and show that it can yield speedups in end-to-end runtime experiments, both in transfer learning using already-sparsified networks, and in training sparse networks from scratch. Thus, our results provide the first support for sparse training on commodity hardware.

Large language models (LLMs) with hundreds of billions of parameters have sparked a new wave of exciting AI applications. However, they are computationally expensive at inference time. Sparsity is a natural approach to reduce this cost, but existing methods either require costly retraining, have to forgo LLM's in-context learning ability, or do not yield wall-clock time speedup on modern hardware. We hypothesize that contextual sparsity, which are small, input-dependent sets of attention heads and MLP parameters that yield approximately the same output as the dense model for a given input, can address these issues. We show that contextual sparsity exists, that it can be accurately predicted, and that we can exploit it to speed up LLM inference in wall-clock time without compromising LLM's quality or in-context learning ability. Based on these insights, we propose DejaVu, a system that uses a low-cost algorithm to predict contextual sparsity on the fly given inputs to each layer, along with an asynchronous and hardware-aware implementation that speeds up LLM inference. We validate that DejaVu can reduce the inference latency of OPT-175B by over 2$\times$ compared to the state-of-the-art FasterTransformer, and over 6$\times$ compared to the widely used Hugging Face implementation, without compromising model quality. The code is available at https://github.com/FMInference/DejaVu.

The relational data model was designed to facilitate large-scale data management and analytics. We consider the problem of how to differentiate computations expressed relationally. We show experimentally that a relational engine running an auto-differentiated relational algorithm can easily scale to very large datasets, and is competitive with state-of-the-art, special-purpose systems for large-scale distributed machine learning.

Exploration in environments which differ across episodes has received increasing attention in recent years. Current methods use some combination of global novelty bonuses, computed using the agent's entire training experience, and episodic novelty bonuses, computed using only experience from the current episode. However, the use of these two types of bonuses has been ad-hoc and poorly understood. In this work, we shed light on the behavior of these two types of bonuses through controlled experiments on easily interpretable tasks as well as challenging pixel-based settings. We find that the two types of bonuses succeed in different settings, with episodic bonuses being most effective when there is little shared structure across episodes and global bonuses being effective when more structure is shared. We develop a conceptual framework which makes this notion of shared structure precise by considering the variance of the value function across contexts, and which provides a unifying explanation of our empirical results. We furthermore find that combining the two bonuses can lead to more robust performance across different degrees of shared structure, and investigate different algorithmic choices for defining and combining global and episodic bonuses based on function approximation. This results in an algorithm which sets a new state of the art across 16 tasks from the MiniHack suite used in prior work, and also performs robustly on Habitat and Montezuma's Revenge.

Neural architectures that learn potential energy surfaces from molecular data have undergone fast improvement in recent years. A key driver of this success is the Message Passing Neural Network (MPNN) paradigm. Its favorable scaling with system size partly relies upon a spatial distance limit on messages. While this focus on locality is a useful inductive bias, it also impedes the learning of long-range interactions such as electrostatics and van der Waals forces. To address this drawback, we propose Ewald message passing: a nonlocal Fourier space scheme which limits interactions via a cutoff on frequency instead of distance, and is theoretically well-founded in the Ewald summation method. It can serve as an augmentation on top of existing MPNN architectures as it is computationally inexpensive and agnostic to architectural details. We test the approach with four baseline models and two datasets containing diverse periodic (OC20) and aperiodic structures (OE62). Across all models and datasets, we observe robust improvements in energy mean absolute errors, averaging 10% on OC20 and 16% on OE62. Our analysis shows an outsize impact of these improvements on structures with high long-range contributions to the ground-truth energy.

Data imbalance is a common problem in machine learning that can have a critical effect on the performance of a model. Various solutions exist but their impact on the convergence of the learning dynamics is not understood. Here, we elucidate the significant negative impact of data imbalance on learning, showing that the learning curves for minority and majority classes follow sub-optimal trajectories when training with a gradient-based optimizer. This slowdown is related to the imbalance ratio and can be traced back to a competition between the optimization of different classes. Our main contribution is the analysis of the convergence of full-batch (GD) and stochastic gradient descent (SGD), and of variants that renormalize the contribution of each per-class gradient. We find that GD is not guaranteed to decrease the loss for each class but that this problem can be addressed by performing a per-class normalization of the gradient. With SGD, class imbalance has an additional effect on the direction of the gradients: the minority class suffers from a higher directional noise, which reduces the effectiveness of the per-class gradient normalization. Our findings not only allow us to understand the potential and limitations of strategies involving the per-class gradients, but also the reason for the effectiveness of previously used solutions for class imbalancesuch as oversampling.

Characterizing the remarkable generalization properties of over-parameterized neural networks remains an open problem. A growing body of recent literature shows that the bias of stochastic gradient descent (SGD) and architecture choice implicitly leads to better generalization. In this paper, we show on the contrary that, independently of architecture, SGD can itself be the cause of poor generalization if one does not ensure good initialization. Specifically, we prove that any differentiably parameterized model, trained under gradient flow, obeys a weak spectral bias law which states that sufficiently high frequencies train arbitrarily slowly. This implies that very high frequencies present at initialization will remain after training, and hamper generalization. Further, we empirically test the developed theoretical insights using practical, deep networks. Finally, we contrast our framework with that supplied by the flat-minima conjecture and show that Fourier analysis grants a more reliable framework for understanding the generalization of neural networks.

Recent research shows that when Gradient Descent (GD) is applied to neural networks, the loss almost never decreases monotonically. Instead, the loss oscillates as gradient descent converges to its ``Edge of Stability'' (EoS). Here, we find a quantity that does decrease monotonically throughout GD training: the sharpness attained by the gradient flow solution (GFS)---the solution that would be obtained if, from now until convergence, we train with an infinitesimal step size. Theoretically, we analyze scalar neural networks with the squared loss, perhaps the simplest setting where the EoS phenomena still occur. In this model, we prove that the GFS sharpness decreases monotonically. Using this result, we characterize settings where GD provably converges to the EoS in scalar networks. Empirically, we show that GD monotonically decreases the GFS sharpness in a squared regression model as well as practical neural network architectures.

Having reliable specifications is an unavoidable challenge in achieving verifiable correctness, robustness, and interpretability of AI systems. Existing specifications for neural networks are in the paradigm of data as specification. That is, the local neighborhood centering around a reference input is considered to be correct (or robust). While existing specifications contribute to verifying adversarial robustness, a significant problem in many research domains, our empirical study shows that those verified regions are somewhat tight, and thus fail to allow verification of test set inputs, making them impractical for some real-world applications. To this end, we propose a new family of specifications called neural representation as specification. This form of specifications uses the intrinsic information of neural networks, specifically neural activation patterns (NAPs), rather than input data to specify the correctness and/or robustness of neural network predictions. We present a simple statistical approach to mining neural activation patterns. To show the effectiveness of discovered NAPs, we formally verify several important properties, such as various types of misclassifications will never happen for a given NAP, and there is no ambiguity between different NAPs. We show that by using NAP, we can verify a significant region of the input space, while still recalling 84% of the data on MNIST. Moreover, we can push the verifiable bound to 10 times larger on the CIFAR10 benchmark. Thus, we argue that NAPs can potentially be used as a more reliable and extensible specification for neural network verification.

Applications of machine learning techniques for materials modeling typically involve functions that are known to be equivariant or invariant to specific symmetries. While graph neural networks (GNNs) have proven successful in such applications, conventional GNN approaches that enforce symmetries via the model architecture often reduce expressivity, scalability or comprehensibility. In this paper, we introduce (1) a flexible, model-agnostic framework based on stochastic frame averaging that enforces E(3) equivariance or invariance, without any architectural constraints; (2) FAENet: a simple, fast and expressive GNN that leverages stochastic frame averaging to process geometric information without constraints. We prove the validity of our method theoretically and demonstrate its superior accuracy and computational scalability in materials modeling on the OC20 dataset (S2EF, IS2RE) as well as common molecular modeling tasks (QM9, QM7-X).

We introduce the concept of programmable feature engineering for time series modeling and propose a feature programming framework. This framework generates large amounts of predictive features for noisy multivariate time series while allowing users to incorporate their inductive bias with minimal effort. The key motivation of our framework is to view any multivariate time series as a cumulative sum of fine-grained trajectory increments, with each increment governed by a novel spin-gas dynamical Ising model. This fine-grained perspective motivates the development of a parsimonious set of operators that summarize multivariate time series in an abstract fashion, serving as the foundation for large-scale automated feature engineering. Numerically, we validate the efficacy of our method on several synthetic and real-world noisy time series datasets.

Understanding the neural implementation of complex human behaviors is one of the major goals in neuroscience. To this end, it is crucial to find a true representation of the neural data, which is challenging due to the high complexity of behaviors and the low signal-to-ratio (SNR) of the signals. Here, we propose a novel unsupervised learning framework, Neural Latent Aligner (NLA), to find well-constrained, behaviorally relevant neural representations of complex behaviors. The key idea is to align representations across repeated trials to learn cross-trial consistent information. Furthermore, we propose a novel, fully differentiable time warping model (TWM) to resolve the temporal misalignment of trials. When applied to intracranial electrocorticography (ECoG) of natural speaking, our model learns better representations for decoding behaviors than the baseline models, especially in lower dimensional space. The TWM is empirically validated by measuring behavioral coherence between aligned trials. The proposed framework learns more cross-trial consistent representations than the baselines, and when visualized, the manifold reveals shared neural trajectories across trials.

Decoding seen images from brain activities has been an absorbing field. However, the reconstructed images still suffer from low quality with existing studies. This can be because our visual system is not like a camera that ''remembers'' every pixel. Instead, only part of the information can be perceived with our selective attention, and the brain ''guesses'' the rest to form what we think we see. Most existing approaches ignored the brain completion mechanism. In this work, we propose to reconstruct seen images with both the visual perception and the brain completion process, and design a simple, yet effective visual decoding framework to achieve this goal. Specifically, we first construct a shared discrete representation space for both brain signals and images. Then, a novel self-supervised token-to-token inpainting network is designed to implement visual content completion by building context and prior knowledge about the visual objects from the discrete latent space. Our approach improved the quality of visual reconstruction significantly and achieved state-of-the-art.

Recent works have demonstrated the benefits of capturing long-distance dependency in graphs by deeper graph neural networks (GNNs). But deeper GNNs suffer from the long-lasting scalability challenge due to the neighborhood explosion problem in large-scale graphs. In this work, we propose to capture long-distance dependency in graphs by shallower models instead of deeper models, which leads to a much more efficient model, LazyGNN, for graph representation learning. Moreover, we demonstrate that LazyGNN is compatible with existing scalable approaches (such as sampling methods) for further accelerations through the development of mini-batch LazyGNN. Comprehensive experiments demonstrate its superior prediction performance and scalability on large-scale benchmarks. The implementation of LazyGNN is available at https: //github.com/RXPHD/Lazy_GNN.

Two main families of node feature augmentation schemes have been explored for enhancing GNNs: random features and spectral positional encoding. Surprisingly, however, there is still no clear understanding of the relation between these two augmentation schemes. Here we propose a novel family of positional encoding schemes which draws a link between the above two approaches and improves over both. The new approach, named Random Feature Propagation (RFP), is inspired by the power iteration method and its generalizations. It concatenates several intermediate steps of an iterative algorithm for computing the dominant eigenvectors of a propagation matrix, starting from random node features. Notably, these propagation steps are based on graph-dependent propagation operators that can be either predefined or learned. We explore the theoretical and empirical benefits of RFP. First, we provide theoretical justifications for using random features, for incorporating early propagation steps, and for using multiple random initializations. Then, we empirically demonstrate that RFP significantly outperforms both spectral PE and random features in multiple node classification and graph classification benchmarks.

This paper demonstrates that language models are strong structure-based protein designers. We present LM-Design, a generic approach to reprogramming sequence-based protein language models (pLMs), that have learned massive sequential evolutionary knowledge from the universe of natural protein sequences, to acquire an immediate capability to design preferable protein sequences for given folds. We conduct a structural surgery on pLMs, where a lightweight structural adapter is implanted into pLMs and endows it with structural awareness. During inference, iterative refinement is performed to effectively optimize the generated protein sequences. Experiments show that LM-Design improves the state-of-the-art results by a large margin, leading to 4% to 12% accuracy gains in sequence recovery (e.g., 55.65%/56.63% on CATH 4.2/4.3 single-chain benchmarks, and >60% when designing protein complexes). We provide extensive and in-depth analyses, which verify that LM-Design can (1) indeed leverage both structural and sequential knowledge to accurately handle structurally non-deterministic regions, (2) benefit from scaling data and model size, and (3) generalize to other proteins (e.g., antibodies and de novo proteins).

Multi-resolution hash encoding has recently been proposed to reduce the computational cost of neural renderings, such as NeRF. This method requires accurate camera poses for the neural renderings of given scenes. However, contrary to previous methods jointly optimizing camera poses and 3D scenes, the naive gradient-based camera pose refinement method using multi-resolution hash encoding severely deteriorates performance. We propose a joint optimization algorithm to calibrate the camera pose and learn a geometric representation using efficient multi-resolution hash encoding. Showing that the oscillating gradient flows of hash encoding interfere with the registration of camera poses, our method addresses the issue by utilizing smooth interpolation weighting to stabilize the gradient oscillation for the ray samplings across hash grids. Moreover, the curriculum training procedure helps to learn the level-wise hash encoding, further increasing the pose refinement. Experiments on the novel-view synthesis datasets validate that our learning frameworks achieve state-of-the-art performance and rapid convergence of neural rendering.

Causal structure learning can reveal the causal mechanism behind natural systems. It is well studied that the multiple domain data consisting of observational and interventional samples benefit causal identifiability. However, for non-stationary time series data, domain indexes are often unavailable, making it difficult to distinguish observational samples from interventional samples. To address these issues, we propose a novel Latent Intervened Non-stationary learning (LIN) method to make the domain indexes recovery process and the causal structure learning process mutually promote each other. We characterize and justify a possible faithfulness condition to guarantee the identifiability of the proposed LIN method. Extensive experiments on both synthetic and real-world datasets demonstrate that our method outperforms the baselines on causal structure learning for latent intervened non-stationary data.

In many real-world tasks, some parts of state features, called contexts, are independent of action signals, e.g., customer demand in inventory control, speed of lead car in autonomous driving, etc. One of the challenges of reinforcement learning in these applications is that the true context transitions can be easily exposed some unknown source of contamination, leading to a shift of context transitions between source domains and target domains, which could cause performance degradation for RL algorithms. However, existing methods on robust RL aim at learning robust policies against the deviations of the entire system dynamics. To tackle this problem, this paper proposes the framework of robust situational Markov decision process (RS-MDP) which captures the possible deviations of context transitions explicitly. To scale to large context space, we introduce the softmin smoothed robust Bellman operator to learn the robust Q-value approximately, and apply our RS-MDP framework to existing RL algorithm SAC to learn the desired robust policies. We conduct experiments on several robot control tasks with dynamic contexts and inventory control tasks to demonstrate that our algorithm can generalize better and more robust against deviations of context transitions, and outperform existing robust RL algorithms.

It is believed that Gradient Descent (GD) induces an implicit bias towards good generalization in training machine learning models. This paper provides a fine-grained analysis of the dynamics of GD for the matrix sensing problem, whose goal is to recover a low-rank ground-truth matrix from near-isotropic linear measurements. It is shown that GD with small initialization behaves similarly to the greedy low-rank learning heuristics and follows an incremental learning procedure: GD sequentially learns solutions with increasing ranks until it recovers the ground truth matrix. Compared to existing works which only analyze the first learning phase for rank-1 solutions, our result provides characterizations for the whole learning process. Moreover, besides the over-parameterized regime that many prior works focused on, our analysis of the incremental learning procedure also applies to the under-parameterized regime. Finally, we conduct numerical experiments to confirm our theoretical findings.

General function approximation is a powerful tool to handle large state and action spaces in a broad range of reinforcement learning (RL) scenarios. However, theoretical understanding of non-stationary MDPs with general function approximation is still limited. In this paper, we make the first such an attempt. We first propose a new complexity metric called dynamic Bellman Eluder (DBE) dimension for non-stationary MDPs, which subsumes majority of existing tractable RL problems in static MDPs as well as non-stationary MDPs. Based on the proposed complexity metric, we propose a novel confidence-set based model-free algorithm called SW-OPEA, which features a sliding window mechanism and a new confidence set design for non-stationary MDPs. We then establish an upper bound on the dynamic regret for the proposed algorithm, and show that SW-OPEA is provably efficient as long as the variation budget is not significantly large. We further demonstrate via examples of non-stationary linear and tabular MDPs that our algorithm performs better in small variation budget scenario than the existing UCB-type algorithms. To the best of our knowledge, this is the first dynamic regret analysis in non-stationary MDPs with general function approximation.

Cross-validation (CV) is one of the most popular tools for assessing and selecting predictive models. However, standard CV suffers from high computational cost when the number of folds is large. Recently, under the empirical risk minimization (ERM) framework, a line of works proposed efficient methods to approximate CV based on the solution of the ERM problem trained on the full dataset. However, in large-scale problems, it can be hard to obtain the exact solution of the ERM problem, either due to limited computational resources or due to early stopping as a way of preventing overfitting. In this paper, we propose a new paradigm to efficiently approximate CV when the ERM problem is solved via an iterative first-order algorithm, without running until convergence. Our new method extends existing guarantees for CV approximation to hold along the whole trajectory of the algorithm, including at convergence, thus generalizing existing CV approximation methods. Finally, we illustrate the accuracy and computational efficiency of our method through a range of empirical studies.

Dynamics prediction, which is the problem of predicting future states of scene objects based on current and prior states, is drawing increasing attention as an instance of learning physics. To solve this problem, Region Proposal Convolutional Interaction Network (RPCIN), a vision-based model, was proposed and achieved state-of-the-art performance in long-term prediction. RPCIN only takes raw images and simple object descriptions, such as the bounding box and segmentation mask of each object, as input. However, despite its success, the model's capability can be compromised under conditions of environment misalignment. In this paper, we investigate two challenging conditions for environment misalignment: Cross-Domain and Cross-Context by proposing four datasets that are designed for these challenges: SimB-Border, SimB-Split, BlenB-Border, and BlenB-Split. The datasets cover two domains and two contexts. Using RPCIN as a probe, experiments conducted on the combinations of the proposed datasets reveal potential weaknesses of the vision-based long-term dynamics prediction model. Furthermore, we propose a promising direction to mitigate the Cross-Domain challenge and provide concrete evidence supporting such a direction, which provides dramatic alleviation of the challenge on the proposed datasets.

Recently, the newly emerged multimodal models, which leverage both visual and linguistic modalities to train powerful encoders, have gained increasing attention. However, learning from a large-scale unlabeled dataset also exposes the model to the risk of potential poisoning attacks, whereby the adversary aims to perturb the model's training data to trigger malicious behaviors in it. In contrast to previous work, only poisoning visual modality, in this work, we take the first step to studying poisoning attacks against multimodal models in both visual and linguistic modalities. Specially, we focus on answering two questions: (1) Is the linguistic modality also vulnerable to poisoning attacks? and (2) Which modality is most vulnerable? To answer the two questions, we propose three types of poisoning attacks against multimodal models. Extensive evaluations on different datasets and model architectures show that all three attacks can achieve significant attack performance while maintaining model utility in both visual and linguistic modalities. Furthermore, we observe that the poisoning effect differs between different modalities. To mitigate the attacks, we propose both pre-training and post-training defenses. We empirically show that both defenses can significantly reduce the attack performance while preserving the model's utility. Our code is available at https://github.com/zqypku/mm_poison/.

Recently, Diffusion Models (DMs) boost a wave in AI for Art yet raise new copyright concerns, where infringers benefit from using unauthorized paintings to train DMs and generate novel paintings in a similar style. To address these emerging copyright violations, in this paper, we are the first to explore and propose to utilize adversarial examples for DMs to protect human-created artworks. Specifically, we first build a theoretical framework to define and evaluate the adversarial examples for DMs. Then, based on this framework, we design a novel algorithm to generate these adversarial examples, named AdvDM, which exploits a Monte-Carlo estimation of adversarial examples for DMs by optimizing upon different latent variables sampled from the reverse process of DMs. Extensive experiments show that the generated adversarial examples can effectively hinder DMs from extracting their features. Therefore, our method can be a powerful tool for human artists to protect their copyright against infringers equipped with DM-based AI-for-Art applications. The code of our method is available on GitHub: https://github.com/mist-project/mist.git.

Visual robotic manipulation research and applications often use multiple cameras, or views, to better perceive the world. How else can we utilize the richness of multi-view data? In this paper, we investigate how to learn good representations with multi-view data and utilize them for visual robotic manipulation. Specifically, we train a multi-view masked autoencoder which reconstructs pixels of randomly masked viewpoints and then learn a world model operating on the representations from the autoencoder. We demonstrate the effectiveness of our method in a range of scenarios, including multi-view control and single-view control with auxiliary cameras for representation learning. We also show that the multi-view masked autoencoder trained with multiple randomized viewpoints enables training a policy with strong viewpoint randomization and transferring the policy to solve real-robot tasks without camera calibration and an adaptation procedure. Video demonstrations are available at: https://sites.google.com/view/mv-mwm.

Recently, Language Models (LMs) instruction-tuned on multiple tasks, also known as multitask-prompted fine-tuning (MT), have shown capabilities to generalize to unseen tasks. Previous work has shown that scaling the number of finetuning datasets and instructions is the key component in making stronger MT LMs. In this work, we report surprising findings that show an expert LM trained on just a single task can outperform an MT LM trained with 300+ different tasks on 11 different unseen datasets and on 13 datasets of the BIG-bench benchmark by an average of 3.20% and 1.29%, respectively. This finding casts doubt on the previously held belief that simply scaling the number of tasks makes stronger MT LMs. Leveraging this finding, we further show that this distributed approach of training multiple expert LMs instead of a single MT LM for zero-shot inference possesses many benefits including (1) avoiding negative task transfer that often occurs during instruction tuning, (2) being able to continually learn new tasks without having to re-train on previous tasks to avoid catastrophic forgetting, and (3) showing compositional capabilities when merging individual experts together.

Text-to-audio (TTA) systems have recently gained attention for their ability to synthesize general audio based on text descriptions. However, previous studies in TTA have limited generation quality with high computational costs. In this study, we propose AudioLDM, a TTA system that is built on a latent space to learn continuous audio representations from contrastive language-audio pretraining (CLAP) embeddings. The pretrained CLAP models enable us to train LDMs with audio embeddings while providing text embeddings as the condition during sampling. By learning the latent representations of audio signals without modelling the cross-modal relationship, AudioLDM improves both generation quality and computational efficiency. Trained on AudioCaps with a single GPU, AudioLDM achieves state-of-the-art TTA performance compared to other open-sourced systems, measured by both objective and subjective metrics. AudioLDM is also the first TTA system that enables various text-guided audio manipulations (e.g., style transfer) in a zero-shot fashion. Our implementation and demos are available at https://audioldm.github.io.

Recent advances in weak supervision (WS) techniques allow to mitigate the enormous cost and effort of human data annotation for supervised machine learning by automating it using simple rule-based labelling functions (LFs). However, LFs need to be carefully designed, often requiring expert domain knowledge and extensive validation for existing WS methods to be effective. To tackle this, we propose the Weak Supervision Variational Auto-Encoder (WS-VAE), a novel framework that combines unsupervised representation learning and weak labelling to reduce the dependence of WS on expert and manual engineering of LFs. Our technique learns from inputs and weak labels jointly to capture the input signals distribution with a latent space. The unsupervised representation component of the WS-VAE regularises the inference of weak labels, while a specifically designed decoder allows the model to learn the relevance of LFs for each input. These unique features lead to considerably improved robustness to the quality of LFs, compared to existing methods. An extensive empirical evaluation on a standard WS benchmark shows that our WS-VAE is competitive to state-of-the-art methods and substantially more robust to LF engineering.

Offline model-based optimization aims to maximize a black-box objective function with a static dataset of designs and their scores. In this paper, we focus on biological sequence design to maximize some sequence score. A recent approach employs bidirectional learning, combining a forward mapping for exploitation and a backward mapping for constraint, and it relies on the neural tangent kernel (NTK) of an infinitely wide network to build a proxy model. Though effective, the NTK cannot learn features because of its parametrization, and its use prevents the incorporation of powerful pre-trained Language Models (LMs) that can capture the rich biophysical information in millions of biological sequences. We adopt an alternative proxy model, adding a linear head to a pre-trained LM, and propose a linearization scheme. This yields a closed-form loss and also takes into account the biophysical information in the pre-trained LM. In addition, the forward mapping and the backward mapping play different roles and thus deserve different weights during sequence optimization. To achieve this, we train an auxiliary model and leverage its weak supervision signal via a bi-level optimization framework to effectively learn how to balance the two mappings. Further, by extending the framework, we develop the first learning rate adaptation module *Adaptive*-$\eta$, which is compatible with all gradient-based algorithms for offline model-based optimization. Experimental results on DNA/protein sequence design tasks verify the effectiveness of our algorithm. Our code is available at https://github.com/GGchen1997/BIB-ICML2023-Submission.

Inference from large autoregressive models like Transformers is slow - decoding K tokens takes K serial runs of the model. In this work we introduce speculative decoding - an algorithm to sample from autoregressive models faster without any changes to the outputs, by computing several tokens in parallel. At the heart of our approach lie the observations that (1) hard language-modeling tasks often include easier subtasks that can be approximated well by more efficient models, and (2) using speculative execution and a novel sampling method, we can make exact decoding from the large models faster, by running them in parallel on the outputs of the approximation models, potentially generating several tokens concurrently, and without changing the distribution. Our method can accelerate existing off-the-shelf models without retraining or architecture changes. We demonstrate it on T5-XXL and show a 2X-3X acceleration compared to the standard T5X implementation, with identical outputs.

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a problem which appears throughout natural sciences and machine learning, including in quantum systems, single-cell biological data, and generative modeling. In these settings, we assume access to cross-sectional samples that are uncorrelated over time, rather than full trajectories of samples. In order to better understand the systems under observation, we would like to learn a model of the underlying process that allows us to propagate samples in time and thereby simulate entire individual trajectories. In this work, we propose Action Matching, a method for learning a rich family of dynamics using only independent samples from its time evolution. We derive a tractable training objective, which does not rely on explicit assumptions about the underlying dynamics and does not require back-propagation through differential equations or optimal transport solvers. Inspired by connections with optimal transport, we derive extensions of Action Matching to learn stochastic differential equations and dynamics involving creation and destruction of probability mass. Finally, we showcase applications of Action Matching by achieving competitive performance in a diverse set of experiments from biology, physics, and generative modeling.

