Mainstream 3D representation learning approaches are built upon contrastive or generative modeling pretext tasks, where great improvements in performance on various downstream tasks have been achieved. However, we find these two paradigms have different characteristics: (i) contrastive models are data-hungry that suffer from a representation over-fitting issue; (ii) generative models have a data filling issue that shows inferior data scaling capacity compared to contrastive models. This motivates us to learn 3D representations by sharing the merits of both paradigms, which is non-trivial due to the pattern difference between the two paradigms. In this paper, we propose contrast with reconstruct (ReCon) that unifies these two paradigms. ReCon is trained to learn from both generative modeling teachers and cross-modal contrastive teachers through ensemble distillation, where the generative student is used to guide the contrastive student. An encoder-decoder style ReCon-block is proposed that transfers knowledge through cross attention with stop-gradient, which avoids pretraining over-fitting and pattern difference issues. ReCon achieves a new state-of-the-art in 3D representation learning, e.g., 91.26% accuracy on ScanObjectNN. Codes have been released at https://github.com/qizekun/ReCon.

Machine learning (ML) systems often exhibit unexpectedly poor behavior when they are deployed in real-world domains. We identify underspecification in ML pipelines as a key reason for these failures. An ML pipeline is the full procedure followed to train and validate a predictor. Such a pipeline is underspecified when it can return many distinct predictors with equivalently strong test performance. Underspecification is common in modern ML pipelines that primarily validate predictors on held-out data that follow the same distribution as the training data. Predictors returned by underspecified pipelines are often treated as equivalent based on their training domain performance, but we show here that such predictors can behave very differently in deployment domains. This ambiguity can lead to instability and poor model behavior in practice, and is a distinct failure mode from previously identified issues arising from structural mismatch between training and deployment domains. We provide evidence that underspecfication has substantive implications for practical ML pipelines, using examples from computer vision, medical imaging, natural language processing, clinical risk prediction based on electronic health records, and medical genomics. Our results show the need to explicitly account for underspecification in modeling pipelines that are intended for real-world deployment in any domain.

We introduce a self-supervised learning (SSL) framework BEATs for general audio representation pre-training, where we optimize an acoustic tokenizer and an audio SSL model by iterations. Unlike the previous audio SSL models that employ reconstruction loss for pre-training, our audio SSL model is trained with the discrete label prediction task, where the labels are generated by a semantic-rich acoustic tokenizer. We propose an iterative pipeline to jointly optimize the tokenizer and the pre-trained model, aiming to abstract high-level semantics and discard the redundant details for audio. The experimental results demonstrate our acoustic tokenizers can generate discrete labels with rich audio semantics and our audio SSL models achieve state-of-the-art (SOTA) results across various audio classification benchmarks, even outperforming previous models that use more training data and model parameters significantly. Specifically, we set a new SOTA mAP 50.6% on AudioSet-2M without using any external data, and 98.1% accuracy on ESC-50. The code and pre-trained models are available at https://aka.ms/beats.

Diffusion probabilistic models (DPMs) are a new class of generative models that have achieved state-of-the-art generation quality in various domains. Despite the promise, one major drawback of DPMs is the slow generation speed due to the large number of neural network evaluations required in the generation process. In this paper, we reveal an overlooked dimension---model schedule---for optimizing the trade-off between generation quality and speed. More specifically, we observe that small models, though having worse generation quality when used alone, could outperform large models in certain generation steps. Therefore, unlike the traditional way of using a single model, using different models in different generation steps in a carefully designed model schedule could potentially improve generation quality and speed simultaneously. We design OMS-DPM, a predictor-based search algorithm, to determine the optimal model schedule given an arbitrary generation time budget and a set of pre-trained models. We demonstrate that OMS-DPM can find model schedules that improve generation quality and speed than prior state-of-the-art methods across CIFAR-10, CelebA, ImageNet, and LSUN datasets. When applied to the public checkpoints of the Stable Diffusion model, we are able to accelerate the sampling by 2x while maintaining the generation quality.