We propose new techniques for reducing communication in private federated learning without the need for setting or tuning compression rates. Our on-the-fly methods automatically adjust the compression rate based on the error induced during training, while maintaining provable privacy guarantees through the use of secure aggregation and differential privacy. Our techniques are provably instance-optimal for mean estimation, meaning that they can adapt to the ``hardness of the problem'' with minimal interactivity. We demonstrate the effectiveness of our approach on real-world datasets by achieving favorable compression rates without the need for tuning.

We propose a theoretical framework to analyze semi-supervised classification under the low density separation assumption in a high-dimensional regime. In particular, we introduce QLDS, a linear classification model, where the low density separation assumption is implemented via quadratic margin maximization. The algorithm has an explicit solution with rich theoretical properties, and we show that particular cases of our algorithm are the least-square support vector machine in the supervised case, the spectral clustering in the fully unsupervised regime, and a class of semi-supervised graph-based approaches. As such, QLDS establishes a smooth bridge between these supervised and unsupervised learning methods. Using recent advances in the random matrix theory, we formally derive a theoretical evaluation of the classification error in the asymptotic regime. As an application, we derive a hyperparameter selection policy that finds the best balance between the supervised and the unsupervised terms of our learning criterion. Finally, we provide extensive illustrations of our framework, as well as an experimental study on several benchmarks to demonstrate that QLDS, while being computationally more efficient, improves over cross-validation for hyperparameter selection, indicating a high promise of the usage of random matrix theory for semi-supervised model selection.

The successes of modern deep machine learning methods are founded on their ability to transform inputs across multiple layers to build good high-level representations. It is therefore critical to understand this process of representation learning. However, standard theoretical approaches (formally NNGPs) involving infinite width limits eliminate representation learning. We therefore develop a new infinite width limit, the Bayesian representation learning limit, that exhibits representation learning mirroring that in finite-width models, yet at the same time, retains some of the simplicity of standard infinite-width limits. In particular, we show that Deep Gaussian processes (DGPs) in the Bayesian representation learning limit have exactly multivariate Gaussian posteriors, and the posterior covariances can be obtained by optimizing an interpretable objective combining a log-likelihood to improve performance with a series of KL-divergences which keep the posteriors close to the prior. We confirm these results experimentally in wide but finite DGPs. Next, we introduce the possibility of using this limit and objective as a flexible, deep generalisation of kernel methods, that we call deep kernel machines (DKMs). Like most naive kernel methods, DKMs scale cubically in the number of datapoints. We therefore use methods from the Gaussian process inducing point literature to develop a sparse DKM that scales linearly in the number of datapoints. Finally, we extend these approaches to NNs (which have non-Gaussian posteriors) in the Appendices.

We propose a new method for optimistic planning in infinite-horizon discounted Markov decision processes based on the idea of adding regularization to the updates of an otherwise standard approximate value iteration procedure. This technique allows us to avoid contraction and monotonicity arguments typically required by existing analyses of approximate dynamic programming methods, and in particular to use approximate transition functions estimated via least-squares procedures in MDPs with linear function approximation. We use our method to recover known guarantees in tabular MDPs and to provide a computationally efficient algorithm for learning near-optimal policies in discounted linear mixture MDPs from a single stream of experience, and show it achieves near-optimal statistical guarantees.

We introduce fast algorithms for correlation clustering with respect to the Min Max objective that provide constant factor approximations on complete graphs. Our algorithms are the first purely combinatorial approximation algorithms for this problem. We construct a novel semi-metric on the set of vertices, which we call the correlation metric, that indicates to our clustering algorithms whether pairs of nodes should be in the same cluster. The paper demonstrates empirically that, compared to prior work, our algorithms sacrifice little in the objective quality to obtain significantly better run-time. Moreover, our algorithms scale to larger networks that are effectively intractable for known algorithms.

In this work, we propose introduce a variant of online stochastic gradient descent and prove it converges to Nash equilibria and simultaneously it has sublinear regret for the class of congestion games in the semi-bandit feedback setting. Our proposed method admits convergence rates depending only polynomially on the number of players and the number of facilities, but not on the size of the action set, which can be exponentially large in terms of the number of facilities. Moreover, the running time of our method has polynomial-time dependence on the implicit description of the game. Our analysis exploits techniques from convex geometry, in particular Caratheodory's theorem and recent advances in non-convex stochastic optimization. This work improves upon and answers an open question from (Cui et al 2022).

We consider the problem of global optimization with noisy zeroth order oracles — a well-motivated problem useful for various applications ranging from hyper-parameter tuning for deep learning to new material design. Existing work relies on Gaussian processes or other non-parametric family, which suffers from the curse of dimensionality. In this paper, we propose a new algorithm GO-UCB that leverages a parametric family of functions (e.g., neural networks) instead. Under a realizable assumption and a few other mild geometric conditions, we show that GO-UCB achieves a cumulative regret of $\tilde{O}(\sqrt{T})$ where $T$ is the time horizon. At the core of GO-UCB is a carefully designed uncertainty set over parameters based on gradients that allows optimistic exploration. Synthetic and real-world experiments illustrate GO-UCB works better than popular Bayesian optimization approaches, even if the model is misspecified.

In deep learning, mixture-of-experts (MoE) activates one or few experts (sub-networks) on a per-sample or per-token basis, resulting in significant computation reduction. The recently proposed patch-level routing in MoE (pMoE) divides each input into $n$ patches (or tokens) and sends $l$ patches ($l\ll n$) to each expert through prioritized routing. pMoE has demonstrated great empirical success in reducing training and inference costs while maintaining test accuracy. However, the theoretical explanation of pMoE and the general MoE remains elusive. Focusing on a supervised classification task using a mixture of two-layer convolutional neural networks (CNNs), we show for the first time that pMoE provably reduces the required number of training samples to achieve desirable generalization (referred to as the sample complexity) by a factor in the polynomial order of $n/l$, and outperforms its single-expert counterpart of the same or even larger capacity. The advantage results from the discriminative routing property, which is justified in both theory and practice that pMoE routers can filter label-irrelevant patches and route similar class-discriminative patches to the same expert. Our experimental results on MNIST, CIFAR-10, and CelebA support our theoretical findings on pMoE's generalization and show that pMoE can avoid learning spurious correlations.

Spiking neural networks provide an alternative solution to conventional artificial neural networks with energy-saving and high-efficiency characteristics after hardware implantation. However, due to its non-differentiable activation function and the temporally delayed accumulation in outputs, the direct training of SNNs is extraordinarily tough even adopting a surrogate gradient to mimic the backpropagation. For SNN training, this non-differentiability causes the intrinsic gradient error that would be magnified through layerwise backpropagation, especially through multiple layers. In this paper, we propose a novel approach to reducing gradient error from a new perspective called surrogate module learning (SML). Surrogate module learning tries to construct a shortcut path to back-propagate more accurate gradient to a certain SNN part utilizing the surrogate modules. Then, we develop a new loss function for concurrently training the network and enhancing the surrogate modules' surrogate capacity. We demonstrate that when the outputs of surrogate modules are close to the SNN output, the fraction of the gradient error drops significantly. Our method consistently and significantly enhances the performance of SNNs on all experiment datasets, including CIFAR-10/100, ImageNet, and ES-ImageNet. For example, for spiking ResNet-34 architecture on ImageNet, we increased the SNN accuracy by 3.46%.

This paper proposes a unified diffusion framework (dubbed UniDiffuser) to fit all distributions relevant to a set of multi-modal data in one model. Our key insight is -- learning diffusion models for marginal, conditional, and joint distributions can be unified as predicting the noise in the perturbed data, where the perturbation levels (i.e. timesteps) can be different for different modalities. Inspired by the unified view, UniDiffuser learns all distributions simultaneously with a minimal modification to the original diffusion model -- perturbs data in all modalities instead of a single modality, inputs individual timesteps in different modalities, and predicts the noise of all modalities instead of a single modality. UniDiffuser is parameterized by a transformer for diffusion models to handle input types of different modalities. Implemented on large-scale paired image-text data, UniDiffuser is able to perform image, text, text-to-image, image-to-text, and image-text pair generation by setting proper timesteps without additional overhead. In particular, UniDiffuser is able to produce perceptually realistic samples in all tasks and its quantitative results (e.g., the FID and CLIP score) are not only superior to existing general-purpose models but also comparable to the bespoken models (e.g., Stable Diffusion and DALL-E 2) in representative tasks (e.g., text-to-image generation).

In real life, accurately annotating large-scale datasets is sometimes difficult. Datasets used for training deep learning models are likely to contain label noise. To make use of the dataset containing label noise, two typical methods have been proposed. One is to employ the semi-supervised method by exploiting labeled confident examples and unlabeled unconfident examples. The other one is to model label noise and design statistically consistent classifiers. A natural question remains unsolved: which one should be used for a specific real-world application? In this paper, we answer the question from the perspective of causal data generative process. Specifically, the performance of the semi-supervised based method depends heavily on the data generative process while the method modeling label-noise is not influenced by the generation process. For example, for a given dataset, if it has a causal generative structure that the features cause the label, the semi-supervised based method would not be helpful. When the causal structure is unknown, we provide an intuitive method to discover the causal structure for a given dataset containing label noise.

In this paper, we propose a novel framework, Active Learning based Structural Inference (ALaSI), to infer the existence of directed connections from observed agents' states over a time period in a dynamical system. With the help of deep active learning, ALaSI is competent in learning the representation of connections with a relatively small pool of prior knowledge. Moreover, based on information theory, the proposed inter- and out-of-scope message learning pipelines are remarkably beneficial to structural inference for large dynamical systems. We evaluate ALaSI on various large datasets including simulated systems and real-world networks, to demonstrate that ALaSI is able to outperform previous methods in precisely inferring the existence of connections in large systems under either supervised learning or unsupervised learning.

The fairness of machine learning-based decisions has become an increasingly important focus in the design of supervised machine learning methods. Most fairness approaches optimize a specified trade-off between performance measure(s) (e.g., accuracy, log loss, or AUC) and fairness metric(s) (e.g., demographic parity, equalized odds). This begs the question: are the right performance-fairness trade-offs being specified? We instead re-cast fair machine learning as an imitation learning task by introducing superhuman fairness, which seeks to simultaneously outperform human decisions on multiple predictive performance and fairness measures. We demonstrate the benefits of this approach given suboptimal decisions.

Predictive black-box models can exhibit high-accuracy but their opaque nature hinders their uptake in safety-critical deployment environments. Explanation methods (XAI) can provide confidence for decision-making through increased transparency. However, existing XAI methods are not tailored towards models in sensitive domains where one predictor is of special interest, such as a treatment effect in a clinical model, or ethnicity in policy models. We introduce Path-Wise Shapley effects (PWSHAP), a framework for assessing the targeted effect of a binary (e.g. treatment) variable from a complex outcome model. Our approach augments the predictive model with a user-defined directed acyclic graph (DAG). The method then uses the graph alongside on-manifold Shapley values to identify effects along causal pathways whilst maintaining robustness to adversarial attacks. We establish error bounds for the identified path-wise Shapley effects and for Shapley values. We show PWSHAP can perform local bias and mediation analyses with faithfulness to the model. Further, if the targeted variable is randomised we can quantify local effect modification. We demonstrate the resolution, interpretability and true locality of our approach on examples and a real-world experiment.

Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

Estimating heterogeneous treatment effects from observational data is a crucial task across many fields, helping policy and decision-makers take better actions. There has been recent progress on robust and efficient methods for estimating the conditional average treatment effect (CATE) function, but these methods often do not take into account the risk of hidden confounding, which could arbitrarily and unknowingly bias any causal estimate based on observational data. We propose a meta-learner called the B-Learner, which can efficiently learn sharp bounds on the CATE function under limits on the level of hidden confounding. We derive the B-Learner by adapting recent results for sharp and valid bounds of the average treatment effect (Dorn et al., 2021) into the framework given by Kallus & Oprescu (2023) for robust and model-agnostic learning of conditional distributional treatment effects. The B-Learner can use any function estimator such as random forests and deep neural networks, and we prove its estimates are valid, sharp, efficient, and have a quasi-oracle property with respect to the constituent estimators under more general conditions than existing methods. Semi-synthetic experimental comparisons validate the theoretical findings, and we use real-world data demonstrate how the method might be used in practice.

Collaborative causal inference (CCI) aims to improve the estimation of the causal effect of treatment variables by utilizing data aggregated from multiple self-interested parties. Since their source data are valuable proprietary assets that can be costly or tedious to obtain, every party has to be incentivized to be willing to contribute to the collaboration, such as with a guaranteed fair and sufficiently valuable reward (than performing causal inference on its own). This paper presents a reward scheme designed using the unique statistical properties that are required by causal inference to guarantee certain desirable incentive criteria (e.g., fairness, benefit) for the parties based on their contributions. To achieve this, we propose a data valuation function to value parties' data for CCI based on the distributional closeness of its resulting treatment effect estimate to that utilizing the aggregated data from all parties. Then, we show how to value the parties' rewards fairly based on a modified variant of the Shapley value arising from our proposed data valuation for CCI. Finally, the Shapley fair rewards to the parties are realized in the form of improved, stochastically perturbed treatment effect estimates. We empirically demonstrate the effectiveness of our reward scheme using simulated and real-world datasets.

Recently, many works studied the expressive power of graph neural networks (GNNs) by linking it to the $1$-dimensional Weisfeiler-Leman algorithm ($1\text{-}\mathsf{WL}$). Here, the $1\text{-}\mathsf{WL}$ is a well-studied heuristic for the graph isomorphism problem, which iteratively colors or partitions a graph's vertex set. While this connection has led to significant advances in understanding and enhancing GNNs' expressive power, it does not provide insights into their generalization performance, i.e., their ability to make meaningful predictions beyond the training set. In this paper, we study GNNs' generalization ability through the lens of Vapnik-Chervonenkis (VC) dimension theory in two settings, focusing on graph-level predictions. First, when no upper bound on the graphs' order is known, we show that the bitlength of GNNs' weights tightly bounds their VC dimension. Further, we derive an upper bound for GNNs' VC dimension using the number of colors produced by the $1\text{-}\mathsf{WL}$. Secondly, when an upper bound on the graphs' order is known, we show a tight connection between the number of graphs distinguishable by the $1\text{-}\mathsf{WL}$ and GNNs' VC dimension. Our empirical study confirms the validity of our theoretical findings.

In this paper, we consider non-convex multi-block bilevel optimization (MBBO) problems, which involve $m\gg 1$ lower level problems and have important applications in machine learning. Designing a stochastic gradient and controlling its variance is more intricate due to the hierarchical sampling of blocks and data and the unique challenge of estimating hyper-gradient. We aim to achieve three nice properties for our algorithm: (a) matching the state-of-the-art complexity of standard BO problems with a single block; (b) achieving parallel speedup by sampling $I$ blocks and sampling $B$ samples for each sampled block per-iteration; (c) avoiding the computation of the inverse of a high-dimensional Hessian matrix estimator. However, it is non-trivial to achieve all of these by observing that existing works only achieve one or two of these properties. To address the involved challenges for achieving (a, b, c), we propose two stochastic algorithms by using advanced blockwise variance-reduction techniques for tracking the Hessian matrices (for low-dimensional problems) or the Hessian-vector products (for high-dimensional problems), and prove an iteration complexity of $O(\frac{m\epsilon^{-3}\mathbb{I}(I \textless m)}{I\sqrt{I}}+\frac{m\epsilon^{-3}}{I\sqrt{B}})$ for finding an $\epsilon$-stationary point under appropriate conditions. We also conduct experiments to verify the effectiveness of the proposed algorithms comparing with existing MBBO algorithms.

We consider learning in an adversarial Markov Decision Process (MDP) where the loss functions can change arbitrarily over $K$ episodes and the state space can be arbitrarily large. We assume that the Q-function of any policy is linear in some known features, that is, a linear function approximation exists. The best existing regret upper bound for this setting (Luo et al., 2021) is of order $\tilde{\mathcal O}(K^{2/3})$ (omitting all other dependencies), given access to a simulator. This paper provides two algorithms that improve the regret to $\tilde{\mathcal O}(\sqrt K)$ in the same setting. Our first algorithm makes use of a refined analysis of the Follow-the-Regularized-Leader (FTRL) algorithm with the log-barrier regularizer. This analysis allows the loss estimators to be arbitrarily negative and might be of independent interest. Our second algorithm develops a magnitude-reduced loss estimator, further removing the polynomial dependency on the number of actions in the first algorithm and leading to the optimal regret bound (up to logarithmic terms and dependency on the horizon). Moreover, we also extend the first algorithm to simulator-free linear MDPs, which achieves $\tilde{\mathcal O}(K^{8/9})$ regret and greatly improves over the best existing bound $\tilde{\mathcal O}(K^{14/15})$. This algorithm relies on a better alternative to the Matrix Geometric Resampling procedure by Neu & Olkhovskaya (2020), which could again be of independent interest.

We study the problem of differentially private (DP) stochastic convex optimization (SCO) under the notion of user-level differential privacy. In this problem, there are $n$ users, each contributing $m>1$ samples to the input dataset of the private SCO algorithm, and the notion of indistinguishability embedded in DP is w.r.t. replacing the entire local dataset of any given user. Under smoothness conditions of the loss, we establish the optimal rates for user-level DP-SCO in both the central and local models of DP. In particular, we show, roughly, that the optimal rate is $\frac{1}{\sqrt{nm}}+\frac{\sqrt{d}}{\varepsilon n \sqrt{m}}$ in the central setting and is $\frac{\sqrt{d}}{\varepsilon \sqrt{nm}}$ in the local setting, where $d$ is the dimensionality of the problem and $\varepsilon$ is the privacy parameter. Our algorithms combine new user-level DP mean estimation techniques with carefully designed first-order stochastic optimization methods. For the central DP setting, our optimal rate improves over the rate attained for the same setting in Levy et al. (2021) by $\sqrt{d}$ factor. One of the main ingredients that enabled such an improvement is a novel application of the generalization properties of DP in the context of multi-pass stochastic gradient methods.

We study a $K$-armed bandit with delayed feedback and intermediate observations. We consider a model, where intermediate observations have a form of a finite state, which is observed immediately after taking an action, whereas the loss is observed after an adversarially chosen delay. We show that the regime of the mapping of states to losses determines the complexity of the problem, irrespective of whether the mapping of actions to states is stochastic or adversarial. If the mapping of states to losses is adversarial, then the regret rate is of order $\sqrt{(K+d)T}$ (within log factors), where $T$ is the time horizon and $d$ is a fixed delay. This matches the regret rate of a $K$-armed bandit with delayed feedback and without intermediate observations, implying that intermediate observations are not helpful. However, if the mapping of states to losses is stochastic, we show that the regret grows at a rate of $\sqrt{\big(K+\min\\{|\mathcal{S}|,d\\}\big)T}$ (within log factors), implying that if the number $|\mathcal{S}|$ of states is smaller than the delay, then intermediate observations help. We also provide refined high-probability regret upper bounds for non-uniform delays, together with experimental validation of our algorithms.

We study variants of the online linear optimization (OLO) problem with bandit feedback, where the algorithm has access to external information about the unknown cost vector. Our motivation is the recent body of work on using such ``hints'' towards improving regret bounds for OLO problems in the full-information setting. Unlike in the full-information OLO setting, with bandit feedback, we first show that one cannot improve the standard regret bounds of $\tilde{O}(\sqrt{T})$ by using hints, even if they are always well-correlated with the cost vector. In contrast, if the algorithm is empowered to issue queries and if all the responses are correct, then we show $O(\log T)$ regret is achievable. We then show how to make this result more robust---when some of the query responses can be adversarial---by using a little feedback on the quality of the responses.

Finding the mode of a high dimensional probability distribution $\mathcal{D}$ is a fundamental algorithmic problem in statistics and data analysis. There has been particular interest in efficient methods for solving the problem when $\mathcal{D}$ is represented as a mixture model or kernel density estimate, although few algorithmic results with worst-case approximation and runtime guarantees are known. In this work, we significantly generalize a result of (LeeLiMusco:2021) on mode approximation for Gaussian mixture models. We develop randomized dimensionality reduction methods for mixtures involving a broader class of kernels, including the popular logistic, sigmoid, and generalized Gaussian kernels. As in Lee et al.'s work, our dimensionality reduction results yield quasi-polynomial algorithms for mode finding with multiplicative accuracy $(1-\epsilon)$ for any $\epsilon > 0$. Moreover, when combined with gradient descent, they yield efficient practical heuristics for the problem. In addition to our positive results, we prove a hardness result for box kernels, showing that there is no polynomial time algorithm for finding the mode of a kernel density estimate, unless $\mathit{P} = \mathit{NP}$. Obtaining similar hardness results for kernels used in practice (like Gaussian or logistic kernels) is an interesting future direction.

We study the power of uniform sampling for $k$-Median in various metric spaces. We relate the query complexity for approximating $k$-Median, to a key parameter of the dataset, called the balancedness $\beta \in (0, 1]$ (with $1$ being perfectly balanced). We show that any algorithm must make $\Omega(1 / \beta)$ queries to the point set in order to achieve $O(1)$-approximation for $k$-Median. This particularly implies existing constructions of coresets, a popular data reduction technique, cannot be query-efficient. On the other hand, we show a simple uniform sample of $\mathrm{poly}(k \epsilon^{-1} \beta^{-1})$ points suffices for $(1 + \epsilon)$-approximation for $k$-Median for various metric spaces, which nearly matches the lower bound. We conduct experiments to verify that in many real datasets, the balancedness parameter is usually well bounded, and that the uniform sampling performs consistently well even for the case with moderately large balancedness, which justifies that uniform sampling is indeed a viable approach for solving $k$-Median.

Optimal transport (OT) theory focuses, among all maps $T:\mathbb{R}^d\rightarrow \mathbb{R}^d$ that can morph a probability measure $\mu$ onto another $\nu$, on those that are the ``thriftiest'', i.e. such that the average cost $c(x, T(x))$ between $x$ and its image $T(x)$ is as small as possible. Many computational approaches have been proposed to estimate such *Monge* maps when $c$ is the squared-Euclidean distance, e.g., using entropic maps [Pooladian+2021], or input convex neural networks [Makkuva+2020, Korotin+2020]. We propose a new research direction, that leverages a specific translation invariant cost $c(x, y):=h(x-y)$ inspired by the elastic net. Here, $h:=\tfrac{1}{2}\|\cdot\|_2^2+\tau(\cdot)$, where $\tau$ is a convex function. We highlight a surprising link tying together a generalized entropic map for $h$, *Bregman* centroids induced by $h$, and the proximal operator of $\tau$. We show how setting $\tau$ to be a sparsity-inducing norm results in the first application of *Occam*'s razor to transport. These maps yield, mechanically, displacement vectors $\Delta(x):= T(x)-x$ that are sparse, with sparsity patterns that vary depending on $x$. We showcase the ability of our method to estimate meaningful OT maps for high-dimensional single-cell transcription data. We use our methods in the $34000$-d space of gene counts for cells, *without* using a prior dimensionality reduction, thus retaining the ability to interpret all displacements at the gene level.

We introduce efficient $(1+\varepsilon)$-approximation algorithms for the binary matrix factorization (BMF) problem, where the inputs are a matrix $\mathbf{A}\in\{0,1\}^{n\times d}$, a rank parameter $k>0$, as well as an accuracy parameter $\varepsilon>0$, and the goal is to approximate $\mathbf{A}$ as a product of low-rank factors $\mathbf{U}\in\{0,1\}^{n\times k}$ and $\mathbf{V}\in\{0,1\}^{k\times d}$. Equivalently, we want to find $\mathbf{U}$ and $\mathbf{V}$ that minimize the Frobenius loss $\|\mathbf{U}\mathbf{V} - \mathbf{A}\|_F^2$. Before this work, the state-of-the-art for this problem was the approximation algorithm of Kumar et. al. [ICML 2019], which achieves a $C$-approximation for some constant $C\ge 576$. We give the first $(1+\varepsilon)$-approximation algorithm using running time singly exponential in $k$, where $k$ is typically a small integer. Our techniques generalize to other common variants of the BMF problem, admitting bicriteria $(1+\varepsilon)$-approximation algorithms for $L_p$ loss functions and the setting where matrix operations are performed in $\mathbb{F}_2$. Our approach can be implemented in standard big data models, such as the streaming or distributed models.

Projection maintenance is one of the core data structure tasks. Efficient data structures for projection maintenance have led to recent breakthroughs in many convex programming algorithms. In this work, we further extend this framework to the Kronecker product structure. Given a constraint matrix ${\sf A}$ and a positive semi-definite matrix $W\in \mathbb{R}^{n\times n}$ with a sparse eigenbasis, we consider the task of maintaining the projection in the form of ${\sf B}^\top({\sf B}{\sf B}^\top)^{-1}{\sf B}$, where ${\sf B}={\sf A}(W\otimes I)$ or ${\sf B}={\sf A}(W^{1/2}\otimes W^{1/2})$. At each iteration, the weight matrix $W$ receives a low rank change and we receive a new vector $h$. The goal is to maintain the projection matrix and answer the query ${\sf B}^\top({\sf B}{\sf B}^\top)^{-1}{\sf B}h$ with good approximation guarantees. We design a fast dynamic data structure for this task and it is robust against an adaptive adversary. Following the beautiful and pioneering work of [Beimel, Kaplan, Mansour, Nissim, Saranurak and Stemmer, STOC'22], we use tools from differential privacy to reduce the randomness required by the data structure and further improve the running time.

We consider episodic reinforcement learning in reward-mixing Markov decision processes (RMMDPs): at the beginning of every episode nature randomly picks a latent reward model among $M$ candidates and an agent interacts with the MDP throughout the episode for $H$ time steps. Our goal is to learn a near-optimal policy that nearly maximizes the $H$ time-step cumulative rewards in such a model. Prior work established an upper bound for RMMDPs with $M=2$. In this work, we resolve several open questions for the general RMMDP setting. We consider an arbitrary $M\ge2$ and provide a sample-efficient algorithm--$EM^2$--that outputs an $\epsilon$-optimal policy using $O \left(\epsilon^{-2} \cdot S^d A^d \cdot \text{poly}(H, Z)^d \right)$ episodes, where $S, A$ are the number of states and actions respectively, $H$ is the time-horizon, $Z$ is the support size of reward distributions and $d=O(\min(M,H))$. We also provide a $(SA)^{\Omega(\sqrt{M})} / \epsilon^{2}$ lower bound, supporting that super-polynomial sample complexity in $M$ is necessary.

$k$-Clustering in $\mathbb{R}^d$ (e.g., $k$-median and $k$-means) is a fundamental machine learning problem. While near-linear time approximation algorithms were known in the classical setting for a dataset with cardinality $n$, it remains open to find sublinear-time quantum algorithms. We give quantum algorithms that find coresets for $k$-clustering in $\mathbb{R}^d$ with $\tilde{O}(\sqrt{nk}d^{3/2})$ query complexity. Our coreset reduces the input size from $n$ to $\mathrm{poly}(k\epsilon^{-1}d)$, so that existing $\alpha$-approximation algorithms for clustering can run on top of it and yield $(1 + \epsilon)\alpha$-approximation. This eventually yields a quadratic speedup for various $k$-clustering approximation algorithms. We complement our algorithm with a nearly matching lower bound, that any quantum algorithm must make $\Omega(\sqrt{nk})$ queries in order to achieve even $O(1)$-approximation for $k$-clustering.

The Johnson-Lindenstaruss lemma (Johnson & Lindenstrauss, 1984) is a cornerstone result in dimensionality reduction, stating it is possible to embed a set of $n$ points in $d$-dimensional Euclidean space into optimal $k=O(\varepsilon^{-2} \ln n)$ dimensions, while preserving all pairwise distances to within a factor $(1 \pm \varepsilon)$. The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) supports computing the embedding of a data point in $O(d \ln d +k \ln^2 n)$ time, where the $d \ln d$ term comes from multiplication with a $d \times d$ Hadamard matrix and the $k \ln^2 n$ term comes from multiplication with a sparse $k \times d$ matrix. Despite the Fast JL transform being more than a decade old, it is one of the fastest dimensionality reduction techniques for many tradeoffs between $\varepsilon, d$ and $n$. In this work, we give a surprising new analysis of the Fast JL transform, showing that the $k \ln^2 n$ term in the embedding time can be improved to $(k \ln^2 n)/\alpha$ for an $\alpha = \Omega(\min\{\varepsilon^{-1}\ln(1/\varepsilon), \ln n\})$. The improvement follows by using an even sparser matrix. We complement our improved analysis with a lower bound showing that our new analysis is in fact tight.

The study of universal approximation properties (UAP) for neural networks (NN) has a long history. When the network width is unlimited, only a single hidden layer is sufficient for UAP. In contrast, when the depth is unlimited, the width for UAP needs to be not less than the critical width $w^*_{\min}=\max(d_x,d_y)$, where $d_x$ and $d_y$ are the dimensions of the input and output, respectively. Recently, (Cai, 2022) shows that a leaky-ReLU NN with this critical width can achieve UAP for $L^p$ functions on a compact domain $\mathcal{K}$, *i.e.,* the UAP for $L^p(\mathcal{K},\mathbb{R}^{d_y})$. This paper examines a uniform UAP for the function class $C(\mathcal{K},\mathbb{R}^{d_y})$ and gives the exact minimum width of the leaky-ReLU NN as $w_{\min}=\max(d_x+1,d_y)+1_{d_y=d_x+1}$, which involves the effects of the output dimensions. To obtain this result, we propose a novel lift-flow-discretization approach that shows that the uniform UAP has a deep connection with topological theory.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order ${\Omega}\left( \frac{H^3SA}{\epsilon^2} \left( \log \left(\frac{1}{\delta}\right) + S \right)\right)$, being $S$ and $A$ the number of states and actions respectively, $H$ the horizon, $\epsilon$ the desired accuracy, and $\delta$ the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

In this paper, we investigate the online allocation problem of maximizing the overall revenue subject to both lower and upper bound constraints. Compared to the extensively studied online problems with only resource upper bounds, the two-sided constraints affect the prospects of resource consumption more severely. As a result, only limited violations of constraints or pessimistic competitive bounds could be guaranteed. To tackle the challenge, we define a measure of feasibility $\xi^*$ to evaluate the hardness of this problem, and estimate this measurement by an optimization routine with theoretical guarantees. We propose an online algorithm adopting a constructive framework, where we initialize a threshold price vector using the estimation, then dynamically update the price vector and use it for decision-making at each step. It can be shown that the proposed algorithm is $\big(1-O(\frac{\varepsilon}{\xi^*-\varepsilon})\big)$ or $\big(1-O(\frac{\varepsilon}{\xi^*-\sqrt{\varepsilon}})\big)$ competitive with high probability for $\xi^*$ known or unknown respectively. To the best of our knowledge, this is the first result establishing a nearly optimal competitive algorithm for solving two-sided constrained online allocation problems with a high probability of feasibility.

Training data and model sizes are increasing exponentially. One way to reduce training time and resources is to train with a carefully selected subset of the full dataset. Prior work uses the gradient signals obtained during a warm-up or ``pre-training" phase over the full dataset, for determining the core subset; if the pre-training phase is too small, the gradients obtained are chaotic and unreliable. As a result, the pre-training phase itself incurs significant time/resource overhead, and prior work has not gone beyond hyperparameter search to reduce pre-training time. Our work explicitly aims to reduce this $\textbf{pre-training tax}$ in gradient-based subset training. We develop a principled, scalable approach for pre-training in a distributed setup. Our approach is $\textit{lightweight}$ and $\textit{minimizes communication}$ between distributed worker nodes. It is the first to utilize the concept of model-soup based distributed training $\textit{at initialization}$. The key idea is to minimally train an ensemble of models on small, disjointed subsets of the data; we further employ data-driven sparsity and data augmentation for local worker training to boost ensemble diversity. The centralized model, obtained at the end of pre-training by merging the per-worker models, is found to offer stabilized gradient signals to select subsets, on which the main model is further trained. We have validated the effectiveness of our method through extensive experiments on CIFAR-10/100, and ImageNet, using ResNet and WideResNet models. For example, our approach is shown to achieve $\textbf{15.4$\times$}$ pre-training speedup and $\textbf{2.8$\times$}$ end-to-end speedup on CIFAR10 and ResNet18 without loss of accuracy. The code is at https://github.com/moonbucks/LiPT.git.

Agents that can build temporally abstract representations of their environment are better able to understand their world and make plans on extended time scales, with limited computational power and modeling capacity. However, existing methods for automatically learning temporally abstract world models usually require millions of online environmental interactions and incentivize agents to reach every accessible environmental state, which is infeasible for most real-world robots both in terms of data efficiency and hardware safety. In this paper, we present an approach for simultaneously learning sets of skills and temporally abstract, skill-conditioned world models purely from offline data, enabling agents to perform zero-shot online planning of skill sequences for new tasks. We show that our approach performs comparably to or better than a wide array of state-of-the-art offline RL algorithms on a number of simulated robotics locomotion and manipulation benchmarks, while offering a higher degree of adaptability to new goals. Finally, we show that our approach offers a much higher degree of robustness to perturbations in environmental dynamics, compared to policy-based methods.

A complex system with cluttered observations may be a coupled mixture of multiple simple sub-systems corresponding to latent entities. Such sub-systems may hold distinct dynamics in the continuous-time domain; therein, complicated interactions between sub-systems also evolve over time. This setting is fairly common in the real world but has been less considered. In this paper, we propose a sequential learning approach under this setting by decoupling a complex system for handling irregularly sampled and cluttered sequential observations. Such decoupling brings about not only subsystems describing the dynamics of each latent entity but also a meta-system capturing the interaction between entities over time. Specifically, we argue that the meta-system evolving within a simplex is governed by projected differential equations (ProjDEs). We further analyze and provide neural-friendly projection operators in the context of Bregman divergence. Experimental results on synthetic and real-world datasets show the advantages of our approach when facing complex and cluttered sequential data compared to the state-of-the-art.

In time-series analysis, nonlinear temporal misalignment is a major problem that forestalls even simple averaging. An effective learning-based solution for this problem is the Diffeomorphic Temporal Alignment Net (DTAN), that, by relying on a diffeomorphic temporal transformer net and the amortization of the joint-alignment task, eliminates drawbacks of traditional alignment methods. Unfortunately, existing DTAN formulations crucially depend on a regularization term whose optimal hyperparameters are dataset-specific and usually searched via a large number of experiments. Here we propose a regularization-free DTAN that obviates the need to perform such an expensive, and often impractical, search. Concretely, we propose a new well-behaved loss that we call the Inverse Consistency Averaging Error (ICAE), as well as a related new triplet loss. Extensive experiments on 128 UCR datasets show that the proposed method outperforms contemporary methods despite not using a regularization. Moreover, ICAE also gives rise to the first DTAN that supports variable-length signals. Our code is available at https://github.com/BGU-CS-VIL/RF-DTAN.

Image perturbation technique is widely used to generate adversarial examples to attack networks, greatly decreasing the performance of networks. Unlike the existing works, in this paper, we introduce a novel framework Deep Perturbation Learning (DPL), the new insights into understanding image perturbations, to enhance the performance of networks rather than decrease the performance. Specifically, we learn image perturbations to amend the data distribution of training set to improve the performance of networks. This optimization w.r.t data distribution is non-trivial. To approach this, we tactfully construct a differentiable optimization target w.r.t. image perturbations via minimizing the empirical risk. Then we propose an alternating optimization of the network weights and perturbations. DPL can easily be adapted to a wide spectrum of downstream tasks and backbone networks. Extensive experiments demonstrate the effectiveness of our DPL on 6 datasets (CIFAR-10, CIFAR100, ImageNet, MS-COCO, PASCAL VOC, and SBD) over 3 popular vision tasks (image classification, object detection, and semantic segmentation) with different backbone architectures (e.g., ResNet, MobileNet, and ViT).

In federated learning (FL), multiple clients collaborate to train machine learning models together while keeping their data decentralized. Through utilizing more training data, FL suffers from the potential negative transfer problem: the global FL model may even perform worse than the models trained with local data only. In this paper, we propose FedCollab, a novel FL framework that alleviates negative transfer by clustering clients into non-overlapping coalitions based on their distribution distances and data quantities. As a result, each client only collaborates with the clients having similar data distributions, and tends to collaborate with more clients when it has less data. We evaluate our framework with a variety of datasets, models, and types of non-IIDness. Our results demonstrate that FedCollab effectively mitigates negative transfer across a wide range of FL algorithms and consistently outperforms other clustered FL algorithms.

Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and cannot integrate new data points. To address these drawbacks, we propose InfoOT, an information-theoretic extension of optimal transport that maximizes the mutual information between domains while minimizing geometric distances. The resulting objective can still be formulated as a (generalized) optimal transport problem, and can be efficiently solved by projected gradient descent. This formulation yields a new projection method that is robust to outliers and generalizes to unseen samples. Empirically, InfoOT improves the quality of alignments across benchmarks in domain adaptation, cross-domain retrieval, and single-cell alignment.

Training stability is of great importance to Transformers. In this work, we investigate the training dynamics of Transformers by examining the evolution of the attention layers. In particular, we track the attention entropy for each attention head during the course of training, which is a proxy for model sharpness. We identify a common pattern across different architectures and tasks, where low attention entropy is accompanied by high training instability, which can take the form of oscillating loss or divergence. We denote the pathologically low attention entropy, corresponding to highly concentrated attention scores, as $\textit{entropy collapse}$. As a remedy, we propose $\sigma$Reparam, a simple and efficient solution where we reparametrize all linear layers with spectral normalization and an additional learned scalar. We demonstrate that $\sigma$Reparam successfully prevents entropy collapse in the attention layers, promoting more stable training. Additionally, we prove a tight lower bound of the attention entropy, which decreases exponentially fast with the spectral norm of the attention logits, providing additional motivation for our approach. We conduct experiments with $\sigma$Reparam on image classification, image self-supervised learning, machine translation, speech recognition, and language modeling tasks. We show that $\sigma$Reparam provides stability and robustness with respect to the choice of hyperparameters, going so far as enabling training (a) a Vision Transformer to competitive performance without warmup, weight decay, layer normalization or adaptive optimizers; (b) deep architectures in machine translation and (c) speech recognition to competitive performance without warmup and adaptive optimizers. Code is available at https://github.com/apple/ml-sigma-reparam.

The goal of offline black-box optimization (BBO) is to optimize an expensive black-box function using a fixed dataset of function evaluations. Prior works consider forward approaches that learn surrogates to the black-box function and inverse approaches that directly map function values to corresponding points in the input domain of the black-box function. These approaches are limited by the quality of the offline dataset and the difficulty in learning one-to-many mappings in high dimensions, respectively. We propose Denoising Diffusion Optimization Models (DDOM), a new inverse approach for offline black-box optimization based on diffusion models. Given an offline dataset, DDOM learns a conditional generative model over the domain of the black-box function conditioned on the function values. We investigate several design choices in DDOM, such as reweighting the dataset to focus on high function values and the use of classifier-free guidance at test-time to enable generalization to function values that can even exceed the dataset maxima. Empirically, we conduct experiments on the Design-Bench benchmark (Trabucco et al., 2022) and show that DDOM achieves results competitive with state-of-the-art baselines.

We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a multi-step process, involving (1) a subspace estimation step, (2) spectral clustering of trajectories using "pairwise distance estimators," along with refinement using the EM algorithm, (3) a model estimation step, and (4) a classification step for predicting labels of new trajectories. We provide end-to-end performance guarantees, where we only explicitly require the length of trajectories to be linear in the number of states and the number of trajectories to be linear in a mixing time parameter. Experimental results support these guarantees, where we attain 96.6% average accuracy on a mixture of two MDPs in gridworld, outperforming the EM algorithm with random initialization (73.2% average accuracy). We also significantly outperform the EM algorithm on real data from the LastFM song dataset.

Max sliced Wasserstein (Max-SW) distance has been widely known as a solution for less discriminative projections of sliced Wasserstein (SW) distance. In applications that have various independent pairs of probability measures, amortized projection optimization is utilized to predict the ``max" projecting directions given two input measures instead of using projected gradient ascent multiple times. Despite being efficient, Max-SW and its amortized version cannot guarantee metricity property due to the sub-optimality of the projected gradient ascent and the amortization gap. Therefore, we propose to replace Max-SW with distributional sliced Wasserstein distance with von Mises-Fisher (vMF) projecting distribution (v-DSW). Since v-DSW is a metric with any non-degenerate vMF distribution, its amortized version can guarantee the metricity when performing amortization. Furthermore, current amortized models are not permutation invariant and symmetric. To address the issue, we design amortized models based on self-attention architecture. In particular, we adopt efficient self-attention architectures to make the computation linear in the number of supports. With the two improvements, we derive self-attention amortized distributional projection optimization and show its appealing performance in point-cloud reconstruction and its downstream applications

Designing protein sequences with desired biological function is crucial in biology and chemistry. Recent machine learning methods use a surrogate sequence-function model to replace the expensive wet-lab validation. How can we efficiently generate diverse and novel protein sequences with high fitness? In this paper, we propose IsEM-Pro, an approach to generate protein sequences towards a given fitness criterion. At its core, IsEM-Pro is a latent generative model, augmented by combinatorial structure features from a separately learned Markov random fields (MRFs). We develop an Monte Carlo Expectation-Maximization method (MCEM) to learn the model. During inference, sampling from its latent space enhances diversity while its MRFs features guide the exploration in high fitness regions. Experiments on eight protein sequence design tasks show that our IsEM-Pro outperforms the previous best methods by at least 55% on average fitness score and generates more diverse and novel protein sequences.

Recent offline meta-reinforcement learning (meta-RL) methods typically utilize task-dependent behavior policies (e.g., training RL agents on each individual task) to collect a multi-task dataset. However, these methods always require extra information for fast adaptation, such as offline context for testing tasks. To address this problem, we first formally characterize a unique challenge in offline meta-RL: transition-reward distribution shift between offline datasets and online adaptation. Our theory finds that out-of-distribution adaptation episodes may lead to unreliable policy evaluation and that online adaptation with in-distribution episodes can ensure adaptation performance guarantee. Based on these theoretical insights, we propose a novel adaptation framework, called In-Distribution online Adaptation with uncertainty Quantification (IDAQ), which generates in-distribution context using a given uncertainty quantification and performs effective task belief inference to address new tasks. We find a return-based uncertainty quantification for IDAQ that performs effectively. Experiments show that IDAQ achieves state-of-the-art performance on the Meta-World ML1 benchmark compared to baselines with/without offline adaptation.

Copy-Paste is a simple and effective data augmentation strategy for instance segmentation. By randomly pasting object instances onto new background images, it creates new training data for free and significantly boosts the segmentation performance, especially for rare object categories. Although diverse, high-quality object instances used in Copy-Paste result in more performance gain, previous works utilize object instances either from human-annotated instance segmentation datasets or rendered from 3D object models, and both approaches are too expensive to scale up to obtain good diversity. In this paper, we revisit Copy-Paste at scale with the power of newly emerged zero-shot recognition models (e.g., CLIP) and text2image models (e.g., StableDiffusion). We demonstrate for the first time that using a text2image model to generate images or zero-shot recognition model to filter noisily crawled images for different object categories is a feasible way to make Copy-Paste truly scalable. To make such success happen, we design a data acquisition and processing framework, dubbed ``X-Paste", upon which a systematic study is conducted. On the LVIS dataset, X-Paste provides impressive improvements over the strong baseline CenterNet2 with Swin-L as the backbone. Specifically, it archives +2.6 box AP and +2.1 mask AP gains on all classes and even more significant gains with +6.8 box AP +6.5 mask AP on long-tail classes.

Contrastive Language-Image Pretraining (CLIP) has demonstrated impressive zero-shot learning abilities for image understanding, yet limited effort has been made to investigate CLIP for zero-shot video recognition. We introduce Open-VCLIP, a simple yet effective approach that transforms CLIP into a strong zero-shot video classifier that can recognize unseen actions and events at test time. Our framework extends CLIP with minimal modifications to model spatial-temporal relationships in videos, making it a specialized video classifier, while striving for generalization. We formally show that training an Open-VCLIP is equivalent to continual learning with zero historical data. To address this problem, we propose Interpolated Weight Optimization, which utilizes the benefit of weight interpolation in both training and test time. We evaluate our method on three popular and challenging action recognition datasets following various zero-shot evaluation protocols and we demonstrate our approach outperforms state-of-the-art methods by clear margins. In particular, we achieve 87.9%, 58.3%, 81.1% zero-shot accuracy on UCF, HMDB and Kinetics-600 respectively, outperforming state-of-the-art methods by 8.3%, 7.8% and 12.2%. Code is released at https://github.com/wengzejia1/Open-VCLIP.

There has been some recent interest in detecting and addressing memorization of training data by deep neural networks. A formal framework for memorization in generative models, called ``data-copying'' was proposed by Meehan et. al (2020). We build upon their work to show that their framework may fail to detect certain kinds of blatant memorization. Motivated by this and the theory of non-parametric methods, we provide an alternative definition of data-copying that applies more locally. We provide a method to detect data-copying, and provably show that it works with high probability when enough data is available. We also provide lower bounds that characterize the sample requirement for reliable detection.

Optimizing user engagement is a key goal for modern recommendation systems, but blindly pushing users towards increased consumption risks burn-out, churn, or even addictive habits. To promote digital well-being, most platforms now offer a service that periodically prompts users to take breaks. These, however, must be set up manually, and so may be suboptimal for both users and the system. In this paper, we study the role of breaks in recommendation, and propose a framework for learning optimal breaking policies that promote and sustain long-term engagement. Based on the notion that recommendation dynamics are susceptible to both positive and negative feedback, we cast recommendation as a Lotka-Volterra dynamical system, where breaking reduces to a problem of optimal control. We then give an efficient learning algorithm, provide theoretical guarantees, and empirically demonstrate the utility of our approach on semi-synthetic data.

Persistent homology is arguably the most successful technique in Topological Data Analysis. It combines homology, a topological feature of a data set, with persistence, which tracks the evolution of homology over different scales. The persistent Laplacian is a recent theoretical development that combines persistence with the combinatorial Laplacian, the higher-order extension of the well-known graph Laplacian. Crucially, the Laplacian encode both the homology of a data set, and some additional geometric information not captured by the homology. Here, we provide the first investigation into the efficacy of the persistence Laplacian as an embedding of data for downstream classification and regression tasks. We extend the persistent Laplacian to cubical complexes so it can be used on images, then evaluate its performance as an embedding method on the MNIST and MoleculeNet datasets, demonstrating that it consistently outperforms persistent homology across tasks.

Domain decomposition methods (DDMs) are popular solvers for discretized systems of partial differential equations (PDEs), with one-level and multilevel variants. These solvers rely on several algorithmic and mathematical parameters, prescribing overlap, subdomain boundary conditions, and other properties of the DDM. While some work has been done on optimizing these parameters, it has mostly focused on the one-level setting or special cases such as structured-grid discretizations with regular subdomain construction. In this paper, we propose multigrid graph neural networks (MG-GNN), a novel GNN architecture for learning optimized parameters in two-level DDMs. We train MG-GNN using a new unsupervised loss function, enabling effective training on small problems that yields robust performance on unstructured grids that are orders of magnitude larger than those in the training set. We show that MG-GNN outperforms popular hierarchical graph network architectures for this optimization and that our proposed loss function is critical to achieving this improved performance.

Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.

We present a representation-driven framework for reinforcement learning. By representing policies as estimates of their expected values, we leverage techniques from contextual bandits to guide exploration and exploitation. Particularly, embedding a policy network into a linear feature space allows us to reframe the exploration-exploitation problem as a representation-exploitation problem, where good policy representations enable optimal exploration. We demonstrate the effectiveness of this framework through its application to evolutionary and policy gradient-based approaches, leading to significantly improved performance compared to traditional methods. Our framework provides a new perspective on reinforcement learning, highlighting the importance of policy representation in determining optimal exploration-exploitation strategies.

Real-world data can be multimodal distributed, e.g., data describing the opinion divergence in a community, the interspike interval distribution of neurons, and the oscillators natural frequencies. Generating multimodal distributed real-world data has become a challenge to existing generative adversarial networks (GANs). For example, it is often observed that Neural SDEs have only demonstrated successfully performance mainly in generating unimodal time series datasets. In this paper, we propose a novel time series generator, named directed chain GANs (DC-GANs), which inserts a time series dataset (called a neighborhood process of the directed chain or input) into the drift and diffusion coefficients of the directed chain SDEs with distributional constraints. DC-GANs can generate new time series of the same distribution as the neighborhood process, and the neighborhood process will provide the key step in learning and generating multimodal distributed time series. The proposed DC-GANs are examined on four datasets, including two stochastic models from social sciences and computational neuroscience, and two real-world datasets on stock prices and energy consumption. To our best knowledge, DC-GANs are the first work that can generate multimodal time series data and consistently outperforms state-of-the-art benchmarks with respect to measures of distribution, data similarity, and predictive ability.

This paper investigates an interesting weakly supervised regression setting called regression with interval targets (RIT). Although some of the previous methods on relevant regression settings can be adapted to RIT, they are not statistically consistent, and thus their empirical performance is not guaranteed. In this paper, we provide a thorough study on RIT. First, we proposed a novel statistical model to describe the data generation process for RIT and demonstrate its validity. Second, we analyze a simple selecting method for RIT, which selects a particular value in the interval as the target value to train the model. Third, we propose a statistically consistent limiting method for RIT to train the model by limiting the predictions to the interval. We further derive an estimation error bound for our limiting method. Finally, extensive experiments on various datasets demonstrate the effectiveness of our proposed method.

The top-$k$ classification accuracy is a crucial metric in machine learning and is often used to evaluate the performance of deep neural networks. These networks are typically trained using the cross-entropy loss, which optimizes for top-$1$ classification and is considered optimal in the case of infinite data. However, in real-world scenarios, data is often noisy and limited, leading to the need for more robust losses. In this paper, we propose using the Weighted Sampling Without Replacement (WSWR) method as a learning objective for top-$k$ loss. While traditional methods for evaluating **WSWR-based top-$k$ loss** are computationally impractical, we show a novel connection between WSWR and Reinforcement Learning (RL) and apply well-established RL algorithms to estimate gradients. We compared our method with recently proposed top-$k$ losses in various regimes of noise and data size for the prevalent use case of $k = 5$. Our experimental results reveal that our method consistently outperforms all other methods on the top-$k$ metric for noisy datasets, has more robustness on extreme testing scenarios, and achieves competitive results on training with limited data.

Diffusion-based generative models have shown great potential for image synthesis, but there is a lack of research on the security and privacy risks they may pose. In this paper, we investigate the vulnerability of diffusion models to Membership Inference Attacks (MIAs), a common privacy concern. Our results indicate that existing MIAs designed for GANs or VAE are largely ineffective on diffusion models, either due to inapplicable scenarios (e.g., requiring the discriminator of GANs) or inappropriate assumptions (e.g., closer distances between synthetic samples and member samples). To address this gap, we propose Step-wise Error Comparing Membership Inference (SecMI), a query-based MIA that infers memberships by assessing the matching of forward process posterior estimation at each timestep. SecMI follows the common overfitting assumption in MIA where member samples normally have smaller estimation errors, compared with hold-out samples. We consider both the standard diffusion models, e.g., DDPM, and the text-to-image diffusion models, e.g., Latent Diffusion Models and Stable Diffusion. Experimental results demonstrate that our methods precisely infer the membership with high confidence on both of the two scenarios across multiple different datasets. Code is available at https://github.com/jinhaoduan/SecMI.

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state spaces, including many scientific applications. Here, we develop a theoretical formulation for arbitrary discrete-state Markov processes in the forward diffusion process using exact (as opposed to variational) analysis. We relate the theory to the existing continuous-state Gaussian diffusion as well as other approaches to discrete diffusion, and identify the corresponding reverse-time stochastic process and score function in the continuous-time setting, and the reverse-time mapping in the discrete-time setting. As an example of this framework, we introduce ``Blackout Diffusion'', which learns to produce samples from an empty image instead of from noise. Numerical experiments on the CIFAR-10, Binarized MNIST, and CelebA datasets confirm the feasibility of our approach. Generalizing from specific (Gaussian) forward processes to discrete-state processes without a variational approximation sheds light on how to interpret diffusion models, which we discuss.