In data poisoning attacks, an adversary tries to change a model's prediction by adding, modifying, or removing samples in the training data. Recently, *ensemble-based* approaches for obtaining *provable* defenses against data poisoning have been proposed where predictions are done by taking a majority vote across multiple base models. In this work, we show that merely considering the majority vote in ensemble defenses is wasteful as it does not effectively utilize available information in the logits layers of the base models. Instead, we propose *Run-Off Election (ROE)*, a novel aggregation method based on a two-round election across the base models: In the first round, models vote for their preferred class and then a second, *Run-Off* election is held between the top two classes in the first round. Based on this approach, we propose DPA+ROE and FA+ROE defense methods based on Deep Partition Aggregation (DPA) and Finite Aggregation (FA) approaches from prior work. We evaluate our methods on MNIST, CIFAR-10, and GTSRB and obtain improvements in certified accuracy by up to $3\%$-$4\%$. Also, by applying ROE on a boosted version of DPA, we gain improvements around $12\%$-$27\%$ comparing to the current state-of-the-art, establishing **a new state-of-the-art** in (pointwise) certified robustness against data poisoning. In many cases, our approach outperforms the state-of-the-art, even when using 32 times less computational power.

In this paper, we address the problem of adapting models from a source domain to a target domain, a task that has become increasingly important due to the brittle generalization of deep neural networks. While several test-time adaptation techniques have emerged, they typically rely on synthetic toolbox data augmentations in cases of limited target data availability. We consider the challenging setting of single-shot adaptation and explore the design of augmentation strategies. We argue that augmentations utilized by existing methods are insufficient to handle large distribution shifts, and hence propose a new approach SiSTA, which first fine-tunes a generative model from the source domain using a single-shot target, and then employs novel sampling strategies for curating synthetic target data. Using experiments on a variety of benchmarks, distribution shifts and image corruptions, we find that SiSTA produces significantly improved generalization over existing baselines in face attribute detection and multi-class object recognition. Furthermore, SiSTA performs competitively to models obtained by training on larger target datasets. Our codes can be accessed at https://github.com/Rakshith-2905/SiSTA

Antibodies are Y-shaped proteins that neutralize pathogens and constitute the core of our adaptive immune system. De novo generation of new antibodies that target specific antigens holds the key to accelerating vaccine discovery. However, this co-design of the amino acid sequence and the 3D structure subsumes and accentuates, some central challenges from multiple tasks including protein folding (sequence to structure), inverse folding (structure to sequence), and docking (binding). We strive to surmount these challenges with a new generative model AbODE that extends graph PDEs to accommodate both contextual information and external interactions. Unlike existing approaches, AbODE uses a single round of full-shot decoding, and elicits continuous differential attention that encapsulates, and evolves with, latent interactions within the antibody as well as those involving the antigen. We unravel fundamental connections between AbODE and temporal networks as well as graph-matching networks. The proposed model significantly outperforms existing methods on standard metrics across benchmarks.

Spurious correlations that degrade model generalization or lead the model to be right for the wrong reasons are one of the main robustness concerns for real-world deployments. However, mitigating these correlations during pre-training for large-scale models can be costly and impractical, particularly for those without access to high-performance computing resources. This paper proposes a novel approach to address spurious correlations during fine-tuning for a given domain of interest. With a focus on multi-modal models (e.g., CLIP), the proposed method leverages different modalities in these models to detect and explicitly set apart spurious attributes from the affected class, achieved through a multi-modal contrastive loss function that expresses spurious relationships through language. Our experimental results and in-depth visualizations on CLIP show that such an intervention can effectively i) improve the model's accuracy when spurious attributes are not present, and ii) directs the model's activation maps towards the actual class rather than the spurious attribute when present. In particular, on the Waterbirds dataset, our algorithm achieved a worst-group accuracy 23% higher than ERM on CLIP with a ResNet-50 backbone, and 32% higher on CLIP with a ViT backbone, while maintaining the same average accuracy as ERM.