Multi-step learning applies lookahead over multiple time steps and has proved valuable in policy evaluation settings. However, in the optimal control case, the impact of multi-step learning has been relatively limited despite a number of prior efforts. Fundamentally, this might be because multi-step policy improvements require operations that cannot be approximated by stochastic samples, hence hindering the widespread adoption of such methods in practice. To address such limitations, we introduce doubly multi-step off-policy VI (DoMo-VI), a novel oracle algorithm that combines multi-step policy improvements and policy evaluations. DoMo-VI enjoys guaranteed convergence speed-up to the optimal policy and is applicable in general off-policy learning settings. We then propose doubly multi-step off-policy actor-critic (DoMo-AC), a practical instantiation of the DoMo-VI algorithm. DoMo-AC introduces a bias-variance trade-off that ensures improved policy gradient estimates. When combined with the IMPALA architecture, DoMo-AC has showed improvements over the baseline algorithm on Atari-57 game benchmarks.

In reinforcement learning, the credit assignment problem is to distinguish luck from skill, that is, separate the inherent randomness in the environment from the controllable effects of the agent's actions. This paper proposes two novel algorithms, Quantile Credit Assignment (QCA) and Hindsight QCA (HQCA), which incorporate distributional value estimation to perform credit assignment. QCA uses a network that predicts the quantiles of the return distribution, whereas HQCA additionally incorporates information about the future. Both QCA and HQCA have the appealing interpretation of leveraging an estimate of the quantile level of the return (interpreted as the level of "luck") in order to derive a "luck-dependent" baseline for policy gradient methods. We show theoretically that this approach gives an unbiased policy gradient estimate that can yield significant variance reductions over a standard value estimate baseline. QCA and HQCA significantly outperform prior state-of-the-art methods on a range of extremely difficult credit assignment problems.

Multi armed bandit (MAB) algorithms have been increasingly used to complement or integrate with A/B tests and randomized clinical trials in e-commerce, healthcare, and policymaking. Recent developments incorporate possible delayed feedback. While existing MAB literature often focuses on maximizing the expected cumulative reward outcomes (or, equivalently, regret minimization), few efforts have been devoted to establish valid statistical inference approaches to quantify the uncertainty of learned policies. We attempt to fill this gap by providing a unified statistical inference framework for policy evaluation where a target policy is allowed to differ from the data collecting policy, and our framework allows delay to be associated with the treatment arms. We present an adaptively weighted estimator that on one hand incorporates the arm-dependent delaying mechanism to achieve consistency, and on the other hand mitigates the variance inflation across stages due to vanishing sampling probability. In particular, our estimator does not critically depend on the ability to estimate the unknown delay mechanism. Under appropriate conditions, we prove that our estimator converges to a normal distribution as the number of time points goes to infinity, which provides guarantees for large-sample statistical inference. We illustrate the finite-sample performance of our approach through Monte Carlo experiments.

We consider collaborative multi-user reinforcement learning, where multiple users have the same state-action space and transition probabilities but different rewards. Under the assumption that the reward matrix of the $N$ users has a low-rank structure -- a standard and practically successful assumption in the collaborative filtering setting -- we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with $N$ user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When $N$ is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms. Our main technical contribution is a method to construct policies which obtain data such that low rank matrix completion is possible (without a generative model). This goes beyond the regular RL framework and is closely related to mean field limits of multi-agent RL.

In this paper, we present a model-based offline reinforcement learning method that integrates count-based conservatism, named $\texttt{Count-MORL}$. Our method utilizes the count estimates of state-action pairs to quantify model estimation error, marking the first algorithm of demonstrating the efficacy of count-based conservatism in model-based offline deep RL to the best of our knowledge. For our proposed method, we first show that the estimation error is inversely proportional to the frequency of state-action pairs. Secondly, we demonstrate that the learned policy under the count-based conservative model offers near-optimality performance guarantees. Through extensive numerical experiments, we validate that $\texttt{Count-MORL}$ with hash code implementation significantly outperforms existing offline RL algorithms on the D4RL benchmark datasets. The code is accessible at https://github.com/oh-lab/Count-MORL.

A prominent paradigm for graph neural networks is based on the message-passing framework. In this framework, information communication is realized only between neighboring nodes. The challenge of approaches that use this paradigm is to ensure efficient and accurate long-distance communication between nodes, as deep convolutional networks are prone to over smoothing. In this paper, we present a novel method based on time derivative graph diffusion (TIDE) to overcome these structural limitations of the message-passing framework. Our approach allows for optimizing the spatial extent of diffusion across various tasks and network channels, thus enabling medium and long-distance communication efficiently. Furthermore, we show that our architecture design also enables local message-passing and thus inherits from the capabilities of local message-passing approaches. We show that on both widely used graph benchmarks and synthetic mesh and graph datasets, the proposed framework outperforms state-of-the-art methods by a significant margin.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena. Code is available at https://github.com/grasp-lyrl/pictureofspaceoftasks.

Diffusion models are a class of generative models that learn to synthesize samples by inverting a diffusion process that gradually maps data into noise. While these models have enjoyed great success recently, a full theoretical understanding of their observed properties is still lacking, in particular, their weak sensitivity to the choice of noise family and the role of adequate scheduling of noise levels for good synthesis. By identifying a correspondence between diffusion models and a well-known paradigm in cognitive science known as serial reproduction, whereby human agents iteratively observe and reproduce stimuli from memory, we show how the aforementioned properties of diffusion models can be explained as a natural consequence of this correspondence. We then complement our theoretical analysis with simulations that exhibit these key features. Our work highlights how classic paradigms in cognitive science can shed light on state-of-the-art machine learning problems.

When trying to solve a computational problem, we are often faced with a choice between algorithms that are guaranteed to return the right answer but differ in their runtime distributions (e.g., SAT solvers, sorting algorithms). This paper aims to lay theoretical foundations for such choices by formalizing preferences over runtime distributions. It might seem that we should simply prefer the algorithm that minimizes expected runtime. However, such preferences would be driven by exactly how slow our algorithm is on bad inputs, whereas in practice we are typically willing to cut off occasional, sufficiently long runs before they finish. We propose a principled alternative, taking a utility-theoretic approach to characterize the scoring functions that describe preferences over algorithms. These functions depend on the way our value for solving our problem decreases with time and on the distribution from which captimes are drawn. We describe examples of realistic utility functions and show how to leverage a maximum-entropy approach for modeling underspecified captime distributions. Finally, we show how to efficiently estimate an algorithm's expected utility from runtime samples.

Learning to control an agent from offline data collected in a rich pixel-based visual observation space is vital for real-world applications of reinforcement learning (RL). A major challenge in this setting is the presence of input information that is hard to model and irrelevant to controlling the agent. This problem has been approached by the theoretical RL community through the lens of exogenous information, i.e., any control-irrelevant information contained in observations. For example, a robot navigating in busy streets needs to ignore irrelevant information, such as other people walking in the background, textures of objects, or birds in the sky. In this paper, we focus on the setting with visually detailed exogenous information and introduce new offline RL benchmarks that offer the ability to study this problem. We find that contemporary representation learning techniques can fail on datasets where the noise is a complex and time-dependent process, which is prevalent in practical applications. To address these, we propose to use multi-step inverse models to learn Agent-Centric Representations for Offline-RL (ACRO). Despite being simple and reward-free, we show theoretically and empirically that the representation created by this objective greatly outperforms baselines.

Language models such as mBERT, XLM-R, and BLOOM aim to achieve multilingual generalization or compression to facilitate transfer to a large number of (potentially unseen) languages. However, these models should ideally also be private, linguistically fair, and transparent, by relating their predictions to training data. Can these requirements be simultaneously satisfied? We show that multilingual compression and linguistic fairness are compatible with differential privacy, but that differential privacy is at odds with training data influence sparsity, an objective for transparency. We further present a series of experiments on two common NLP tasks and evaluate multilingual compression and training data influence sparsity under different privacy guarantees, exploring these trade-offs in more detail. Our results suggest that we need to develop ways to jointly optimize for these objectives in order to find practical trade-offs.

Inverse Reinforcement Learning (IRL) is a powerful set of techniques for imitation learning that aims to learn a reward function that rationalizes expert demonstrations. Unfortunately, traditional IRL methods suffer from a computational weakness: they require repeatedly solving a hard reinforcement learning (RL) problem as a subroutine. This is counter-intuitive from the viewpoint of reductions: we have reduced the easier problem of imitation learning to repeatedly solving the harder problem of RL. Another thread of work has proved that access to the side-information of the distribution of states where a strong policy spends time can dramatically reduce the sample and computational complexities of solving an RL problem. In this work, we demonstrate for the first time a more informed imitation learning reduction where we utilize the state distribution of the expert to alleviate the global exploration component of the RL subroutine, providing an exponential speedup in theory. In practice, we find that we are able to significantly speed up the prior art on continuous control tasks.

A classic result in the theory of extensive-form games asserts that the set of strategies available to any perfect-recall player is strategically equivalent to a low-dimensional convex polytope, called the sequence-form polytope. Online convex optimization tools operating on this polytope are the current state-of-the-art for computing several notions of equilibria in games, and have been crucial in landmark applications of computational game theory. However, when optimizing over the joint strategy space of a team of players, one cannot use the sequence form to obtain a strategically-equivalent convex description of the strategy set of the team. In this paper, we provide new complexity results on the computation of optimal strategies for teams, and propose a new representation, coined team belief DAG (TB-DAG), that describes team strategies as a convex set. The TB-DAG enjoys state-of-the-art parameterized complexity bounds, while at the same time enjoying the advantages of efficient regret minimization techniques. We show that TB-DAG can be exponentially smaller and can be computed exponentially faster than all other known representations, and that the converse is never true. Experimentally, we show that the TB-DAG, when paired with learning techniques, yields state of the art on a wide variety of benchmark team games.

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a $\mathcal{O} (K^2\cdot T^{2/3})$ regret after $T$ iterations, where $K$ is the number of effort levels of the agent. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.

This study explores the impact of content creators' competition on user welfare in recommendation platforms, as well as the long-term dynamics of relevance-driven recommendations. We establish a model of creator competition, under the setting where the platform uses a top-$K$ recommendation policy, user decisions are guided by the Random Utility model, and creators, in absence of explicit utility functions, employ arbitrary no-regret learning algorithms for strategy updates. We study the user welfare guarantee through the lens of Price of Anarchy and show that the fraction of user welfare loss due to creator competition is always upper bounded by a small constant depending on $K$ and randomness in user decisions; we also prove the tightness of this bound. Our result discloses an intrinsic merit of the relevance-driven recommendation policy, as long as users' decisions involve randomness and the platform provides reasonably many alternatives to its users.

Pre-trained language models can be fine-tuned to solve diverse NLP tasks, including in few-shot settings. Thus fine-tuning allows the model to quickly pick up task-specific "skills," but there has been limited study of *where* these newly-learnt skills reside inside the massive model. This paper introduces the term *skill localization* for this problem and proposes a solution. Given the downstream task and a model fine-tuned on that task, a simple optimization is used to identify a very small subset of parameters ($\sim$0.01% of model parameters) responsible for (>95%) of the model's performance, in the sense that *grafting* the fine-tuned values for just this tiny subset onto the pre-trained model gives performance almost as well as the fine-tuned model. While reminiscent of recent works on parameter-efficient fine-tuning, the novel aspects here are that: (i) No further retraining is needed on the subset (unlike, say, with lottery tickets). (ii) Notable improvements are seen over vanilla fine-tuning with respect to calibration of predictions in-distribution (40-90% error reduction) as well as quality of predictions out-of-distribution (OOD). In models trained on multiple tasks, a stronger notion of skill localization is observed, where the sparse regions corresponding to different tasks are almost disjoint, and their overlap (when it happens) is a proxy for task similarity. Experiments suggest that localization via grafting can assist certain forms continual learning.

It has previously been reported that the representation that is learned in the first layer of deep Convolutional Neural Networks (CNNs) is highly consistent across initializations and architectures. In this work, we quantify this consistency by considering the first layer as a filter bank and measuring its energy distribution. We find that the energy distribution is very different from that of the initial weights and is remarkably consistent across random initializations, datasets, architectures and even when the CNNs are trained with random labels. In order to explain this consistency, we derive an analytical formula for the energy profile of linear CNNs and show that this profile is mostly dictated by the second order statistics of image patches in the training set and it will approach a whitening transformation when the number of iterations goes to infinity. Finally, we show that this formula for linear CNNs also gives an excellent fit for the energy profiles learned by commonly used nonlinear CNNs such as ResNet and VGG, and that the first layer of these CNNs indeed performs approximate whitening of their inputs.

Recent work has highlighted the complex influence training hyperparameters, e.g., the number of training epochs, can have on the prunability of machine learning models. Perhaps surprisingly, a systematic approach to predict precisely how adjusting a specific hyperparameter will affect prunability remains elusive. To address this gap, we introduce a phenomenological model grounded in the statistical mechanics of learning. Our approach uses temperature-like and load-like parameters to model the impact of neural network (NN) training hyperparameters on pruning performance. A key empirical result we identify is a sharp transition phenomenon: depending on the value of a load-like parameter in the pruned model, increasing the value of a temperature-like parameter in the pre-pruned model may either enhance or impair subsequent pruning performance. Based on this transition, we build a three-regime model by taxonomizing the global structure of the pruned NN loss landscape. Our model reveals that the dichotomous effect of high temperature is associated with transitions between distinct types of global structures in the post-pruned model. Based on our results, we present three case-studies: 1) determining whether to increase or decrease a hyperparameter for improved pruning; 2) selecting the best model to prune from a family of models; and 3) tuning the hyperparameter of the Sharpness Aware Minimization method for better pruning performance.

Representational drift refers to over-time changes in neural activation accompanied by a stable task performance. Despite being observed in the brain and in artificial networks, the mechanisms of drift and its implications are not fully understood. Motivated by recent experimental findings of stimulus-dependent drift in the piriform cortex, we use theory and simulations to study this phenomenon in a two-layer linear feedforward network. Specifically, in a continual online learning scenario, we study the drift induced by the noise inherent in the Stochastic Gradient Descent (SGD). By decomposing the learning dynamics into the normal and tangent spaces of the minimum-loss manifold, we show the former corresponds to a finite variance fluctuation, while the latter could be considered as an effective diffusion process on the manifold. We analytically compute the fluctuation and the diffusion coefficients for the stimuli representations in the hidden layer as functions of network parameters and input distribution. Further, consistent with experiments, we show that the drift rate is slower for a more frequently presented stimulus. Overall, our analysis yields a theoretical framework for better understanding of the drift phenomenon in biological and artificial neural networks.

As previous representations for reinforcement learning cannot effectively incorporate a human-intuitive understanding of the 3D environment, they usually suffer from sub-optimal performances. In this paper, we present Semantic-aware Neural Radiance Fields for Reinforcement Learning (SNeRL), which jointly optimizes semantic-aware neural radiance fields (NeRF) with a convolutional encoder to learn 3D-aware neural implicit representation from multi-view images. We introduce 3D semantic and distilled feature fields in parallel to the RGB radiance fields in NeRF to learn semantic and object-centric representation for reinforcement learning. SNeRL outperforms not only previous pixel-based representations but also recent 3D-aware representations both in model-free and model-based reinforcement learning.

Uncertainty estimation is a key factor that makes deep learning reliable in practical applications. Recently proposed evidential neural networks explicitly account for different uncertainties by treating the network's outputs as evidence to parameterize the Dirichlet distribution, and achieve impressive performance in uncertainty estimation. However, for high data uncertainty samples but annotated with the one-hot label, the evidence-learning process for those mislabeled classes is over-penalized and remains hindered. To address this problem, we propose a novel method, Fisher Information-based Evidential Deep Learning ($\mathcal{I}$-EDL). In particular, we introduce Fisher Information Matrix (FIM) to measure the informativeness of evidence carried by each sample, according to which we can dynamically reweight the objective loss terms to make the network more focus on the representation learning of uncertain classes. The generalization ability of our network is further improved by optimizing the PAC-Bayesian bound. As demonstrated empirically, our proposed method consistently outperforms traditional EDL-related algorithms in multiple uncertainty estimation tasks, especially in the more challenging few-shot classification settings.

Graph Neural Networks (GNNs) have shown exceptional performance in the task of link prediction. Despite their effectiveness, the high latency brought by non-trivial neighborhood data dependency limits GNNs in practical deployments. Conversely, the known efficient MLPs are much less effective than GNNs due to the lack of relational knowledge. In this work, to combine the advantages of GNNs and MLPs, we start with exploring direct knowledge distillation (KD) methods for link prediction, i.e., predicted logit-based matching and node representation-based matching. Upon observing direct KD analogs do not perform well for link prediction, we propose a relational KD framework, Linkless Link Prediction (LLP), to distill knowledge for link prediction with MLPs. Unlike simple KD methods that match independent link logits or node representations, LLP distills relational knowledge that is centered around each (anchor) node to the student MLP. Specifically, we propose rank-based matching and distribution-based matching strategies that complement each other. Extensive experiments demonstrate that LLP boosts the link prediction performance of MLPs with significant margins and even outperforms the teacher GNNs on 7 out of 8 benchmarks. LLP also achieves a 70.68x speedup in link prediction inference compared to GNNs on the large-scale OGB dataset.

Large language models can be prompted to pro- duce fluent output for a wide range of tasks without being specifically trained to do so. Nevertheless, it is notoriously difficult to control their generation in such a way that it satisfies user-specified constraints. In this paper, we present InstructCTG, a simple controlled text generation framework that incorporates different constraints by verbalizing them as natural language instructions. We annotate natural texts through a combination of off-the-shelf NLP tools and simple heuristics with the linguistic and extra-linguistic constraints they satisfy. Then, we verbalize the constraints into natural language instructions to form weakly supervised training data, i.e., we prepend the natural language verbalizations of the constraints in front of their corresponding natural language sentences. Next, we fine-tune a pre-trained language model on the augmented corpus. Compared to existing methods, InstructCTG is more flexible in terms of the types of constraints it allows the practitioner to use. It also does not require any modification of the decoding procedure. Finally, InstructCTG allows the model to adapt to new constraints without re-training through the use of in-context learning.

Federated Learning (FL) aims to train machine learning models for multiple clients without sharing their own private data. Due to the heterogeneity of clients' local data distribution, recent studies explore the personalized FL that learns and deploys distinct local models with the help of auxiliary global models. However, the clients can be heterogeneous in terms of not only local data distribution, but also their computation and communication resources. The capacity and efficiency of personalized models are restricted by the lowest-resource clients, leading to sub-optimal performance and limited practicality of personalized FL. To overcome these challenges, we propose a novel approach named pFedGate for efficient personalized FL by adaptively and efficiently learning sparse local models. With a lightweight trainable gating layer, pFedGate enables clients to reach their full potential in model capacity by generating different sparse models accounting for both the heterogeneous data distributions and resource constraints. Meanwhile, the computation and communication efficiency are both improved thanks to the adaptability between the model sparsity and clients' resources. Further, we theoretically show that the proposed pFedGate has superior complexity with guaranteed convergence and generalization error. Extensive experiments show that pFedGate achieves superior global accuracy, individual accuracy and efficiency simultaneously over state-of-the-art methods. We also demonstrate that pFedGate performs better than competitors in the novel clients participation and partial clients participation scenarios, and can learn meaningful sparse local models adapted to different data distributions.

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler-Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve graph isomorphism distinguishing power of message passing neural networks. The method is then extended to higher-dimensional WL, leading to a novel $k,l$-WL algorithm, a more general framework than $k$-WL. We further introduce the subgraph concept into our hierarchy and propose a localized $k,l$-WL framework, incorporating a wide range of existing work, including many subgraph GNNs. Theoretically, we analyze the expressivity of $k,l$-WL w.r.t. $k$ and $l$ and compare it with the traditional $k$-WL. Complexity reduction methods are also systematically discussed to build powerful and practical $k,l$-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our $k,l$-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.

Multi-modal contrastive learning (MMCL) has recently garnered considerable interest due to its superior performance in visual tasks, achieved by embedding multi-modal data, such as visual-language pairs. However, there still lack theoretical understandings of how MMCL extracts useful visual representation from multi-modal pairs, and particularly, how MMCL outperforms previous approaches like self-supervised contrastive learning (SSCL). In this paper, by drawing an intrinsic connection between MMCL and asymmetric matrix factorization, we establish the first generalization guarantees of MMCL for visual downstream tasks. Based on this framework, we further unify MMCL and SSCL by showing that MMCL implicitly performs SSCL with (pseudo) positive pairs induced by text pairs. Through this unified perspective, we characterize the advantage of MMCL by showing that text pairs induce more semantically consistent and diverse positive pairs, which, according to our analysis, provably benefit downstream generalization. Inspired by this finding, we propose several methods to significantly improve the downstream performance of SSCL on ImageNet by leveraging multi-modal information. Code is available at https://github.com/PKU-ML/CLIP-Help-SimCLR.

Test-Time Adaptation (TTA) has recently gained significant attention as a new paradigm for tackling distribution shifts. Despite the sheer number of existing methods, the inconsistent experimental conditions and lack of standardization in prior literature make it difficult to measure their actual efficacies and progress. To address this issue, we present a large-scale open-sourced Test-Time Adaptation Benchmark, dubbed TTAB, which includes nine state-of-the-art algorithms, a diverse array of distribution shifts, and two comprehensive evaluation protocols. Through extensive experiments, we identify three common pitfalls in prior efforts: (i) choosing appropriate hyper-parameter, especially for model selection, is exceedingly difficult due to online batch dependency; (ii) the effectiveness of TTA varies greatly depending on the quality of the model being adapted; (iii) even under optimal algorithmic conditions, existing methods still systematically struggle with certain types of distribution shifts. Our findings suggest that future research in the field should be more transparent about their experimental conditions, ensure rigorous evaluations on a broader set of models and shifts, and re-examine the assumptions underlying the potential success of TTA for practical applications.

We study counterfactual identifiability in causal models with bijective generation mechanisms (BGM), a class that generalizes several widely-used causal models in the literature. We establish their counterfactual identifiability for three common causal structures with unobserved confounding, and propose a practical learning method that casts learning a BGM as structured generative modeling. Learned BGMs enable efficient counterfactual estimation and can be obtained using a variety of deep conditional generative models. We evaluate our techniques in a visual task and demonstrate its application in a real-world video streaming simulation task.

To characterize the functions spaces explored by multi-layer neural networks (NNs), we introduce Neural Hilbert Ladders (NHLs), a collection of reproducing kernel Hilbert spaces (RKHSes) that are defined iteratively and adaptive to training. First, we prove a correspondence between functions expressed by L-layer NNs and those belonging to L-level NHLs. Second, we prove generalization guarantees for learning the NHL based on a new complexity measure. Third, corresponding to the training of multi-layer NNs in the infinite-width mean-field limit, we derive an evolution of the NHL characterized by the dynamics of multiple random fields. Finally, we examine linear and shallow NNs from the new perspective and complement the theory with numerical results.

We introduce in this paper the mechanism of graph random features (GRFs). GRFs can be used to construct unbiased randomized estimators of several important kernels defined on graphs' nodes, in particular the regularized Laplacian kernel. As regular RFs for non-graph kernels, they provide means to scale up kernel methods defined on graphs to larger networks. Importantly, they give substantial computational gains also for smaller graphs, while applied in downstream applications. Consequently, GRFs address the notoriously difficult problem of cubic (in the number of the nodes of the graph) time complexity of graph kernels algorithms. We provide a detailed theoretical analysis of GRFs and an extensive empirical evaluation: from speed tests, through Frobenius relative error analysis to kmeans graph-clustering with graph kernels. We show that the computation of GRFs admits an embarrassingly simple distributed algorithm that can be applied if the graph under consideration needs to be split across several machines. We also introduce a (still unbiased) quasi Monte Carlo variant of GRFs, q-GRFs, relying on the so-called reinforced random walks that might be used to optimize the variance of GRFs. As a byproduct, we obtain a novel approach to solve certain classes of linear equations with positive and symmetric matrices.

We study Stochastic Gradient Descent with AdaGrad stepsizes: a popular adaptive (self-tuning) method for first-order stochastic optimization. Despite being well studied, existing analyses of this method suffer from various shortcomings: they either assume some knowledge of the problem parameters, impose strong global Lipschitz conditions, or fail to give bounds that hold with high probability. We provide a comprehensive analysis of this basic method without any of these limitations, in both the convex and non-convex (smooth) cases, that additionally supports a general ``affine variance'' noise model and provides sharp rates of convergence in both the low-noise and high-noise regimes.

Off-policy evaluation (OPE) aims to estimate the return of a target policy using some pre-collected observational data generated by a potentially different behavior policy. In many cases, there exist unmeasured variables that confound the action-reward or action-next-state relationships, rendering many existing OPE approaches ineffective. This paper develops an instrumental variable (IV)-based method for consistent OPE in confounded sequential decision making. Similar to single-stage decision making, we show that IV enables us to correctly identify the target policy's value in infinite horizon settings as well. Furthermore, we propose a number of policy value estimators and illustrate their effectiveness through extensive simulations and real data analysis from a world-leading short-video platform.

In collaborative learning with streaming data, nodes (e.g., organizations) jointly and continuously learn a machine learning (ML) model by sharing the latest model updates computed from their latest streaming data. For the more resourceful nodes to be willing to share their model updates, they need to be fairly incentivized. This paper explores an incentive design that guarantees fairness so that nodes receive rewards commensurate to their contributions. Our approach leverages an explore-then-exploit formulation to estimate the nodes' contributions (i.e., exploration) for realizing our theoretically guaranteed fair incentives (i.e., exploitation). However, we observe a "rich get richer" phenomenon arising from the existing approaches to guarantee fairness and it discourages the participation of the less resourceful nodes. To remedy this, we additionally preserve asymptotic equality, i.e., less resourceful nodes achieve equal performance eventually to the more resourceful/``rich'' nodes. We empirically demonstrate in two settings with real-world streaming data: federated online incremental learning and federated reinforcement learning, that our proposed approach outperforms existing baselines in fairness and learning performance while remaining competitive in preserving equality.

The integration of machine learning models in various real-world applications is becoming more prevalent to assist humans in their daily decision-making tasks as a result of recent advancements in this field. However, it has been discovered that there is a tradeoff between the accuracy and fairness of these decision-making tasks. In some cases, these AI systems can be unfair by exhibiting bias or discrimination against certain social groups, which can have severe consequences in real life. Inspired by one of the most well-known human learning skills called grouping, we address this issue by proposing a novel machine learning (ML) framework where the ML model learns to group a diverse set of problems into distinct subgroups to solve each subgroup using its specific sub-model. Our proposed framework involves three stages of learning, which are formulated as a three-level optimization problem: 1) grouping problems into subgroups, 2) learning group-specific sub-models for problem-solving, and 3) updating group assignments of training examples by minimizing validation loss. These three learning stages are performed end-to-end in a joint manner using gradient descent. To improve fairness and accuracy, we develop an efficient optimization algorithm to solve this three-level optimization problem. To further decrease the risk of overfitting in small datasets using our LBG method, we incorporate domain adaptation techniques in the second stage of training. We further apply our method to differentiable neural architecture search (NAS) methods.

Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent training on bilevel problems to the decentralized setting is a natural generalization, and there has been a flurry of work studying decentralized bilevel optimization algorithms. However, it remains unknown how to design the distributed algorithm with sample complexity and convergence rate comparable to SGD for stochastic optimization, and at the same time without directly computing the exact Hessian or Jacobian matrices. In this paper we propose such an algorithm. More specifically, we propose a novel decentralized stochastic bilevel optimization (DSBO) algorithm that only requires first order stochastic oracle, Hessian-vector product and Jacobian-vector product oracle. The sample complexity of our algorithm matches the currently best known results for DSBO, while our algorithm does not require estimating the full Hessian and Jacobian matrices, thereby possessing to improved per-iteration complexity.

In recent years, multiple notions of algorithmic fairness have arisen. One such notion is individual fairness (IF), which requires that individuals who are similar receive similar treatment. In parallel, matrix estimation (ME) has emerged as a natural paradigm for handling noisy data with missing values. In this work, we connect the two concepts. We show that pre-processing data using ME can improve an algorithm's IF without sacrificing performance. Specifically, we show that using a popular ME method known as singular value thresholding (SVT) to pre-process the data provides a strong IF guarantee under appropriate conditions. We then show that, under analogous conditions, SVT pre-processing also yields estimates that are consistent and approximately minimax optimal. As such, the ME pre-processing step does not, under the stated conditions, increase the prediction error of the base algorithm, i.e., does not impose a fairness-performance trade-off. We verify these results on synthetic and real data.

We study principal component analysis (PCA), where given a dataset in $\mathbb R^d$ from a distribution, the task is to find a unit vector $v$ that approximately maximizes the variance of the distribution after being projected along $v$. Despite being a classical task, standard estimators fail drastically if the data contains even a small fraction of outliers, motivating the problem of robust PCA. Recent work has developed computationally-efficient algorithms for robust PCA that either take super-linear time or have sub-optimal error guarantees. Our main contribution is to develop a nearly linear time algorithm for robust PCA with near-optimal error guarantees. We also develop a single-pass streaming algorithm for robust PCA with memory usage nearly-linear in the dimension.

Several recent studies have elucidated why knowledge distillation (KD) improves model performance. However, few have researched the other advantages of KD in addition to its improving model performance. In this study, we have attempted to show that KD enhances the interpretability as well as the accuracy of models. We measured the number of concept detectors identified in network dissection for a quantitative comparison of model interpretability. We attributed the improvement in interpretability to the class-similarity information transferred from the teacher to student models. First, we confirmed the transfer of class-similarity information from the teacher to student model via logit distillation. Then, we analyzed how class-similarity information affects model interpretability in terms of its presence or absence and degree of similarity information. We conducted various quantitative and qualitative experiments and examined the results on different datasets, different KD methods, and according to different measures of interpretability. Our research showed that KD models by large models could be used more reliably in various fields. The code is available at https://github.com/Rok07/KD_XAI.git.

We introduce Neuro-Symbolic Continual Learning, where a model has to solve a sequence of neuro-symbolic tasks, that is, it has to map sub-symbolic inputs to high-level concepts and compute predictions by reasoning consistently with prior knowledge. Our key observation is that neuro-symbolic tasks, although different, often share concepts whose semantics remains stable over time. Traditional approaches fall short: existing continual strategies ignore knowledge altogether, while stock neuro-symbolic architectures suffer from catastrophic forgetting. We show that leveraging prior knowledge by combining neuro-symbolic architectures with continual strategies does help avoid catastrophic forgetting, but also that doing so can yield models affected by reasoning shortcuts. These undermine the semantics of the acquired concepts, even when detailed prior knowledge is provided upfront and inference is exact, and in turn continual performance. To overcome these issues, we introduce COOL, a COncept-level cOntinual Learning strategy tailored for neuro-symbolic continual problems that acquires high-quality concepts and remembers them over time. Our experiments on three novel benchmarks highlights how COOL attains sustained high performance on neuro-symbolic continual learning tasks in which other strategies fail.

Recent data-driven approaches based on machine learning aim to directly solve a downstream forecasting or projection task by learning a data-driven functional mapping using deep neural networks. However, these networks are trained using curated and homogeneous climate datasets for specific spatiotemporal tasks, and thus lack the generality of currently used computationally intensive physics-informed numerical models for weather and climate modeling. We develop and demonstrate ClimaX, a flexible and generalizable deep learning model for weather and climate science that can be trained using heterogeneous datasets spanning different variables, spatio-temporal coverage, and physical groundings. ClimaX extends the Transformer architecture with novel encoding and aggregation blocks that allow effective use of available compute and data while maintaining general utility. ClimaX is pretrained with a self-supervised learning objective on climate datasets derived from CMIP6. The pretrained ClimaX can then be fine-tuned to address a breadth of climate and weather tasks, including those that involve atmospheric variables and spatio-temporal scales unseen during pretraining. Compared to existing data-driven baselines, we show that this generality in ClimaX results in superior performance on benchmarks for weather forecasting and climate projections, even when pretrained at lower resolutions and compute budgets. Our source code is available at https://github.com/microsoft/ClimaX.

Dataset Distillation is a newly emerging area that aims to distill large datasets into much smaller and highly informative synthetic ones to accelerate training and reduce storage. Among various dataset distillation methods, trajectory-matching-based methods (MTT) have achieved SOTA performance in many tasks, e.g., on CIFAR-10/100. However, due to exorbitant memory consumption when unrolling optimization through SGD steps, MTT fails to scale to large-scale datasets such as ImageNet-1K. Can we scale this SOTA method to ImageNet-1K and does its effectiveness on CIFAR transfer to ImageNet-1K? To answer these questions, we first propose a procedure to exactly compute the unrolled gradient with constant memory complexity, which allows us to scale MTT to ImageNet-1K seamlessly with $\sim 6$x reduction in memory footprint. We further discover that it is challenging for MTT to handle datasets with a large number of classes, and propose a novel soft label assignment that drastically improves its convergence. The resulting algorithm sets new SOTA on ImageNet-1K: we can scale up to 50 IPCs (Image Per Class) on ImageNet-1K on a single GPU (all previous methods can only scale to 2 IPCs on ImageNet-1K), leading to the best accuracy (only 5.9% accuracy drop against full dataset training) while utilizing only 4.2% of the number of data points - an 18.2% absolute gain over prior SOTA.

Federated learning suffers from a latency bottleneck induced by network stragglers, which hampers the training efficiency significantly. In addition, due to the heterogeneous data distribution and security requirements, simple and fast averaging aggregation is not feasible anymore. Instead, complicated aggregation operations, such as knowledge distillation, are required. The time cost for complicated aggregation becomes a new bottleneck that limits the computational efficiency of FL. In this work, we claim that the root cause of training latency actually lies in the aggregation-then-broadcasting workflow of the server. By swapping the computational order of aggregation and broadcasting, we propose a novel and efficient parallel federated learning (PFL) framework that unlocks the edge nodes during global computation and the central server during local computation. This fully asynchronous and parallel pipeline enables handling complex aggregation and network stragglers, allowing flexible device participation as well as achieving scalability in computation. We theoretically prove that synchronous and asynchronous PFL can achieve a similar convergence rate as vanilla FL. Extensive experiments empirically show that our framework brings up to $5.56\times$ speedup compared with traditional FL. Code is available at: https://github.com/Hypervoyager/PFL.

Robot design aims at learning to create robots that can be easily controlled and perform tasks efficiently. Previous works on robot design have proven its ability to generate robots for various tasks. However, these works searched the robots directly from the vast design space and ignored common structures, resulting in abnormal robots and poor performance. To tackle this problem, we propose a Symmetry-Aware Robot Design (SARD) framework that exploits the structure of the design space by incorporating symmetry searching into the robot design process. Specifically, we represent symmetries with the subgroups of the dihedral group and search for the optimal symmetry in structured subgroups. Then robots are designed under the searched symmetry. In this way, SARD can design efficient symmetric robots while covering the original design space, which is theoretically analyzed. We further empirically evaluate SARD on various tasks, and the results show its superior efficiency and generalizability.

Deep ensemble is a simple yet powerful way to improve the performance of deep neural networks. Under this motivation, recent works on mode connectivity have shown that parameters of ensembles are connected by low-loss subspaces, and one can efficiently collect ensemble parameters in those subspaces. While this provides a way to efficiently train ensembles, for inference, multiple forward passes should still be executed using all the ensemble parameters, which often becomes a serious bottleneck for real-world deployment. In this work, we propose a novel framework to reduce such costs. Given a low-loss subspace connecting two modes of a neural network, we build an additional neural network that predicts the output of the original neural network evaluated at a certain point in the low-loss subspace. The additional neural network, which we call a ``bridge'', is a lightweight network that takes minimal features from the original network and predicts outputs for the low-loss subspace without forward passes through the original network. We empirically demonstrate that we can indeed train such bridge networks and significantly reduce inference costs with the help of bridge networks.

Vision Transformer (ViT) is an attention-based model architecture that has demonstrated superior performance on many computer vision tasks. However, its security properties, in particular, the robustness against adversarial attacks, are yet to be thoroughly studied. Recent works have shown that ViT is vulnerable to attention-based adversarial patch attacks, which cover 1-3% area of the input image using adversarial patches and degrades the model accuracy to 0%. This work provides a generic study targeting the attention-based patch attack. First, we experimentally observe that adversarial patches only activate in a few layers and become lazy during attention updating. According to experiments, we study the theory of how a small adversarial patch perturbates the whole model. Based on understanding adversarial patch attacks, we propose a simple but efficient defense that correctly detects more than 95% of adversarial patches.

Independence testing is a classical statistical problem that has been extensively studied in the batch setting when one fixes the sample size before collecting data. However, practitioners often prefer procedures that adapt to the complexity of a problem at hand instead of setting sample size in advance. Ideally, such procedures should (a) stop earlier on easy tasks (and later on harder tasks), hence making better use of available resources, and (b) continuously monitor the data and efficiently incorporate statistical evidence after collecting new data, while controlling the false alarm rate. Classical batch tests are not tailored for streaming data: valid inference after data peeking requires correcting for multiple testing which results in low power. Following the principle of testing by betting, we design sequential kernelized independence tests that overcome such shortcomings. We exemplify our broad framework using bets inspired by kernelized dependence measures, e.g., the Hilbert-Schmidt independence criterion. Our test is also valid under non-i.i.d. time-varying settings. We demonstrate the power of our approaches on both simulated and real data.

We introduce new differentially private (DP) mechanisms for gradient-based machine learning (ML) with multiple passes (epochs) over a dataset, substantially improving the achievable privacy-utility-computation tradeoffs. We formalize the problem of DP mechanisms for adaptive streams with multiple participations and introduce a non-trivial extension of online matrix factorization DP mechanisms to our setting. This includes establishing the necessary theory for sensitivity calculations and efficient computation of optimal matrices. For some applications like $>\!\! 10,000$ SGD steps, applying these optimal techniques becomes computationally expensive. We thus design an efficient Fourier-transform-based mechanism with only a minor utility loss. Extensive empirical evaluation on both example-level DP for image classification and user-level DP for language modeling demonstrate substantial improvements over all previous methods, including the widely-used DP-SGD. Though our primary application is to ML, our main DP results are applicable to arbitrary linear queries and hence may have much broader applicability.

In this paper, we develop an approximation scheme for solving bilevel programs with equilibrium constraints, which are generally difficult to solve. Among other things, calculating the first-order derivative in such a problem requires differentiation across the hierarchy, which is computationally intensive, if not prohibitive. To bypass the hierarchy, we propose to bound such bilevel programs, equivalent to multiple-followers Stackelberg games, with two new hierarchy-free problems: a $T$-step Cournot game and a $T$-step monopoly model. Since they are standard equilibrium or optimization problems, both can be efficiently solved via first-order methods. Importantly, we show that the bounds provided by these problems --- the upper bound by the $T$-step Cournot game and the lower bound by the $T$-step monopoly model --- can be made arbitrarily tight by increasing the step parameter $T$ for a wide range of problems. We prove that a small $T$ usually suffices under appropriate conditions to reach an approximation acceptable for most practical purposes. Eventually, the analytical insights are highlighted through numerical examples.

Dirichlet Process mixture models (DPMM) in combination with Gaussian kernels have been an important modeling tool for numerous data domains arising from biological, physical, and social sciences. However, this versatility in applications does not extend to strong theoretical guarantees for the underlying parameter estimates, for which only a logarithmic rate is achieved. In this work, we (re)introduce and investigate a metric, named Orlicz-Wasserstein distance, in the study of the Bayesian contraction behavior for the parameters. We show that despite the overall slow convergence guarantees for all the parameters, posterior contraction for parameters happens at almost polynomial rates in outlier regions of the parameter space. Our theoretical results provide new insight in understanding the convergence behavior of parameters arising from various settings of hierarchical Bayesian nonparametric models. In addition, we provide an algorithm to compute the metric by leveraging Sinkhorn divergences and validate our findings through a simulation study.

We study differentially private mechanisms for sharing training data in machine learning settings. Our goal is to enable learning of an accurate predictive model while protecting the privacy of each user's label. Previous work established privacy guarantees that assumed the features are public and given exogenously, a setting known as label differential privacy. In some scenarios, this can be a strong assumption that removes the interplay between features and labels from the privacy analysis. We relax this approach and instead assume the features are drawn from a distribution that depends on the private labels. We first show that simply adding noise to the label, as in previous work, can lead to an arbitrarily weak privacy guarantee, and also present methods for estimating this privacy loss from data. We then present a new mechanism that replaces some training examples with synthetically generated data, and show that our mechanism has a much better privacy-utility tradeoff if the synthetic data is ‘realistic’, in a certain quantifiable sense. Finally, we empirically validate our theoretical analysis.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only $O(n)$ integer variables, where $n$ is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with $O(n^2)$ Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

Discount regularization, using a shorter planning horizon when calculating the optimal policy, is a popular choice to restrict planning to a less complex set of policies when estimating an MDP from sparse or noisy data (Jiang et al., 2015). It is commonly understood that discount regularization functions by de-emphasizing or ignoring delayed effects. In this paper, we reveal an alternate view of discount regularization that exposes unintended consequences. We demonstrate that planning under a lower discount factor produces an identical optimal policy to planning using any prior on the transition matrix that has the same distribution for all states and actions. In fact, it functions like a prior with stronger regularization on state-action pairs with more transition data. This leads to poor performance when the transition matrix is estimated from data sets with uneven amounts of data across state-action pairs. Our equivalence theorem leads to an explicit formula to set regularization parameters locally for individual state-action pairs rather than globally. We demonstrate the failures of discount regularization and how we remedy them using our state-action-specific method across simple empirical examples as well as a medical cancer simulator.

Normalizing flows are powerful non-parametric statistical models that function as a hybrid between density estimators and generative models. Current learning algorithms for normalizing flows assume that data points are sampled independently, an assumption that is frequently violated in practice, which may lead to erroneous density estimation and data generation. We propose a likelihood objective of normalizing flows incorporating dependencies between the data points, for which we derive a flexible and efficient learning algorithm suitable for different dependency structures. We show that respecting dependencies between observations can improve empirical results on both synthetic and real-world data, and leads to higher statistical power in a downstream application to genome-wide association studies.

In this paper, we introduce a variant of Bayesian online change point detection with a reducedrank Student-t process (TP) and dependent Student-t noise, as a nonparametric time series model. Our method builds and improves upon the state-of-the-art Gaussian process (GP) change point model benchmark of Saatci et al. (2010). The Student-t process generalizes the concept of a GP and hence yields a more flexible alternative. Additionally, unlike a GP, the predictive variance explicitly depends on the training observations, while the use of an entangled Student-t noise model preserves analytical tractability. Our approach also uses a Hilbert space reduced-rank representation of the TP kernel, derived from an eigenfunction expansion of the Laplace operator (Solin & Sarkka, 2020), to alleviate its computational complexity. Improvements in prediction and training time are demonstrated with real-world data-sets

When physical sensors are involved, such as image sensors, the uncertainty over the input data is often a major component of the output uncertainty of machine learning models. In this work, we address the problem of input uncertainty propagation through trained neural networks. We do not rely on a Gaussian distribution assumption of the output or of any intermediate layer. We propagate instead a Gaussian Mixture Model (GMM) that offers much more flexibility, using the Split&Merge algorithm. This paper's main contribution is the computation of a Wasserstein criterion to control the Gaussian splitting procedure for which theoretical guarantees of convergence on the output distribution estimates are derived. The methodology is tested against a wide range of datasets and networks. It shows robustness, and genericity and offers highly accurate output probability density function estimation while maintaining a reasonable computational cost compared with the standard Monte Carlo (MC) approach.

Iterative methods are ubiquitous in large-scale scientific computing applications, and a number of approaches based on meta-learning have been recently proposed to accelerate them. However, a systematic study of these approaches and how they differ from meta-learning is lacking. In this paper, we propose a framework to analyze such learning-based acceleration approaches, where one can immediately identify a departure from classical meta-learning. We theoretically show that this departure may lead to arbitrary deterioration of model performance, and at the same time, we identify a methodology to ameliorate it by modifying the loss objective, leading to a novel training method for learning-based acceleration of iterative algorithms. We demonstrate the significant advantage and versatility of the proposed approach through various numerical applications.

We consider the stochastic linear contextual bandit problem with high-dimensional features. We analyze the Thompson sampling algorithm using special classes of sparsity-inducing priors (e.g., spike-and-slab) to model the unknown parameter and provide a nearly optimal upper bound on the expected cumulative regret. To the best of our knowledge, this is the first work that provides theoretical guarantees of Thompson sampling in high-dimensional and sparse contextual bandits. For faster computation, we use variational inference instead of Markov Chain Monte Carlo (MCMC) to approximate the posterior distribution. Extensive simulations demonstrate the improved performance of our proposed algorithm over existing ones.

$k$-nearest neighbor classification is a popular non-parametric method because of desirable properties like automatic adaption to distributional scale changes. Unfortunately, it has thus far proved difficult to design active learning strategies for the training of local voting-based classifiers that naturally retain these desirable properties, and hence active learning strategies for $k$-nearest neighbor classification have been conspicuously missing from the literature. In this work, we introduce a simple and intuitive active learning algorithm for the training of $k$-nearest neighbor classifiers, the first in the literature which retains the concept of the $k$-nearest neighbor vote at prediction time. We provide consistency guarantees for a modified $k$-nearest neighbors classifier trained on samples acquired via our scheme, and show that when the conditional probability function $\mathbb{P}(Y=y|X=x)$ is sufficiently smooth and the Tsybakov noise condition holds, our actively trained classifiers converge to the Bayes optimal classifier at a faster asymptotic rate than passively trained $k$-nearest neighbor classifiers.

In this paper, we derive a semi-dual formulation for the problem of unbalanced quadratic optimal transport and we study its stability properties, namely we give upper and lower bounds for the Bregman divergence of the new objective that hold globally. We observe that the new objective gains even more convexity than in the balanced case. We use this formulation to prove the first results on statistical estimation of UOT potentials and we leverage the extra convexity to recover super-parametric rates. Interestingly, unlike in the balanced case, we do not require the potentials to be smooth. Then, use variable metric descent to solve the semi-dual problem for which we prove convergence at a $1/k$ rate for strongly convex potentials and exponential convergence in the balanced case when potentials are also smooth. We emphasize that our convergence results has an interest on its own as it generalizes previous convergence results to non-equivalent metrics. Last, we instantiate a proof-of-concept tractable version of our theoretical algorithm that we benchmark on a 2D experiment in the balanced case and on a medium dimension synthetic experiment in the unbalanced case.

The performance of a bandit algorithm is usually measured by the cumulative rewards of the actions chosen by the algorithm. However, in many real-world applications, the rewards in each round should be good enough for reasons such as safety and fairness. In this paper, we investigate the contextual conservative interleaving bandit problem, which has a performance constraint that requires the chosen actions to be not much worse than given baseline actions in each round. This work is the first to simultaneously consider the following practical situations: (1) multiple actions are chosen in a round, (2) the feature vectors associated with given actions depend on the round, and (3) the performance constraints in each round that depend only on the actions chosen in that round. We propose a meta-algorithm, Greedy on Confidence Widths (GCW), that satisfies the performance constraints with high probability. GCW uses a standard bandit algorithm and achieves minimax optimal regret up to logarithmic factors if the algorithm used is also minimax optimal. We improve the existing analyses for the C${}^2$UCB algorithm and the Thompson sampling to combine with GCW. We show that these algorithms achieve near-optimal regret when the feasible sets of given actions are the bases of a matroid. Our numerical experiments on a real-world dataset demonstrate that GCW with the standard bandit algorithms efficiently improves performance while satisfying the performance constraints.

Recent work has observed an intriguing "Neural Collapse'' phenomenon in well-trained neural networks, where the last-layer representations of training samples with the same label collapse into each other. This appears to suggest that the last-layer representations are completely determined by the labels, and do not depend on the intrinsic structure of input distribution. We provide evidence that this is not a complete description, and that the apparent collapse hides important fine-grained structure in the representations. Specifically, even when representations apparently collapse, the small amount of remaining variation can still faithfully and accurately captures the intrinsic structure of input distribution. As an example, if we train on CIFAR-10 using only 5 coarse-grained labels (by combining two classes into one super-class) until convergence, we can reconstruct the original 10-class labels from the learned representations via unsupervised clustering. The reconstructed labels achieve 93% accuracy on the CIFAR-10 test set, nearly matching the normal CIFAR-10 accuracy for the same architecture. We also provide an initial theoretical result showing the fine-grained representation structure in a simplified synthetic setting. Our results show concretely how the structure of input data can play a significant role in determining the fine-grained structure of neural representations, going beyond what Neural Collapse predicts.

We consider the prediction of the Hamiltonian matrix, which finds use in quantum chemistry and condensed matter physics. Efficiency and equivariance are two important, but conflicting factors. In this work, we propose a SE(3)-equivariant network, named QHNet, that achieves efficiency and equivariance. Our key advance lies at the innovative design of QHNet architecture, which not only obeys the underlying symmetries, but also enables the reduction of number of tensor products by 92%. In addition, QHNet prevents the exponential growth of channel dimension when more atom types are involved. We perform experiments on MD17 datasets, including four molecular systems. Experimental results show that our QHNet can achieve comparable performance to the state of the art methods at a significantly faster speed. Besides, our QHNet consumes 50% less memory due to its streamlined architecture. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

Dynamical systems with complex behaviours, e.g. immune system cells interacting with a pathogen, are commonly modelled by splitting the behaviour in different regimes, or modes, each with simpler dynamics, and then learn the switching behaviour from one mode to another. To achieve this, Switching Dynamical Systems (SDS) are a powerful tool that automatically discovers these modes and mode-switching behaviour from time series data. While effective, these methods focus on independent objects, where the modes of one object are independent of the modes of the other objects. In this paper, we focus on the more general interacting object setting for switching dynamical systems, where the per-object dynamics also depend on an unknown and dynamically changing subset of other objects and their modes. To this end, we propose a novel graph-based approach for switching dynamical systems, GRAph Switching dynamical Systems (GRASS), in which we use a dynamic graph to characterize interactions between objects and learn both intra-object and inter-object mode-switching behaviour. For benchmarking, we create two new datasets, a synthesized ODE-driven particles dataset and a real-world Salsa-couple dancing dataset. Experiments show that GRASS can consistently outperforms previous state-of-the-art methods. We will release code and data after acceptance.

Interpretable models are designed to make decisions in a human-interpretable manner. Representatively, Concept Bottleneck Models (CBM) follow a two-step process of concept prediction and class prediction based on the predicted concepts. CBM provides explanations with high-level concepts derived from concept predictions; thus, reliable concept predictions are important for trustworthiness. In this study, we address the ambiguity issue that can harm reliability. While the existence of a concept can often be ambiguous in the data, CBM predicts concepts deterministically without considering this ambiguity. To provide a reliable interpretation against this ambiguity, we propose Probabilistic Concept Bottleneck Models (ProbCBM). By leveraging probabilistic concept embeddings, ProbCBM models uncertainty in concept prediction and provides explanations based on the concept and its corresponding uncertainty. This uncertainty enhances the reliability of the explanations. Furthermore, as class uncertainty is derived from concept uncertainty in ProbCBM, we can explain class uncertainty by means of concept uncertainty. Code is publicly available at https://github.com/ejkim47/prob-cbm.

Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired predictive functions into neural network training. In this work, we approach regularization in neural networks from a probabilistic perspective and show that by viewing parameter-space regularization as specifying an empirical prior distribution over the model parameters, we can derive a probabilistically well-motivated regularization technique that allows explicitly encoding information about desired predictive functions into neural network training. This method---which we refer to as function-space empirical Bayes (FS-EB)---includes both parameter- and function-space regularization, is mathematically simple, easy to implement, and incurs only minimal computational overhead compared to standard regularization techniques. We evaluate the utility of this regularization technique empirically and demonstrate that the proposed method leads to near-perfect semantic shift detection, highly-calibrated predictive uncertainty estimates, successful task adaption from pre-trained models, and improved generalization under covariate shift.

Contextual bandit algorithms appear in several applications, such as online advertisement and recommendation systems like personalized education or personalized medicine. Individually-tailored recommendations boost the performance of the underlying application; nevertheless, providing individual suggestions becomes costly and even implausible as the number of users grows. As such, to efficiently serve the demands of several users in modern applications, it is imperative to identify the underlying users' clusters, i.e., the groups of users for which a single recommendation might be (near-)optimal. We propose CLUB-HG, a novel algorithm that integrates a game-theoretic approach into clustering inference. Our algorithm achieves Nash equilibrium at each inference step and discovers the underlying clusters. We also provide regret analysis within a standard linear stochastic noise setting. Finally, experiments on synthetic and real-world datasets show the superior performance of our proposed algorithm compared to the state-of-the-art algorithms.

Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule and learns the update direction as a black-box network. While the generic approach is widely applicable, the learned model can overfit and may not generalize well to out-of-distribution test sets. In this paper, we derive the basic mathematical conditions that successful update rules commonly satisfy. Consequently, we propose a novel L2O model with a mathematics-inspired structure that is broadly applicable and generalized well to out-of-distribution problems. Numerical simulations validate our theoretical findings and demonstrate the superior empirical performance of the proposed L2O model.

In this work, we present a variety of novel information-theoretic generalization bounds for learning algorithms, from the supersample setting of Steinke & Zakynthinou (2020)—the setting of the ``conditional mutual information'' framework. Our development exploits projecting the loss pair (obtained from a training instance and a testing instance) down to a single number and correlating loss values with a Rademacher sequence (and its shifted variants). The presented bounds include square-root bounds, fast-rate bounds, including those based on variance and sharpness, and bounds for interpolating algorithms etc. We show theoretically or empirically that these bounds are tighter than all information-theoretic bounds known to date on the same supersample setting.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by $1$, we show that our algorithm only needs to explore $\tilde O\left( d^2\varepsilon^{-2}\right)$ episodes to find an $\varepsilon$-optimal policy, where $d$ is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is "horizon-free''. In addition, we provide an $\Omega\left(d^2\varepsilon^{-2}\right)$ sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

Reinforcement Learning (RL) algorithms are often known for sample inefficiency and difficult generalization. Recently, Unsupervised Environment Design (UED) emerged as a new paradigm for zero-shot generalization by simultaneously learning a task distribution and agent policies on the generated tasks. This is a non-stationary process where the task distribution evolves along with agent policies; creating an instability over time. While past works demonstrated the potential of such approaches, sampling effectively from the task space remains an open challenge, bottlenecking these approaches. To this end, we introduce CLUTR: a novel unsupervised curriculum learning algorithm that decouples task representation and curriculum learning into a two-stage optimization. It first trains a recurrent variational autoencoder on randomly generated tasks to learn a latent task manifold. Next, a teacher agent creates a curriculum by maximizing a minimax REGRET-based objective on a set of latent tasks sampled from this manifold. Using the fixed-pretrained task manifold, we show that CLUTR successfully overcomes the non-stationarity problem and improves stability. Our experimental results show CLUTR outperforms PAIRED, a principled and popular UED method, in the challenging CarRacing and navigation environments: achieving 10.6X and 45% improvement in zero-shot generalization, respectively. CLUTR also performs comparably to the non-UED state-of-the-art for CarRacing, while requiring 500X fewer environment interactions. We open source our code at https://github.com/clutr/clutr.

In recent years, reinforcement learning (RL) has been applied to real-world problems with increasing success. Such applications often require to put constraints on the agent's behavior. Existing algorithms for constrained RL (CRL) rely on gradient descent-ascent, but this approach comes with a caveat. While these algorithms are guaranteed to converge on average, they do not guarantee last-iterate convergence, i.e., the current policy of the agent may never converge to the optimal solution. In practice, it is often observed that the policy alternates between satisfying the constraints and maximizing the reward, rarely accomplishing both objectives simultaneously. Here, we address this problem by introducing Reinforcement Learning with Optimistic Ascent-Descent (ReLOAD), a principled CRL method with guaranteed last-iterate convergence. We demonstrate its empirical effectiveness on a wide variety of CRL problems including discrete MDPs and continuous control. In the process we establish a benchmark of challenging CRL problems.

We consider the problem of computing bounds for causal queries on quasi-Markovian graphs with unobserved confounders and discrete valued observed variables, where identifiability does not hold. Existing non-parametric approaches for computing such bounds use multilinear programming (MP) formulations that are often intractable for existing solvers when the degree of the polynomial objective is greater than two. Hence, one often has to resort to either fast approximate heuristics which are not guaranteed to contain the true query value, or more accurate but computationally intensive procedures. We show how to construct an equivalent MP with a polynomial objective of lower degree. In particular, the degree of the objective in the new MP is equal to only the number of C-components that are intervened upon, instead of the total number of C-components. As a result, we can compute exact bounds for significantly larger causal inference problems as compared to what is possible using existing techniques. We also propose a very efficient Frank-Wolfe heuristic that produces very high quality bounds, and scales to large multilinear problems of higher degree.

Clustering is a fundamental building block of modern statistical analysis pipelines. Fair clustering has seen much attention from the machine learning community in recent years. We are some of the first to study fairness in the context of hierarchical clustering, after the results of Ahmadian et al. from NeurIPS in 2020. We evaluate our results using Dasgupta's cost function, perhaps one of the most prevalent theoretical metrics for hierarchical clustering evaluation. Our work vastly improves the previous $O(n^{5/6}poly\log(n))$ fair approximation for cost to a near polylogarithmic $O(n^\delta poly\log(n))$ fair approximation for any constant $\delta\in(0,1)$. This result establishes a cost fairness tradeoff and extends to broader fairness constraints than the previous work. We also show how to alter existing hierarchical clusterings to guarantee fairness and cluster balance across any level in the hierarchy.

The goal in episodic memory (EM) is to search a long egocentric video to answer a natural language query (e.g., “where did I leave my purse?”). Existing EM methods exhaustively extract expensive fixed-length clip features to look everywhere in the video for the answer, which is infeasible for long wearable-camera videos that span hours or even days. We propose SpotEM, an approach to achieve efficiency for a given EM method while maintaining good accuracy. SpotEM consists of three key ideas: 1) a novel clip selector that learns to identify promising video regions to search conditioned on the language query; 2) a set of low-cost semantic indexing features that capture the context of rooms, objects, and interactions that suggest where to look; and 3) distillation losses that address the optimization issues arising from end-to-end joint training of the clip selector and EM model. Our experiments on 200+ hours of video from the Ego4D EM Natural Language Queries benchmark and three different EM models demonstrate the effectiveness of our approach: computing only 10% – 25% of the clip features, we preserve 84% – 97% of the original EM model’s accuracy. Project page: https://vision.cs.utexas.edu/projects/spotem

Typical machine learning applications always assume the data follows independent and identically distributed (IID) assumptions. In contrast, this assumption is frequently violated in real-world circumstances, leading to the Out-of-Distribution (OOD) generalization problem and a major drop in model robustness. To mitigate this issue, the invariant learning technique is leveraged to distinguish between spurious features and invariant features among all input features and to train the model purely on the basis of the invariant features. Numerous invariant learning strategies imply that the training data should contain domain information. Such information includes the environment index or auxiliary information acquired from prior knowledge. However, acquiring these information is typically impossible in practice. In this study, we present TIVA for environment-independent invariance learning, which requires no environment-specific information in training data. We discover and prove that, given certain mild data conditions, it is possible to train an environment partitioning policy based on attributes that are independent of the targets and then conduct invariant risk minimization. We examine our method in comparison to other baseline methods, which demonstrate superior performance and excellent robustness under OOD, using multiple benchmarks.

Unsupervised denoising is a crucial challenge in real-world imaging applications. Unsupervised deep-learning methods have demonstrated impressive performance on benchmarks based on synthetic noise. However, no metrics exist to evaluate these methods in an unsupervised fashion. This is highly problematic for the many practical applications where ground-truth clean images are not available. In this work, we propose two novel metrics: the unsupervised mean squared error (MSE) and the unsupervised peak signal-to-noise ratio (PSNR), which are computed using only noisy data. We provide a theoretical analysis of these metrics, showing that they are asymptotically consistent estimators of the supervised MSE and PSNR. Controlled numerical experiments with synthetic noise confirm that they provide accurate approximations in practice. We validate our approach on real-world data from two imaging modalities: videos in raw format and transmission electron microscopy. Our results demonstrate that the proposed metrics enable unsupervised evaluation of denoising methods based exclusively on noisy data.

A hallmark of intelligence is the ability to autonomously learn new flexible, cognitive behaviors - that is, behaviors where the appropriate action depends not just on immediate stimuli (as in simple reflexive stimulus-response associations), but on contextual information that must be adequately acquired, stored and processed. While many meta-learning algorithms can design agents that autonomously learn new tasks, cognitive tasks adds another level of learning and memory to typical ``learning-to-learn'' problems. Here we evolve neural networks, endowed with plastic connections and neuromodulation, over a sizable set of simple cognitive tasks adapted from a computational neuroscience framework. The resulting evolved networks can automatically modify their own connectivity to acquire a novel simple cognitive task, never seen during evolution, from stimuli and rewards alone, through the spontaneous operation of their evolved neural organization and plasticity system. Our results emphasize the importance of carefully considering the multiple learning loops involved in the emergence of intelligent behavior.

We propose Automatic Feature Explanation using Contrasting Concepts (FALCON), an interpretability framework to explain features of image representations. For a target feature, FALCON captions its highly activating cropped images using a large captioning dataset (like LAION-400m) and a pre-trained vision-language model like CLIP. Each word among the captions is scored and ranked leading to a small number of shared, human-understandable concepts that closely describe the target feature. FALCON also applies contrastive interpretation using lowly activating (counterfactual) images, to eliminate spurious concepts. Although many existing approaches interpret features independently, we observe in state-of-the-art self-supervised and supervised models, that less than 20% of the representation space can be explained by individual features. We show that features in larger spaces become more interpretable when studied in groups and can be explained with high-order scoring concepts through FALCON. We discuss how extracted concepts can be used to explain and debug failures in downstream tasks. Finally, we present a technique to transfer concepts from one (explainable) representation space to another unseen representation space by learning a simple linear transformation.

Explainability methods for NLP systems encounter a version of the fundamental problem of causal inference: for a given ground-truth input text, we never truly observe the counterfactual texts necessary for isolating the causal effects of model representations on outputs. In response, many explainability methods make no use of counterfactual texts, assuming they will be unavailable. In this paper, we show that robust causal explainability methods can be created using approximate counterfactuals, which can be written by humans to approximate a specific counterfactual or simply sampled using metadata-guided heuristics. The core of our proposal is the Causal Proxy Model (CPM). A CPM explains a black-box model $\mathcal{N}$ because it is trained to have the same *actual* input/output behavior as $\mathcal{N}$ while creating neural representations that can be intervened upon to simulate the *counterfactual* input/output behavior of $\mathcal{N}$. Furthermore, we show that the best CPM for $\mathcal{N}$ performs comparably to $\mathcal{N}$ in making factual predictions, which means that the CPM can simply replace $\mathcal{N}$, leading to more explainable deployed models.

Modeling spatiotemporal dynamics with neural differential equations has become a major line of research that opens new ways to handle various real-world scenarios (e.g., missing observations, irregular times, etc.). Despite such progress, most existing methods still face challenges in providing a general framework for analyzing time series. To tackle this, we adopt stochastic differential games to suggest a new philosophy of utilizing interacting collective intelligence in time series analysis. For the implementation, we develop the novel gradient descent-based algorithm called deep neural fictitious play to approximate the Nash equilibrium. We theoretically analyze the convergence result of the proposed algorithm and discuss the advantage of cooperative games in handling noninformative observation. Throughout the experiments on various datasets, we demonstrate the superiority of our framework over all the tested benchmarks in modeling time-series prediction by capitalizing on the advantages of applying cooperative games. An ablation study shows that neural agents of the proposed framework learn intrinsic temporal relevance to make accurate time-series predictions.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Fair representation learning (FRL) is a popular class of methods aiming to produce fair classifiers via data preprocessing. Recent regulatory directives stress the need for FRL methods that provide practical certificates, i.e., provable upper bounds on the unfairness of any downstream classifier trained on preprocessed data, which directly provides assurance in a practical scenario. Creating such FRL methods is an important challenge that remains unsolved. In this work, we address that challenge and introduce FARE (Fairness with Restricted Encoders), the first FRL method with practical fairness certificates. FARE is based on our key insight that restricting the representation space of the encoder enables the derivation of practical guarantees, while still permitting favorable accuracy-fairness tradeoffs for suitable instantiations, such as one we propose based on fair trees. To produce a practical certificate, we develop and apply a statistical procedure that computes a finite sample high-confidence upper bound on the unfairness of any downstream classifier trained on FARE embeddings. In our comprehensive experimental evaluation, we demonstrate that FARE produces practical certificates that are tight and often even comparable with purely empirical results obtained by prior methods, which establishes the practical value of our approach.

Visual Prompt Tuning (VPT) is an effective tuning method for adapting pretrained Vision Transformers (ViTs) to downstream tasks. It leverages extra learnable tokens, known as prompts, which steer the frozen pretrained ViTs. Although VPT has demonstrated its applicability with supervised vision transformers, it often underperforms with self-supervised ones. Through empirical observations, we deduce that the effectiveness of VPT hinges largely on the ViT blocks with which the prompt tokens interact. Specifically, VPT shows improved performance on image classification tasks for MAE and MoCo v3 when the prompt tokens are inserted into later blocks rather than the first block. These observations suggest that there exists an optimal location of blocks for the insertion of prompt tokens. Unfortunately, identifying the optimal blocks for prompts within each self-supervised ViT for diverse future scenarios is a costly process. To mitigate this problem, we propose a simple yet effective method that learns a gate for each ViT block to adjust its intervention into the prompt tokens. With our method, prompt tokens are selectively influenced by blocks that require steering for task adaptation. Our method outperforms VPT variants in FGVC and VTAB image classification and ADE20K semantic segmentation. The code is available at https://github.com/ryongithub/GatedPromptTuning.

In this paper, we examine the effectiveness of pre-training for visuo-motor control tasks. We revisit a simple Learning-from-Scratch (LfS) baseline that incorporates data augmentation and a shallow ConvNet, and find that this baseline is surprisingly competitive with recent approaches (PVR, MVP, R3M) that leverage frozen visual representations trained on large-scale vision datasets -- across a variety of algorithms, task domains, and metrics in simulation and on a real robot. Our results demonstrate that these methods are hindered by a significant domain gap between the pre-training datasets and current benchmarks for visuo-motor control, which is alleviated by finetuning. Based on our findings, we provide recommendations for future research in pre-training for control and hope that our simple yet strong baseline will aid in accurately benchmarking progress in this area. Code: https://github.com/gemcollector/learning-from-scratch.

Few-shot classification consists of a training phase where a model is learned on a relatively large dataset and an adaptation phase where the learned model is adapted to previously-unseen tasks with limited labeled samples. In this paper, we empirically prove that the training algorithm and the adaptation algorithm can be completely disentangled, which allows algorithm analysis and design to be done individually for each phase. Our meta-analysis for each phase reveals several interesting insights that may help better understand key aspects of few-shot classification and connections with other fields such as visual representation learning and transfer learning. We hope the insights and research challenges revealed in this paper can inspire future work in related directions. Code and pre-trained models (in PyTorch) are available at https://github.com/Frankluox/CloserLookAgainFewShot.

Bilevel optimization has gained significant popularity in recent years due to its ability to formulate various machine learning problems. For instance, in meta-learning, the upper-level (UL) problem offers a good initialization for the lower-level (LL) model to facilitate adaptation. However, the decision variables can impact data features and outcomes, leading to the phenomenon known as performativity. In this work, we investigate the inclusion of decision-dependent distributions in bilevel optimization. Specifically, we consider the scenarios where the UL data distribution depends on the LL optimization variable, and the LL data distribution also depends on the UL decision variable. We first establish sufficient conditions for the existence of performatively stable (PS) solutions in this class of bilevel problems. Also, we propose efficient stochastic algorithms to find the PS point with theoretical convergence rate analysis and discuss the theoretical optimality of the obtained solution. Our theoretical analysis is corroborated through a series of numerical experiments, wherein we evaluate the performance of the bilevel performative prediction algorithms alongside non-performative counterparts in the context of meta strategic learning problems.

Despite the great success of Transformer networks in various applications such as natural language processing and computer vision, their theoretical aspects are not well understood. In this paper, we study the approximation and estimation ability of Transformers as sequence-to-sequence functions with infinite dimensional inputs. Although inputs and outputs are both infinite dimensional, we show that when the target function has anisotropic smoothness, Transformers can avoid the curse of dimensionality due to their feature extraction ability and parameter sharing property. In addition, we show that even if the smoothness changes depending on each input, Transformers can estimate the importance of features for each input and extract important features dynamically. Then, we proved that Transformers achieve similar convergence rate as in the case of the fixed smoothness. Our theoretical results support the practical success of Transformers for high dimensional data.

This paper studies federated linear contextual bandits under the notion of user-level differential privacy (DP). We first introduce a unified federated bandits framework that can accommodate various definitions of DP in the sequential decision-making setting. We then formally introduce user-level central DP (CDP) and local DP (LDP) in the federated bandits framework, and investigate the fundamental trade-offs between the learning regrets and the corresponding DP guarantees in a federated linear contextual bandits model. For CDP, we propose a federated algorithm termed as $\texttt{ROBIN}$ and show that it is near-optimal in terms of the number of clients $M$ and the privacy budget $\varepsilon$ by deriving nearly-matching upper and lower regret bounds when user-level DP is satisfied. For LDP, we obtain several lower bounds, indicating that learning under user-level $(\varepsilon,\delta)$-LDP must suffer a regret blow-up factor at least $\min\{1/\varepsilon,M\}$ or $\min\{1/\sqrt{\varepsilon},\sqrt{M}\}$ under different conditions.

Algorithms for online learning typically require one or more boundedness assumptions: that the domain is bounded, that the losses are Lipschitz, or both. In this paper, we develop a new setting for online learning with unbounded domains and non-Lipschitz losses. For this setting we provide an algorithm which guarantees $R_{T}(u)\le \tilde O(G\|u\|\sqrt{T}+L\|u\|^{2}\sqrt{T})$ regret on any problem where the subgradients satisfy $\|g_{t}\|\le G+L\|w_{t}\|$, and show that this bound is unimprovable without further assumptions. We leverage this algorithm to develop new saddle-point optimization algorithms that converge in duality gap in unbounded domains, even in the absence of meaningful curvature. Finally, we provide the first algorithm achieving non-trivial dynamic regret in an unbounded domain for non-Lipschitz losses, as well as a matching lower bound. The regret of our dynamic regret algorithm automatically improves to a novel $L^{*}$ bound when the losses are smooth.

We consider online learning in multi-player smooth monotone games. Existing algorithms have limitations such as (1) being only applicable to strongly monotone games; (2) lacking the no-regret guarantee; (3) having only asymptotic or slow $\mathcal{O}(\frac{1}{\sqrt{T}})$ last-iterate convergence rate to a Nash equilibrium. While the $\mathcal{O}(\frac{1}{\sqrt{T}})$ rate is tight for a large class of algorithms including the well-studied extragradient algorithm and optimistic gradient algorithm, it is not optimal for all gradient-based algorithms. We propose the *accelerated optimistic gradient* (AOG) algorithm, the first doubly optimal no-regret learning algorithm for smooth monotone games. Namely, our algorithm achieves both (i) the optimal $\mathcal{O}(\sqrt{T})$ regret in the adversarial setting under smooth and convex loss functions and (ii) the optimal $\mathcal{O}(\frac{1}{T})$ last-iterate convergence rate to a Nash equilibrium in multi-player smooth monotone games. As a byproduct of the accelerated last-iterate convergence rate, we further show that each player suffers only an $\mathcal{O}(\log T)$ individual *worst-case dynamic regret*, providing an exponential improvement over the previous state-of-the-art $\mathcal{O}(\sqrt{T})$ bound.

Transformers are central to recent successes in natural language processing and computer vision. Transformers have a mostly uniform backbone where layers alternate between feed-forward and self-attention in order to build a deep network. Here we investigate this design choice and find that more complex blocks that have different permutations of layer primitives can be more efficient. Using this insight, we develop a complex block, named Brainformer, that consists of a diverse sets of layers such as sparsely gated feed-forward layers, dense feed-forward layers, attention layers, and various forms of layer normalization and activation functions. Brainformer consistently outperforms the state-of-the-art dense and sparse Transformers, in terms of both quality and efficiency. A Brainformer model with 8 billion activated parameters per token demonstrates 2x faster training convergence and 5x faster step time compared to its GLaM counterpart. In downstream task evaluation, Brainformer also demonstrates a 3% higher SuperGLUE score with fine-tuning compared to GLaM with a similar number of activated parameters. Finally, Brainformer largely outperforms a Primer dense model derived with NAS with similar computation per token on fewshot evaluations.

Sharpness of minima is a promising quantity that can correlate with generalization in deep networks and, when optimized during training, can improve generalization. However, standard sharpness is not invariant under reparametrizations of neural networks, and, to fix this, reparametrization-invariant sharpness definitions have been proposed, most prominently adaptive sharpness (Kwon et al., 2021). But does it really capture generalization in modern practical settings? We comprehensively explore this question in a detailed study of various definitions of adaptive sharpness in settings ranging from training from scratch on ImageNet and CIFAR-10 to fine-tuning CLIP on ImageNet and BERT on MNLI. We focus mostly on transformers for which little is known in terms of sharpness despite their widespread usage. Overall, we observe that sharpness does not correlate well with generalization but rather with some training parameters like the learning rate that can be positively or negatively correlated with generalization depending on the setup. Interestingly, in multiple cases, we observe a consistent negative correlation of sharpness with OOD generalization implying that sharper minima can generalize better. Finally, we illustrate on a simple model that the right sharpness measure is highly data-dependent, and that we do not understand well this aspect for realistic data distributions.

We consider a federated learning (FL) setting where a machine learning model with a fully connected first layer is trained between different clients and a central server using FedAvg, and where the aggregation step can be performed with secure aggregation (SA). We present SRATTA an attack relying only on aggregated models which, under realistic assumptions, (i) recovers data samples from the different clients, and (ii) groups data samples coming from the same client together. While sample recovery has already been explored in an FL setting, the ability to group samples per client, despite the use of SA, is novel. This poses a significant unforeseen security threat to FL and effectively breaks SA. We show that SRATTA is both theoretically grounded and can be used in practice on realistic models and datasets. We also propose counter-measures, and claim that clients should play an active role to guarantee their privacy during training.

Indiscriminate data poisoning attacks aim to decrease a model's test accuracy by injecting a small amount of corrupted training data. Despite significant interest, existing attacks remain relatively ineffective against modern machine learning (ML) architectures. In this work, we introduce the notion of model poisoning reachability as a technical tool to explore the intrinsic limits of data poisoning attacks towards target parameters (i.e., model-targeted attacks). We derive an easily computable threshold to establish and quantify a surprising phase transition phenomenon among popular ML models: data poisoning attacks can achieve certain target parameters only when the poisoning ratio exceeds our threshold. Building on existing parameter corruption attacks and refining the Gradient Canceling attack, we perform extensive experiments to confirm our theoretical findings, test the predictability of our transition threshold, and significantly improve existing indiscriminate data poisoning baselines over a range of datasets and models. Our work highlights the critical role played by the poisoning ratio, and sheds new insights on existing empirical results, attacks and mitigation strategies in data poisoning.

Although powerful graph neural networks (GNNs) have boosted numerous real-world applications, the potential privacy risk is still underexplored. To close this gap, we perform the first comprehensive study of graph reconstruction attack that aims to reconstruct the adjacency of nodes. We show that a range of factors in GNNs can lead to the surprising leakage of private links. Especially by taking GNNs as a Markov chain and attacking GNNs via a flexible chain approximation, we systematically explore the underneath principles of graph reconstruction attack, and propose two information theory-guided mechanisms: (1) the chain-based attack method with adaptive designs for extracting more private information; (2) the chain-based defense method that sharply reduces the attack fidelity with moderate accuracy loss. Such two objectives disclose a critical belief that to recover better in attack, you must extract more multi-aspect knowledge from the trained GNN; while to learn safer for defense, you must forget more link-sensitive information in training GNNs. Empirically, we achieve state-of-the-art results on six datasets and three common GNNs. The code is publicly available at: https://github.com/tmlr-group/MC-GRA.

Partial label learning (PLL) aims to train multiclass classifiers from the examples each annotated with a set of candidate labels where a fixed but unknown candidate label is correct. In the last few years, the instance-independent generation process of candidate labels has been extensively studied, on the basis of which many theoretical advances have been made in PLL. Nevertheless, the candidate labels are always instance-dependent in practice and there is no theoretical guarantee that the model trained on the instance-dependent PLL examples can converge to an ideal one. In this paper, a theoretically grounded and practically effective approach named POP, i.e. PrOgressive Purification for instance-dependent partial label learning, is proposed. Specifically, POP updates the learning model and purifies each candidate label set progressively in every epoch. Theoretically, we prove that POP enlarges the region appropriately fast where the model is reliable, and eventually approximates the Bayes optimal classifier with mild assumptions. Technically, POP is flexible with arbitrary PLL losses and could improve the performance of the previous PLL losses in the instance-dependent case. Experiments on the benchmark datasets and the real-world datasets validate the effectiveness of the proposed method.

In this paper, a unified framework for exploration in reinforcement learning (RL) is proposed based on an option-critic architecture. The proposed framework learns to integrate a set of diverse exploration strategies so that the agent can adaptively select the most effective exploration strategy to realize an effective exploration-exploitation trade-off for each given task. The effectiveness of the proposed exploration framework is demonstrated by various experiments in the MiniGrid and Atari environments.

We study the problem of generating diverse candidates in the context of Multi-Objective Optimization. In many applications of machine learning such as drug discovery and material design, the goal is to generate candidates which simultaneously optimize a set of potentially conflicting objectives. Moreover, these objectives are often imperfect evaluations of some underlying property of interest, making it important to generate diverse candidates to have multiple options for expensive downstream evaluations. We propose Multi-Objective GFlowNets (MOGFNs), a novel method for generating diverse Pareto optimal solutions, based on GFlowNets. We introduce two variants of MOGFNs: MOGFN-PC, which models a family of independent sub-problems defined by a scalarization function, with reward-conditional GFlowNets, and MOGFN-AL, which solves a sequence of sub-problems defined by an acquisition function in an active learning loop. Our experiments on wide variety of synthetic and benchmark tasks demonstrate advantages of the proposed methods in terms of the Pareto performance and importantly, improved candidate diversity, which is the main contribution of this work.

Health conditions among patients in intensive care units (ICUs) are monitored via electronic health records (EHRs), composed of numerical time series and lengthy clinical note sequences, both taken at $\textit{irregular}$ time intervals. Dealing with such irregularity in every modality, and integrating irregularity into multimodal representations to improve medical predictions, is a challenging problem. Our method first addresses irregularity in each single modality by (1) modeling irregular time series by dynamically incorporating hand-crafted imputation embeddings into learned interpolation embeddings via a gating mechanism, and (2) casting a series of clinical note representations as multivariate irregular time series and tackling irregularity via a time attention mechanism. We further integrate irregularity in multimodal fusion with an interleaved attention mechanism across temporal steps. To the best of our knowledge, this is the first work to thoroughly model irregularity in multimodalities for improving medical predictions. Our proposed methods for two medical prediction tasks consistently outperforms state-of-the-art (SOTA) baselines in each single modality and multimodal fusion scenarios. Specifically, we observe relative improvements of 6.5%, 3.6%, and 4.3% in F1 for time series, clinical notes, and multimodal fusion, respectively. These results demonstrate the effectiveness of our methods and the importance of considering irregularity in multimodal EHRs.

We consider the problem of generating musical soundtracks in sync with rhythmic visual cues. Most existing works rely on pre-defined music representations, leading to the incompetence of generative flexibility and complexity. Other methods directly generating video-conditioned waveforms suffer from limited scenarios, short lengths, and unstable generation quality. To this end, we present Long-Term Rhythmic Video Soundtracker (LORIS), a novel framework to synthesize long-term conditional waveforms. Specifically, our framework consists of a latent conditional diffusion probabilistic model to perform waveform synthesis. Furthermore, a series of context-aware conditioning encoders are proposed to take temporal information into consideration for a long-term generation. Notably, we extend our model's applicability from dances to multiple sports scenarios such as floor exercise and figure skating. To perform comprehensive evaluations, we establish a benchmark for rhythmic video soundtracks including the pre-processed dataset, improved evaluation metrics, and robust generative baselines. Extensive experiments show that our model generates long-term soundtracks with state-of-the-art musical quality and rhythmic correspondence. Codes are available at https://github.com/OpenGVLab/LORIS.

Concept shift is a prevailing problem in natural tasks like medical image segmentation where samples usually come from different subpopulations with variant correlations between features and labels. One common type of concept shift in medical image segmentation is the "information imbalance" between label-sparse samples with few (if any) segmentation labels and label-dense samples with plentiful labeled pixels. Existing distributionally robust algorithms have focused on adaptively truncating/down-weighting the "less informative" (i.e., label-sparse in our context) samples. To exploit data features of label-sparse samples more efficiently, we propose an adaptively weighted online optimization algorithm --- AdaWAC --- to incorporate data augmentation consistency regularization in sample reweighting. Our method introduces a set of trainable weights to balance the supervised loss and unsupervised consistency regularization of each sample separately. At the saddle point of the underlying objective, the weights assign label-dense samples to the supervised loss and label-sparse samples to the unsupervised consistency regularization. We provide a convergence guarantee by recasting the optimization as online mirror descent on a saddle point problem. Our empirical results demonstrate that AdaWAC not only enhances the segmentation performance and sample efficiency but also improves the robustness to concept shift on various medical image segmentation tasks with different UNet-style backbones.

Neural network approaches for meta-learning distributions over functions have desirable properties such as increased flexibility and a reduced complexity of inference. Building on the successes of denoising diffusion models for generative modelling, we propose Neural Diffusion Processes (NDPs), a novel approach that learns to sample from a rich distribution over functions through its finite marginals. By introducing a custom attention block we are able to incorporate properties of stochastic processes, such as exchangeability, directly into the NDP's architecture. We empirically show that NDPs can capture functional distributions close to the true Bayesian posterior, demonstrating that they can successfully emulate the behaviour of Gaussian processes and surpass the performance of neural processes. NDPs enable a variety of downstream tasks, including regression, implicit hyperparameter marginalisation, non-Gaussian posterior prediction and global optimisation.

Estimating the effects of multi-dimensional treatments (i.e., joint treatment effects) is critical in many data-intensive domains, including genetics and drug evaluation. The main challenges for studying the joint treatment effects include the need for large sample sizes to explore different treatment combinations as well as potentially unsafe treatment interactions. In this paper, we develop machinery for estimating joint treatment effects by combining data from multiple experimental datasets. In particular, first, we develop new identification conditions for determining whether a joint treatment effect can be computed in terms of multiple interventional distributions under various scenarios. Further, we develop estimators with statistically appealing properties, including consistency and robustness to model misspecification and slow convergence. Finally, we perform simulation studies, which corroborate the effectiveness of the proposed methods.

We propose a new class of online learning algorithms, generalized implicit Follow-The-Regularized-Leader (FTRL), that expands the scope of FTRL framework. Generalized implicit FTRL can recover known algorithms, such as FTRL with linearized losses and implicit FTRL, and it allows the design of new update rules, as extensions of aProx and Mirror-Prox to FTRL. Our theory is constructive in the sense that it provides a simple unifying framework to design updates that directly improve the worst-case upper bound on the regret. The key idea is substituting the linearization of the losses with a Fenchel-Young inequality. We show the flexibility of the framework by proving that some known algorithms, like the Mirror-Prox updates, are instantiations of the generalized implicit FTRL. Finally, the new framework allows us to recover the temporal variation bound of implicit OMD, with the same computational complexity.

Large language models (LLMs) have demonstrated an impressive ability to perform arithmetic and symbolic reasoning tasks, when provided with a few examples at test time ("few-shot prompting"). Much of this success can be attributed to prompting methods such as "chain-of-thought", which employ LLMs for both understanding the problem description by decomposing it into steps, as well as solving each step of the problem. While LLMs seem to be adept at this sort of step-by-step decomposition, LLMs often make logical and arithmetic mistakes in the solution part, even when the problem is decomposed correctly. In this paper, we present Program-Aided Language models (PAL): a novel approach that uses the LLM to read natural language problems and generate programs as the intermediate reasoning steps, but offloads the solution step to a runtime such as a Python interpreter. With PAL, decomposing the natural language problem into runnable steps remains the only learning task for the LLM, while solving is delegated to the interpreter. We demonstrate this synergy between a neural LLM and a symbolic interpreter across 13 mathematical, symbolic, and algorithmic reasoning tasks from BIG-Bench Hard and others. In all these natural language reasoning tasks, generating code using an LLM and reasoning using a Python interpreter leads to more accurate results than much larger models. For example, PAL using Codex achieves state-of-the-art few-shot accuracy on GSM8K, surpassing PaLM which uses chain-of-thought by absolute 15% top-1.

We present a framework for using transformer networks as universal computers by programming them with specific weights and placing them in a loop. Our input sequence acts as a punchcard, consisting of instructions and memory for data read/writes. We demonstrate that a constant number of encoder layers can emulate basic computing blocks, including lexicographic operations, non-linear functions, function calls, program counters, and conditional branches. Using this framework, we emulate a computer using a simple instruction-set architecture, which allows us to map iterative algorithms to programs that can be executed by a constant depth looped transformer network. We show how a single frozen transformer, instructed by its input, can emulate a basic calculator, a basic linear algebra library, and even a full backpropagation, in-context learning algorithm. Our findings reveal the potential of transformer networks as programmable compute units and offer insight into the mechanics of attention.

Likelihood-free inference (LFI) is a set of techniques for inference in implicit statistical models. A longstanding question in LFI has been how to design or learn good summary statistics of data, but this might now seem unnecessary due to the advent of recent end-to-end (i.e. neural network-based) LFI methods. In this work, we rethink this question with a new method for learning summary statistics. We show that learning sufficient statistics may be easier than direct posterior inference, as the former problem can be reduced to a set of low-dimensional, easy-to-solve learning problems. This suggests us to explicitly decouple summary statistics learning from posterior inference in LFI. Experiments on diverse inference tasks with different data types validate our hypothesis.

Hypersphere classification is a classical and foundational method that can provide easy-to-process explanations for the classification of real-valued as well as binary data. However, obtaining an (ideally concise) explanation via hypersphere classification is much more difficult when dealing with binary data as opposed to real-valued data. In this paper, we perform the first complexity-theoretic study of the hypersphere classification problem for binary data. We use the fine-grained parameterized complexity paradigm to analyze the impact of structural properties that may be present in the input data as well as potential conciseness constraints. Our results include not only stronger lower bounds but also a number of new fixed-parameter algorithms for hypersphere classification of binary data, which can find an exact and concise explanation when one exists.

The higher-order correlation clustering problem is an expressive model, and recently, local search heuristics have been proposed for several applications. Certifying optimality, however, is NP-hard and practically hampered already by the complexity of the problem statement. Here, we focus on establishing partial optimality conditions for the special case of complete graphs and cubic objective functions. In addition, we define and implement algorithms for testing these conditions and examine their effect numerically, on two datasets.

Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is quasar-convexity, a non-convex generalization of convexity that subsumes convex functions. Existing algorithms for minimizing quasar-convex functions in the stochastic setting have either high complexity or slow convergence, which prompts us to derive a new class of stochastic methods for optimizing smooth quasar-convex functions. We demonstrate that our algorithms have fast convergence and outperform existing algorithms on several examples, including the classical problem of learning linear dynamical systems. We also present a unified analysis of our newly proposed algorithms and a previously studied deterministic algorithm.

The average reward criterion is relatively less studied as most existing works in the Reinforcement Learning literature consider the discounted reward criterion. There are few recent works that present on-policy average reward actor-critic algorithms, but average reward off-policy actor-critic is relatively less explored. In this work, we present both on-policy and off-policy deterministic policy gradient theorems for the average reward performance criterion. Using these theorems, we also present an Average Reward Off-Policy Deep Deterministic Policy Gradient (ARO-DDPG) Algorithm. We first show asymptotic convergence analysis using the ODE-based method. Subsequently, we provide a finite time analysis of the resulting stochastic approximation scheme with linear function approximator and obtain an $\epsilon$-optimal stationary policy with a sample complexity of $\Omega(\epsilon^{-2.5})$. We compare the average reward performance of our proposed ARO-DDPG algorithm and observe better empirical performance compared to state-of-the-art on-policy average reward actor-critic algorithms over MuJoCo-based environments.

We study a variation of vanilla stochastic gradient descent where the optimizer only has access to a Markovian sampling scheme. These schemes encompass applications that range from decentralized optimization with a random walker (token algorithms), to RL and online system identification problems. We focus on obtaining rates of convergence under the least restrictive assumptions possible on the underlying Markov chain and on the functions optimized. We first unveil the theoretical lower bound for methods that sample stochastic gradients along the path of a Markov chain, making appear a dependency in the hitting time of the underlying Markov chain. We then study Markov chain SGD (MC-SGD) under much milder regularity assumptions than prior works. We finally introduce MC-SAG, an alternative to MC-SGD with variance reduction, that only depends on the hitting time of the Markov chain, therefore obtaining a communication-efficient token algorithm.

Learning in MDPs with highly complex state representations is currently possible due to multiple advancements in reinforcement learning algorithm design. However, this incline in complexity, and furthermore the increase in the dimensions of the observation came at the cost of volatility that can be taken advantage of via adversarial attacks (i.e. moving along worst-case directions in the observation space). To solve this policy instability problem we propose a novel method to detect the presence of these non-robust directions via local quadratic approximation of the deep neural policy loss. Our method provides a theoretical basis for the fundamental cut-off between safe observations and adversarial observations. Furthermore, our technique is computationally efficient, and does not depend on the methods used to produce the worst-case directions. We conduct extensive experiments in the Arcade Learning Environment with several different adversarial attack techniques. Most significantly, we demonstrate the effectiveness of our approach even in the setting where non-robust directions are explicitly optimized to circumvent our proposed method.

Moment restrictions and their conditional counterparts emerge in many areas of machine learning and statistics ranging from causal inference to reinforcement learning. Estimators for these tasks, generally called methods of moments, include the prominent generalized method of moments (GMM) which has recently gained attention in causal inference. GMM is a special case of the broader family of empirical likelihood estimators which are based on approximating a population distribution by means of minimizing a $\varphi$-divergence to an empirical distribution. However, the use of $\varphi$-divergences effectively limits the candidate distributions to reweightings of the data samples. We lift this long-standing limitation and provide a method of moments that goes beyond data reweighting. This is achieved by defining an empirical likelihood estimator based on maximum mean discrepancy which we term the kernel method of moments (KMM). We provide a variant of our estimator for conditional moment restrictions and show that it is asymptotically first-order optimal for such problems. Finally, we show that our method achieves competitive performance on several conditional moment restriction tasks.

We propose to minimize a generic differentiable objective with $L_1$ constraint using a simple reparametrization and straightforward stochastic gradient descent. Our proposal is the direct generalization of previous ideas that the $L_1$ penalty may be equivalent to a differentiable reparametrization with weight decay. We prove that the proposed method, spred, is an exact differentiable solver of $L_1$ and that the reparametrization trick is completely ``benign" for a generic nonconvex function. Practically, we demonstrate the usefulness of the method in (1) training sparse neural networks to perform gene selection tasks, which involves finding relevant features in a very high dimensional space, and (2) neural network compression task, to which previous attempts at applying the $L_1$-penalty have been unsuccessful. Conceptually, our result bridges the gap between the sparsity in deep learning and conventional statistical learning.

Graph neural networks (GNNs) achieve remarkable performance in graph machine learning tasks but can be hard to train on large-graph data, where their learning dynamics are not well understood. We investigate the training dynamics of large-graph GNNs using graph neural tangent kernels (GNTKs) and graphons. In the limit of large width, optimization of an overparametrized NN is equivalent to kernel regression on the NTK. Here, we investigate how the GNTK evolves as another independent dimension is varied: the graph size. We use graphons to define limit objects---graphon NNs for GNNs, and graphon NTKs for GNTKs---, and prove that, on a sequence of graphs, the GNTKs converge to the graphon NTK. We further prove that the spectrum of the GNTK, which is related to the problem's learning directions, converges to the spectrum of the GNTK. This implies that in the large-graph limit, the GNTK fitted on a graph of moderate size can be used to solve the same task on the large graph, and to infer the learning dynamics of the large-graph GNN. These results are verified empirically on node regression and classification tasks.

It is desirable for statistical models to detect signals of interest independently of their position. If the data is generated by some smooth process, this additional structure should be taken into account. We introduce a new class of neural networks that are shift invariant and preserve smoothness of the data: functional neural networks (FNNs). For this, we use methods from functional data analysis (FDA) to extend multi-layer perceptrons and convolutional neural networks to functional data. We propose different model architectures, show that the models outperform a benchmark model from FDA in terms of accuracy and successfully use FNNs to classify electroencephalography (EEG) data.

Neural Posterior Estimation methods for simulation-based inference can be ill-suited for dealing with posterior distributions obtained by conditioning on multiple observations, as they tend to require a large number of simulator calls to learn accurate approximations. In contrast, Neural Likelihood Estimation methods can handle multiple observations at inference time after learning from individual observations, but they rely on standard inference methods, such as MCMC or variational inference, which come with certain performance drawbacks. We introduce a new method based on conditional score modeling that enjoys the benefits of both approaches. We model the scores of the (diffused) posterior distributions induced by individual observations, and introduce a way of combining the learned scores to approximately sample from the target posterior distribution. Our approach is sample-efficient, can naturally aggregate multiple observations at inference time, and avoids the drawbacks of standard inference methods.

Source separation involves the ill-posed problem of retrieving a set of source signals that have been observed through a mixing operator. Solving this problem requires prior knowledge, which is commonly incorporated by imposing regularity conditions on the source signals, or implicitly learned through supervised or unsupervised methods from existing data. While data-driven methods have shown great promise in source separation, they often require large amounts of data, which rarely exists in planetary space missions. To address this challenge, we propose an unsupervised source separation scheme for domains with limited data access that involves solving an optimization problem in the wavelet scattering covariance representation space---an interpretable, low-dimensional representation of stationary processes. We present a real-data example in which we remove transient, thermally-induced microtilts---known as glitches---from data recorded by a seismometer during NASA's InSight mission on Mars. Thanks to the wavelet scattering covariances' ability to capture non-Gaussian properties of stochastic processes, we are able to separate glitches using only a few glitch-free data snippets.

Decision-based attacks construct adversarial examples against a machine learning (ML) model by making only hard-label queries. These attacks have mainly been applied directly to standalone neural networks. However, in practice, ML models are just one component of a larger learning system. We find that by adding a single preprocessor in front of a classifier, state-of-the-art query-based attacks are up to seven× less effective at attacking a prediction pipeline than at attacking the model alone. We explain this discrepancy by the fact that most preprocessors introduce some notion of invariance to the input space. Hence, attacks that are unaware of this invariance inevitably waste a large number of queries to re-discover or overcome it. We, therefore, develop techniques to (i) reverse-engineer the preprocessor and then (ii) use this extracted information to attack the end-to-end system. Our preprocessors extraction method requires only a few hundred queries, and our preprocessor-aware attacks recover the same efficacy as when attacking the model alone. The code can be found at https://github.com/google-research/preprocessor-aware-black-box-attack.

The primary goal in recommendation is to suggest relevant content to users, but optimizing for accuracy often results in recommendations that lack diversity. To remedy this, conventional approaches such as re-ranking improve diversity by presenting more diverse items. Here we argue that to promote inherent and prolonged diversity, the system must encourage its creation. Towards this, we harness the performative nature of recommendation, and show how learning can incentivize strategic content creators to create diverse content. Our approach relies on a novel form of regularization that anticipates strategic changes to content, and penalizes for content homogeneity. We provide analytic and empirical results that demonstrate when and how diversity can be incentivized, and experimentally demonstrate the utility of our approach on synthetic and semi-synthetic data.

Machine learning models frequently experience performance drops under distribution shifts. The underlying cause of such shifts may be multiple simultaneous factors such as changes in data quality, differences in specific covariate distributions, or changes in the relationship between label and features. When a model does fail during deployment, attributing performance change to these factors is critical for the model developer to identify the root cause and take mitigating actions. In this work, we introduce the problem of attributing performance differences between environments to distribution shifts in the underlying data generating mechanisms. We formulate the problem as a cooperative game where the players are distributions. We define the value of a set of distributions to be the change in model performance when only this set of distributions has changed between environments, and derive an importance weighting method for computing the value of an arbitrary set of distributions. The contribution of each distribution to the total performance change is then quantified as its Shapley value. We demonstrate the correctness and utility of our method on synthetic, semi-synthetic, and real-world case studies, showing its effectiveness in attributing performance changes to a wide range of distribution shifts.

This article introduces a novel structured random matrix composed blockwise from subsampled randomized Hadamard transforms (SRHTs). The block SRHT is expected to outperform well-known dimension reduction maps, including SRHT and Gaussian matrices on distributed architectures. We prove that a block SRHT with enough rows is an oblivious subspace embedding, i.e., an approximate isometry for an arbitrary low-dimensional subspace with high probability. Our estimate of the required number of rows is similar to that of the standard SRHT. This suggests that the two transforms should provide the same accuracy of approximation in the algorithms. The block SRHT can be readily incorporated into randomized methods for computing a low-rank approximation of a large-scale matrix, such as the Nyström method. For completeness, we revisit this method with a discussion of its implementation on distributed architectures.

Despite the significant recent progress in deep generative models, the underlying structure of their latent spaces is still poorly understood, thereby making the task of performing semantically meaningful latent traversals an open research challenge. Most prior work has aimed to solve this challenge by modeling latent structures linearly, and finding corresponding linear directions which result in `disentangled' generations. In this work, we instead propose to model latent structures with a learned dynamic potential landscape, thereby performing latent traversals as the flow of samples down the landscape's gradient. Inspired by physics, optimal transport, and neuroscience, these potential landscapes are learned as physically realistic partial differential equations, thereby allowing them to flexibly vary over both space and time. To achieve disentanglement, multiple potentials are learned simultaneously, and are constrained by a classifier to be distinct and semantically self-consistent. Experimentally, we demonstrate that our method achieves both more qualitatively and quantitatively disentangled trajectories than state-of-the-art baselines. Further, we demonstrate that our method can be integrated as a regularization term during training, thereby acting as an inductive bias towards the learning of structured representations, ultimately improving model likelihood on similarly structured data. Code is available at https://github.com/KingJamesSong/PDETraversal.

We study the problem of convergence to a stationary point in zero-sum games. We propose competitive gradient optimization (CGO), a gradient-based method that incorporates the interactions between two players in zero-sum games for its iterative updates. We provide a continuous-time analysis of CGO and its convergence properties while showing that in the continuous limit, previous methods degenerate to their gradient descent ascent (GDA) variants. We further provide a rate of convergence to stationary points in the discrete-time setting. We propose a generalized class of $\alpha$-coherent functions and show that for strictly $\alpha$-coherent functions, CGO ensures convergence to a saddle point. Moreover, we propose optimistic CGO (oCGO), an optimistic variant, for which we show a convergence rate of $O(\frac{1}{n})$ to saddle points for $\alpha$-coherent functions.

We study the problem of temporal-difference-based policy evaluation in reinforcement learning. In particular, we analyse the use of a distributional reinforcement learning algorithm, quantile temporal-difference learning (QTD), for this task. We reach the surprising conclusion that even if a practitioner has no interest in the return distribution beyond the mean, QTD (which learns predictions about the full distribution of returns) may offer performance superior to approaches such as classical TD learning, which predict only the mean return, even in the tabular setting.

Transformer-based detection and segmentation methods use a list of learned detection queries to retrieve information from the transformer network and learn to predict the location and category of one specific object from each query. We empirically find that random convex combinations of the learned queries are still good for the corresponding models. We then propose to learn a convex combination with dynamic coefficients based on the high-level semantics of the image. The generated dynamic queries, named as modulated queries, better capture the prior of object locations and categories in the different images. Equipped with our modulated queries, a wide range of DETR-based models achieve consistent and superior performance across multiple tasks (object detection, instance segmentation, panoptic segmentation) and on different benchmarks (MS COCO, CityScapes, YoutubeVIS).

Foundation models have shown impressive adaptation and scalability in supervised and self-supervised learning problems, but so far these successes have not fully translated to reinforcement learning (RL). In this work, we demonstrate that training an RL agent at scale leads to a general in-context learning algorithm that can adapt to open-ended novel embodied 3D problems as quickly as humans. In a vast space of held-out environment dynamics, our adaptive agent (AdA) displays on-the-fly hypothesis-driven exploration, efficient exploitation of acquired knowledge, and can successfully be prompted with first-person demonstrations. Adaptation emerges from three ingredients: (1) meta-reinforcement learning across a vast, smooth and diverse task distribution, (2) a policy parameterised as a large-scale attention-based memory architecture, and (3) an effective automated curriculum that prioritises tasks at the frontier of an agent's capabilities. We demonstrate characteristic scaling laws with respect to network size, memory length, and richness of the training task distribution. We believe our results lay the foundation for increasingly general and adaptive RL agents that perform well across ever-larger open-ended domains.

We study the gradients of a maxout network with respect to inputs and parameters and obtain bounds for the moments depending on the architecture and the parameter distribution. We observe that the distribution of the input-output Jacobian depends on the input, which complicates a stable parameter initialization. Based on the moments of the gradients, we formulate parameter initialization strategies that avoid vanishing and exploding gradients in wide networks. Experiments with deep fully-connected and convolutional networks show that this strategy improves SGD and Adam training of deep maxout networks. In addition, we obtain refined bounds on the expected number of linear regions, results on the expected curve length distortion, and results on the NTK.

Disentangling the factors of variation in data is a fundamental concept in machine learning and has been studied in various ways by different researchers, leading to a multitude of definitions. Despite the numerous empirical studies, more theoretical research is needed to fully understand the defining properties of disentanglement and how different definitions relate to each other. This paper presents a meta-analysis of existing definitions of disentanglement, using category theory as a unifying and rigorous framework. We propose that the concepts of the cartesian and monoidal products should serve as the core of disentanglement. With these core concepts, we show the similarities and crucial differences in dealing with (i) functions, (ii) equivariant maps, (iii) relations, and (iv) stochastic maps. Overall, our meta-analysis deepens our understanding of disentanglement and its various formulations and can help researchers navigate different definitions and choose the most appropriate one for their specific context.

We study single-machine scheduling of jobs, each belonging to a job type that determines its duration distribution. We start by analyzing the scenario where the type characteristics are known and then move to two learning scenarios where the types are unknown: non-preemptive problems, where each started job must be completed before moving to another job; and preemptive problems, where job execution can be paused in the favor of moving to a different job. In both cases, we design algorithms that achieve sublinear excess cost, compared to the performance with known types, and prove lower bounds for the non-preemptive case. Notably, we demonstrate, both theoretically and through simulations, how preemptive algorithms can greatly outperform non-preemptive ones when the durations of different job types are far from one another, a phenomenon that does not occur when the type durations are known.

Adversarial attacks in reinforcement learning (RL) often assume highly-privileged access to the victim’s parameters, environment, or data. Instead, this paper proposes a novel adversarial setting called a Cheap Talk MDP in which an Adversary can merely append deterministic messages to the Victim’s observation, resulting in a minimal range of influence. The Adversary cannot occlude ground truth, influence underlying environment dynamics or reward signals, introduce non-stationarity, add stochasticity, see the Victim’s actions, or access their parameters. Additionally, we present a simple meta-learning algorithm called Adversarial Cheap Talk (ACT) to train Adversaries in this setting. We demonstrate that an Adversary trained with ACT can still significantly influence the Victim’s training and testing performance, despite the highly constrained setting. Affecting train-time performance reveals a new attack vector and provides insight into the success and failure modes of existing RL algorithms. More specifically, we show that an ACT Adversary is capable of harming performance by interfering with the learner’s function approximation, or instead helping the Victim’s performance by outputting useful features. Finally, we show that an ACT Adversary can manipulate messages during train-time to directly and arbitrarily control the Victim at test-time.

We address the problem of stably and efficiently training a deep neural network robust to adversarial perturbations bounded by an $l_1$ norm. We demonstrate that achieving robustness against $l_1$-bounded perturbations is more challenging than in the $l_2$ or $l_\infty$ cases, because adversarial training against $l_1$-bounded perturbations is more likely to suffer from catastrophic overfitting and yield training instabilities. Our analysis links these issues to the coordinate descent strategy used in existing methods. We address this by introducing Fast-EG-$l_1$, an efficient adversarial training algorithm based on Euclidean geometry and free of coordinate descent. Fast-EG-$l_1$ comes with no additional memory costs and no extra hyper-parameters to tune. Our experimental results on various datasets demonstrate that Fast-EG-$l_1$ yields the best and most stable robustness against $l_1$-bounded adversarial attacks among the methods of comparable computational complexity. Code and the checkpoints are available at https://github.com/IVRL/FastAdvL.

To mitigate the privacy leakages and communication burdens of Federated Learning (FL), decentralized FL (DFL) discards the central server and each client only communicates with its neighbors in a decentralized communication network. However, existing DFL suffers from high inconsistency among local clients, which results in severe distribution shift and inferior performance compared with centralized FL (CFL), especially on heterogeneous data or sparse communication topologies. To alleviate this issue, we propose two DFL algorithms named DFedSAM and DFedSAM-MGS to improve the performance of DFL. Specifically, DFedSAM leverages gradient perturbation to generate local flat models via Sharpness Aware Minimization (SAM), which searches for models with uniformly low loss values. DFedSAM-MGS further boosts DFedSAM by adopting Multiple Gossip Steps (MGS) for better model consistency, which accelerates the aggregation of local flat models and better balances communication complexity and generalization. Theoretically, we present improved convergence rates $\small \mathcal{O}\big(\frac{1}{\sqrt{KT}}+\frac{1}{T}+\frac{1}{K^{1/2}T^{3/2}(1-\lambda)^2}\big)$ and $\small \mathcal{O}\big(\frac{1}{\sqrt{KT}}+\frac{1}{T}+\frac{\lambda^Q+1}{K^{1/2}T^{3/2}(1-\lambda^Q)^2}\big)$ in non-convex setting for DFedSAM and DFedSAM-MGS, respectively, where $1-\lambda$ is the spectral gap of gossip matrix and $Q$ is the number of MGS. Empirically, our methods can achieve competitive performance compared with CFL methods and outperform existing DFL methods.

This paper considers the unlabeled sparse recovery under multiple measurements, i.e., ${\mathbf{Y}} = {\mathbf{\Pi}}^{\natural} {\mathbf{X}} {\mathbf{B}}^{\natural} + {\mathbf{W}}$, where ${\mathbf{Y}} \in \mathbb{R}^{n\times m}, {\mathbf{\Pi}}^{\natural}\in \mathbb{R}^{n\times n}, {\mathbf{X}} \in \mathbb{R}^{n\times p}, {\mathbf{B}} ^{\natural}\in \mathbb{R}^{p\times m}, {\mathbf{W}}\in \mathbb{R}^{n\times m}$ represents the observations, missing (or incomplete) correspondence information, sensing matrix, sparse signals, and additive sensing noise, respectively. Different from the previous works on multiple measurements ($m > 1$) which all focus on the sufficient samples regime, namely, $n > p$, we consider a sparse matrix $\mathbf{B}^{\natural}$ and investigate the insufficient samples regime (i.e., $n \ll p$) for the first time. To begin with, we establish the lower bound on the sample number and *signal-to-noise ratio* ($ {\mathsf{SNR}}$) for the correct permutation recovery. Moreover, we present a simple yet effective estimator. Under mild conditions, we show that our estimator can restore the correct correspondence information with high probability. Numerical experiments are presented to corroborate our theoretical claims.

Randomized smoothing is a popular method to certify robustness of image classifiers to adversarial input perturbations. It is the only certification technique which scales directly to datasets of higher dimension such as ImageNet. However, current techniques are not able to utilize the fact that any adversarial example has to lie in the image space, that is $[0,1]^d$; otherwise, one can trivially detect it. To address this suboptimality, we derive new certification formulae which lead to significant improvements in the certified $\ell_1$-robustness without the need of adapting the classifiers or change of smoothing distributions. The code is released at https://github.com/vvoracek/L1-smoothing

Although data diffusion embeddings are ubiquitous in unsupervised learning and have proven to be a viable technique for uncovering the underlying intrinsic geometry of data, diffusion embeddings are inherently limited due to their discrete nature. To this end, we propose neural FIM, a method for computing the Fisher information metric (FIM) from point cloud data - allowing for a continuous manifold model for the data. Neural FIM creates an extensible metric space from discrete point cloud data such that information from the metric can inform us of manifold characteristics such as volume and geodesics. We demonstrate Neural FIM's utility in selecting parameters for the PHATE visualization method as well as its ability to obtain information pertaining to local volume illuminating branching points and cluster centers embeddings of a toy dataset and two single-cell datasets of IPSC reprogramming and PBMCs (immune cells).

Evidential deep learning, built upon belief theory and subjective logic, offers a principled and computationally efficient way to turn a deterministic neural network uncertainty-aware. The resultant evidential models can quantify fine-grained uncertainty using the learned evidence. To ensure theoretically sound evidential models, the evidence needs to be non-negative, which requires special activation functions for model training and inference. This constraint often leads to inferior predictive performance compared to standard softmax models, making it challenging to extend them to many large-scale datasets. To unveil the real cause of this undesired behavior, we theoretically investigate evidential models and identify a fundamental limitation that explains the inferior performance: existing evidential activation functions create zero evidence regions, which prevent the model to learn from training samples falling into such regions. A deeper analysis of evidential activation functions based on our theoretical underpinning inspires the design of a novel regularizer that effectively alleviates this fundamental limitation. Extensive experiments over many challenging real-world datasets and settings confirm our theoretical findings and demonstrate the effectiveness of our proposed approach.

Differentiable Search Index is a recently proposed paradigm for document retrieval, that encodes information about a corpus of documents within the parameters of a neural network and directly maps queries to corresponding documents. These models have achieved state-of-the-art performances for document retrieval across many benchmarks. These kinds of models have a significant limitation: it is not easy to add new documents after a model is trained. We propose IncDSI, a method to add documents in real time (about 20-50ms per document), without retraining the model on the entire dataset (or even parts thereof). Instead we formulate the addition of documents as a constrained optimization problem that makes minimal changes to the network parameters. Although orders of magnitude faster, our approach is competitive with re-training the model on the whole dataset and enables the development of document retrieval systems that can be updated with new information in real-time. Our code for IncDSI is available at https://github.com/varshakishore/IncDSI.

Graph Neural Networks (GNNs) are popular models for graph learning problems. GNNs show strong empirical performance in many practical tasks. However, the theoretical properties have not been completely elucidated. In this paper, we investigate whether GNNs can exploit the graph structure from the perspective of the expressive power of GNNs. In our analysis, we consider graph generation processes that are controlled by hidden (or latent) node features, which contain all information about the graph structure. A typical example of this framework is kNN graphs constructed from the hidden features. In our main results, we show that GNNs can recover the hidden node features from the input graph alone, even when all node features, including the hidden features themselves and any indirect hints, are unavailable. GNNs can further use the recovered node features for downstream tasks. These results show that GNNs can fully exploit the graph structure by themselves, and in effect, GNNs can use both the hidden and explicit node features for downstream tasks. In the experiments, we confirm the validity of our results by showing that GNNs can accurately recover the hidden features using a GNN architecture built based on our theoretical analysis.

Quantization methods reduce the number of bits required to represent each parameter in a model, trading accuracy for smaller memory footprints and inference latencies. However, the final model size depends on both the number of parameters of the original model and the rate of compression. For example, a 30B 8-bit model and a 60B 4-bit model have the same number of bits but may have very different zero-shot accuracies. In this work, we study this trade-off by developing inference scaling laws of zero-shot performance in Large Language Models (LLMs) to determine the bit-precision and model size that maximizes zero-shot performance. We run more than 35,000 experiments with 16-bit inputs and k-bit parameters to examine which zero-shot quantization methods improve scaling for 3 to 8-bit precision at scales of 19M to 176B parameters across the LLM families BLOOM, OPT, NeoX/Pythia, and GPT-2. We find that it is challenging to improve the bit-level scaling trade-off, with the only improvements being the use of a small block size -- splitting the parameters into small independently quantized blocks -- and the quantization data type being used (e.g., Int vs Float). Overall, our findings show that 4-bit precision is almost universally optimal for total model bits and zero-shot accuracy.

Universality is a key hypothesis in mechanistic interpretability -- that different models learn similar features and circuits when trained on similar tasks. In this work, we study the universality hypothesis by examining how small networks learn to implement group compositions. We present a novel algorithm by which neural networks may implement composition for any finite group via mathematical representation theory. We then show that these networks consistently learn this algorithm by reverse engineering model logits and weights, and confirm our understanding using ablations. By studying networks trained on various groups and architectures, we find mixed evidence for universality: using our algorithm, we can completely characterize the family of circuits and features that networks learn on this task, but for a given network the precise circuits learned -- as well as the order they develop -- are arbitrary.

Graph generative models become increasingly effective for data distribution approximation and data augmentation. While they have aroused public concerns about their malicious misuses or misinformation broadcasts, just as what Deepfake visual and auditory media has been delivering to society. Hence it is essential to regulate the prevalence of generated graphs. To tackle this problem, we pioneer the formulation of the generated graph detection problem to distinguish generated graphs from real ones. We propose the first framework to systematically investigate a set of sophisticated models and their performance in four classification scenarios. Each scenario switches between seen and unseen datasets/generators during testing to get closer to real-world settings and progressively challenge the classifiers. Extensive experiments evidence that all the models are qualified for generated graph detection, with specific models having advantages in specific scenarios. Resulting from the validated generality and oblivion of the classifiers to unseen datasets/generators, we draw a safe conclusion that our solution can sustain for a decent while to curb generated graph misuses.

We present Language-Image Value learning (LIV), a unified objective for vision-language representation and reward learning from action-free videos with text annotations. Exploiting a novel connection between dual reinforcement learning and mutual information contrastive learning, the LIV objective trains a multi-modal representation that implicitly encodes a universal value function for tasks specified as language or image goals. We use LIV to pre-train the first control-centric vision-language representation from large human video datasets such as EpicKitchen. Given only a language or image goal, the pre-trained LIV model can assign dense rewards to each frame in videos of unseen robots or humans attempting that task in unseen environments. Further, when some target domain-specific data is available, the same objective can be used to fine-tune and improve LIV and even other pre-trained representations for robotic control and reward specification in that domain. In our experiments on several simulated and real-world robot environments, LIV models consistently outperform the best prior input state representations for imitation learning, as well as reward specification methods for policy synthesis. Our results validate the advantages of joint vision-language representation and reward learning within the unified, compact LIV framework.

We describe PromptBoosting, a query-efficient procedure for building a text classifier from a neural language model (LM) without access to the LM's parameters, gradients, or hidden representations. This form of "black-box" classifier training has become increasingly important as the cost of training and inference in large-scale LMs has grown. But existing black-box LM classifier learning approaches are themselves computationally inefficient, typically specializing LMs to the target task by searching in a large space of (discrete or continuous) prompts using zeroth-order optimization methods. Instead of directly optimizing in prompt space, PromptBoosting obtains a small pool of prompts via a gradient-free approach and then constructs a large pool of weak learners by pairing these prompts with different elements of the LM's output distribution. These weak learners are then ensembled using the AdaBoost algorithm. The entire learning process requires only a small number of forward passes and no backward pass. Experiments show that PromptBoosting achieves state-of-the-art performance in multiple black-box few-shot classification tasks, and matches or outperforms full fine-tuning in both few-shot and standard learning paradigms, while training 10x faster than existing black-box methods.

Recent deep-learning-based super-resolution (SR) methods have been successful in recovering high-resolution (HR) images from their low-resolution (LR) counterparts, albeit on the synthetic and simple degradation setting: bicubic downscaling. On the other hand, super-resolution on real-world images demands the capability to handle complex downscaling mechanism which produces different artifacts (e.g., noise, blur, color distortion) upon downscaling factors. To account for complex downscaling mechanism in real-world LR images, there have been a few efforts in constructing datasets consisting of LR images with real-world downsampling degradation. However, making such datasets entails a tremendous amount of time and effort, thereby resorting to very few number of downscaling factors (e.g., $\times$2, $\times$3, $\times$4). To remedy the issue, we propose to generate realistic SR datasets for unseen degradation levels by exploring the latent space of real LR images and thereby producing more diverse yet realistic LR images with complex real-world artifacts. Our quantitative and qualitative experiments demonstrate the accuracy of the generated LR images, and we show that the various conventional SR networks trained with our newly generated SR datasets can produce much better HR images.

We consider a fundamental class of assortment optimization problems in an offline data-driven setting. The firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, based on the principle of pessimism, we propose a novel algorithm called Pessimistic ASsortment opTimizAtion (PASTA for short), which can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish the first regret bound for the offline assortment optimization problem under the celebrated multinomial logit model (MNL). We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Our numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

Nowadays, state-of-the-art learning-to-rank methods are based on gradient-boosted decision trees (GBDT). The most well-known algorithm is LambdaMART which was proposed more than a decade ago. Recently, several other GBDT-based ranking algorithms were proposed. In this paper, we thoroughly analyze these methods in a unified setup. In particular, we address the following questions. Is direct optimization of a smoothed ranking loss preferable over optimizing a convex surrogate? How to properly construct and smooth surrogate ranking losses? To address these questions, we compare LambdaMART with YetiRank and StochasticRank methods and their modifications. We also propose a simple improvement of the YetiRank approach that allows for optimizing specific ranking loss functions. As a result, we gain insights into learning-to-rank techniques and obtain a new state-of-the-art algorithm.

Wasserstein gradient flows of maximum mean discrepancy (MMD) functionals with non-smooth Riesz kernels show a rich structure as singular measures can become absolutely continuous ones and conversely. In this paper we contribute to the understanding of such flows. We propose to approximate the backward scheme of Jordan, Kinderlehrer and Otto for computing such Wasserstein gradient flows as well as a forward scheme for so-called Wasserstein steepest descent flows by neural networks (NNs). Since we cannot restrict ourselves to absolutely continuous measures, we have to deal with transport plans and velocity plans instead of usual transport maps and velocity fields. Indeed, we approximate the disintegration of both plans by generative NNs which are learned with respect to appropriate loss functions. In order to evaluate the quality of both neural schemes, we benchmark them on the interaction energy. Here we provide analytic formulas for Wasserstein schemes starting at a Dirac measure and show their convergence as the time step size tends to zero. Finally, we illustrate our neural MMD flows by numerical examples.

We study the connection between multicalibration and boosting for squared error regression. First we prove a useful characterization of multicalibration in terms of a ``swap regret'' like condition on squared error. Using this characterization, we give an exceedingly simple algorithm that can be analyzed both as a boosting algorithm for regression and as a multicalibration algorithm for a class $\mathcal{H}$ that makes use only of a standard squared error regression oracle for $\mathcal{H}$. We give a weak learning assumption on $\mathcal{H}$ that ensures convergence to Bayes optimality without the need to make any realizability assumptions --- giving us an agnostic boosting algorithm for regression. We then show that our weak learning assumption on $\mathcal{H}$ is both necessary and sufficient for multicalibration with respect to $\mathcal{H}$ to imply Bayes optimality, answering an open question. We also show that if $\mathcal{H}$ satisfies our weak learning condition relative to another class $\mathcal{C}$ then multicalibration with respect to $\mathcal{H}$ implies multicalibration with respect to $\mathcal{C}$. Finally we investigate the empirical performance of our algorithm experimentally.

We consider the problem of multi-agent navigation and collision avoidance when observations are limited to the local neighborhood of each agent. We propose InforMARL, a novel architecture for multi-agent reinforcement learning (MARL) which uses local information intelligently to compute paths for all the agents in a decentralized manner. Specifically, InforMARL aggregates information about the local neighborhood of agents for both the actor and the critic using a graph neural network and can be used in conjunction with any standard MARL algorithm. We show that (1) in training, InforMARL has better sample efficiency and performance than baseline approaches, despite using less information, and (2) in testing, it scales well to environments with arbitrary numbers of agents and obstacles. We illustrate these results using four task environments, including one with predetermined goals for each agent, and one in which the agents collectively try to cover all goals.

Recent work has shown that forward- and reverse- mode automatic differentiation (AD) over the reals is almost always correct in a mathematically precise sense. However, actual programs work with machine-representable numbers (e.g., floating-point numbers), not reals. In this paper, we study the correctness of AD when the parameter space of a neural network consists solely of machine-representable numbers. In particular, we analyze two sets of parameters on which AD can be incorrect: the incorrect set on which the network is differentiable but AD does not compute its derivative, and the non-differentiable set on which the network is non-differentiable. For a neural network with bias parameters, we first prove that the incorrect set is always empty. We then prove a tight bound on the size of the non-differentiable set, which is linear in the number of non-differentiabilities in activation functions, and give a simple necessary and sufficient condition for a parameter to be in this set. We further prove that AD always computes a Clarke subderivative even on the non-differentiable set. We also extend these results to neural networks possibly without bias parameters.

Despite remarkable successes, deep reinforcement learning algorithms remain sample inefficient: they require an enormous amount of trial and error to find good policies. Model-based algorithms promise sample efficiency by building an environment model that can be used for planning. Posterior Sampling for Reinforcement Learning is such a model-based algorithm that has attracted significant interest due to its performance in the tabular setting. This paper introduces Posterior Sampling for Deep Reinforcement Learning (PSDRL), the first truly scalable approximation of Posterior Sampling for Reinforcement Learning that retains its model-based essence. PSDRL combines efficient uncertainty quantification over latent state space models with a specially tailored incremental planning algorithm based on value-function approximation. Extensive experiments on the Atari benchmark show that PSDRL significantly outperforms previous state-of-the-art attempts at scaling up posterior sampling while being competitive with a state-of-the-art (model-based) reinforcement learning method, both in sample efficiency and computational efficiency.

We address multi-agent best arm identification with privacy guarantees. In this setting, agents collaborate by communicating to find the optimal arm. To avoid leaking sensitive data through messages, we consider two notions of privacy withholding different kinds of information: differential privacy and $(\epsilon, \eta)$-privacy. For each privacy definition, we propose an algorithm based on a two-level successive elimination scheme. We provide theoretical guarantees for the privacy level, accuracy and sample complexity of our algorithms. Experiments on various settings support our theoretical findings.

Empirical neural tangent kernels (eNTKs) can provide a good understanding of a given network's representation: they are often far less expensive to compute and applicable more broadly than infinite-width NTKs. For networks with $O$ output units (e.g. an $O$-class classifier), however, the eNTK on $N$ inputs is of size $NO \times NO$, taking $\mathcal O\big( (N O)^2\big)$ memory and up to $\mathcal O\big( (N O)^3 \big)$ computation to use. Most existing applications have therefore used one of a handful of approximations yielding $N \times N$ kernel matrices, saving orders of magnitude of computation, but with limited to no justification. We prove that one such approximation, which we call "sum of logits," converges to the true eNTK at initialization. Our experiments demonstrate the quality of this approximation for various uses across a range of settings.

We consider the problem of fairly allocating a sequence of indivisible items that arrive online in an arbitrary order to a group of $n$ agents with additive normalized valuation functions, we consider the allocation of goods and chores separately and propose algorithms for approximating maximin share (MMS) allocations for both settings. When agents have identical valuation functions the problem coincides with the semi-online machine covering problem (when items are goods) and load balancing problem (when items are chores), for both of which optimal competitive ratios have been achieved. In this paper we consider the case when agents have general additive valuation functions. For the allocation of goods we show that no competitive algorithm exists even when there are only three agents and propose an optimal $0.5$-competitive algorithm for the case of two agents. For the allocation of chores we propose a $(2-1/n)$-competitive algorithm for $n\geq 3$ agents and a $\sqrt{2}\approx 1.414$-competitive algorithm for two agents. Additionally, we show that no algorithm can do better than $15/11\approx 1.364$-competitive for two agents.

Supervised learning is often affected by a covariate shift in which the marginal distributions of instances (covariates $x$) of training and testing samples $p_\text{tr}(x)$ and $p_\text{te}(x)$ are different but the label conditionals coincide. Existing approaches address such covariate shift by either using the ratio $p_\text{te}(x)/p_\text{tr}(x)$ to weight training samples (reweighted methods) or using the ratio $p_\text{tr}(x)/p_\text{te}(x)$ to weight testing samples (robust methods). However, the performance of such approaches can be poor under support mismatch or when the above ratios take large values. We propose a minimax risk classification (MRC) approach for covariate shift adaptation that avoids such limitations by weighting both training and testing samples. In addition, we develop effective techniques that obtain both sets of weights and generalize the conventional kernel mean matching method. We provide novel generalization bounds for our method that show a significant increase in the effective sample size compared with reweighted methods. The proposed method also achieves enhanced classification performance in both synthetic and empirical experiments.

Based on binary inquiries, we developed an algorithm to estimate population quantiles under Local Differential Privacy (LDP). By self-normalizing, our algorithm provides asymptotically normal estimation with valid inference, resulting in tight confidence intervals without the need for nuisance parameters to be estimated. Our proposed method can be conducted fully online, leading to high computational efficiency and minimal storage requirements with $\mathcal{O}(1)$ space. We also proved an optimality result by an elegant application of one central limit theorem of Gaussian Differential Privacy (GDP) when targeting the frequently encountered median estimation problem. With mathematical proof and extensive numerical testing, we demonstrate the validity of our algorithm both theoretically and experimentally.

Deep graph clustering, which aims to group the nodes of a graph into disjoint clusters with deep neural networks, has achieved promising progress in recent years. However, the existing methods fail to scale to the large graph with million nodes. To solve this problem, a scalable deep graph clustering method (Dink-Net) is proposed with the idea of dilation and shrink. Firstly, by discriminating nodes, whether being corrupted by augmentations, representations are learned in a self-supervised manner. Meanwhile, the cluster centers are initialized as learnable neural parameters. Subsequently, the clustering distribution is optimized by minimizing the proposed cluster dilation loss and cluster shrink loss in an adversarial manner. By these settings, we unify the two-step clustering, i.e., representation learning and clustering optimization, into an end-to-end framework, guiding the network to learn clustering-friendly features. Besides, Dink-Net scales well to large graphs since the designed loss functions adopt the mini-batch data to optimize the clustering distribution even without performance drops. Both experimental results and theoretical analyses demonstrate the superiority of our method. Compared to the runner-up, Dink-Net achieves $9.62\%$ NMI improvement on the ogbn-papers100M dataset with 111 million nodes and 1.6 billion edges. The source code is released: https://github.com/yueliu1999/Dink-Net. Besides, a collection (papers, codes, and datasets) of deep graph clustering is shared on GitHub https://github.com/yueliu1999/Awesome-Deep-Graph-Clustering.

We introduce MABe22, a large-scale, multi-agent video and trajectory benchmark to assess the quality of learned behavior representations. This dataset is collected from a variety of biology experiments, and includes triplets of interacting mice (4.7 million frames video+pose tracking data, 10 million frames pose only), symbiotic beetle-ant interactions (10 million frames video data), and groups of interacting flies (4.4 million frames of pose tracking data). Accompanying these data, we introduce a panel of real-life downstream analysis tasks to assess the quality of learned representations by evaluating how well they preserve information about the experimental conditions (e.g. strain, time of day, optogenetic stimulation) and animal behavior. We test multiple state-of-the-art self-supervised video and trajectory representation learning methods to demonstrate the use of our benchmark, revealing that methods developed using human action datasets do not fully translate to animal datasets. We hope that our benchmark and dataset encourage a broader exploration of behavior representation learning methods across species and settings.

Based on the offset Rademacher complexity, this work outlines a systematical framework for deriving sharp excess risk bounds in statistical learning without Bernstein condition. In addition to recovering fast rates in a unified way for some parametric and nonparametric supervised learning models with minimum identifiability assumptions, we also obtain new and improved results for LAD (sparse) linear regression and deep logistic regression with deep ReLU neural networks, respectively.

The reward hypothesis posits that, "all of what we mean by goals and purposes can be well thought of as maximization of the expected value of the cumulative sum of a received scalar signal (reward)." We aim to fully settle this hypothesis. This will not conclude with a simple affirmation or refutation, but rather specify completely the implicit requirements on goals and purposes under which the hypothesis holds.

Evaluating the performance of perception modules in autonomous driving is one of the most critical tasks in developing the complex intelligent system. While module-level unit test metrics adopted from traditional computer vision tasks are feasible to some extent, it remains far less explored to measure the impact of perceptual noise on the driving quality of autonomous vehicles in a consistent and holistic manner. In this work, we propose a principled framework that provides a coherent and systematic understanding of the impact an error in the perception module imposes on an autonomous agent's planning that actually controls the vehicle. Specifically, the planning process is formulated as expected utility maximisation, where all input signals from upstream modules jointly provide a world state description, and the planner strives for the optimal action by maximising the expected utility determined by both world states and actions. We show that, under practical conditions, the objective function can be represented as an inner product between the world state description and the utility function in a Hilbert space. This geometric interpretation enables a novel way to analyse the impact of noise in world state estimation on planning and leads to a universal metric for evaluating perception. The whole framework resembles the idea of transcendental idealism in the classical philosophical literature, which gives the name to our approach.

We study the problem of histogram estimation under user-level differential privacy, where the goal is to preserve the privacy of all entries of any single user. We consider the heterogeneous scenario where the quantity of data can be different for each user. In this scenario, the amount of noise injected into the histogram to obtain differential privacy is proportional to the maximum user contribution, which can be amplified by few outliers. One approach to circumvent this would be to bound (or limit) the contribution of each user to the histogram. However, if users are limited to small contributions, a significant amount of data will be discarded. In this work, we propose algorithms to choose the best user contribution bound for histogram estimation under both bounded and unbounded domain settings. When the size of the domain is bounded, we propose a user contribution bounding strategy that almost achieves a two-approximation with respect to the best contribution bound in hindsight. For unbounded domain histogram estimation, we propose an algorithm that is logarithmic-approximation with respect to the best contribution bound in hindsight. This result holds without any distribution assumptions on the data. Experiments on both real and synthetic datasets verify our theoretical findings and demonstrate the effectiveness of our algorithms. We also show that clipping bias introduced by bounding user contribution may be reduced under mild distribution assumptions, which can be of independent interest.