Reliable application of machine learning is of primary importance to the practical deployment of deep learning methods. A fundamental challenge is that models are often unreliable due to overconfidence. In this paper, we estimate a model's reliability by measuring the agreement between its latent space, and the latent space of a foundation model. However, it is challenging to measure the agreement between two different latent spaces due to their incoherence, e.g., arbitrary rotations and different dimensionality. To overcome this incoherence issue, we design a neighborhood agreement measure between latent spaces and find that this agreement is surprisingly well-correlated with the reliability of a model's predictions. Further, we show that fusing neighborhood agreement into a model's predictive confidence in a post-hoc way significantly improves its reliability. Theoretical analysis and extensive experiments on failure detection across various datasets verify the effectiveness of our method on both in-distribution and out-of-distribution settings.

Out-of-distribution generalization is challenging for non-participating clients of federated learning under distribution shifts. A proven strategy is to explore those invariant relationships between input and target variables, working equally well for non-participating clients. However, learning invariant relationships is often in an explicit manner from data, representation, and distribution, which violates the federated principles of privacy-preserving and limited communication. In this paper, we propose FedIIR, which implicitly learns invariant relationships from parameter for out-of-distribution generalization, adhering to the above principles. Specifically, we utilize the prediction disagreement to quantify invariant relationships and implicitly reduce it through inter-client gradient alignment. Theoretically, we demonstrate the range of non-participating clients to which FedIIR is expected to generalize and present the convergence results for FedIIR in the massively distributed with limited communication. Extensive experiments show that FedIIR significantly outperforms relevant baselines in terms of out-of-distribution generalization of federated learning.

Deep networks for computer vision are not reliable when they encounter adversarial examples. In this paper, we introduce a framework that uses the dense intrinsic constraints in natural images to robustify inference. By introducing constraints at inference time, we can shift the burden of robustness from training to testing, thereby allowing the model to dynamically adjust to each individual image's unique and potentially novel characteristics at inference time. Our theoretical results show the importance of having dense constraints at inference time. In contrast to existing single-constraint methods, we propose to use equivariance, which naturally allows dense constraints at a fine-grained level in the feature space. Our empirical experiments show that restoring feature equivariance at inference time defends against worst-case adversarial perturbations. The method obtains improved adversarial robustness on four datasets (ImageNet, Cityscapes, PASCAL VOC, and MS-COCO) on image recognition, semantic segmentation, and instance segmentation tasks.

Representation learning and exploration are among the key challenges for any deep reinforcement learning agent. In this work, we provide a singular value decomposition based method that can be used to obtain representations that preserve the underlying transition structure in the domain. Perhaps interestingly, we show that these representations also capture the relative frequency of state visitations, thereby providing an estimate for pseudo-counts for free. To scale this decomposition method to large-scale domains, we provide an algorithm that never requires building the transition matrix, can make use of deep networks, and also permits mini-batch training. Further, we draw inspiration from predictive state representations and extend our decomposition method to partially observable environments. With experiments on multi-task settings with partially observable domains, we show that the proposed method can not only learn useful representation on DM-Lab-30 environments (that have inputs involving language instructions, pixel images, rewards, among others) but it can also be effective at hard exploration tasks in DM-Hard-8 environments.

In private federated learning (FL), a server aggregates differentially private updates from a large number of clients in order to train a machine learning model. The main challenge in this setting is balancing privacy with both classification accuracy of the learnt model as well as the number of bits communicated between the clients and server. Prior work has achieved a good trade-off by designing a privacy-aware compression mechanism, called the minimum variance unbiased (MVU) mechanism, that numerically solves an optimization problem to determine the parameters of the mechanism. This paper builds upon it by introducing a new interpolation procedure in the numerical design process that allows for a far more efficient privacy analysis. The result is the new Interpolated MVU mechanism that is more scalable, has a better privacy-utility trade-off, and provides SOTA results on communication-efficient private FL on a variety of datasets.

Behavior constrained policy optimization has been demonstrated to be a successful paradigm for tackling Offline Reinforcement Learning. By exploiting historical transitions, a policy is trained to maximize a learned value function while constrained by the behavior policy to avoid a significant distributional shift. In this paper, we propose our closed-form policy improvement operators. We make a novel observation that the behavior constraint naturally motivates the use of first-order Taylor approximation, leading to a linear approximation of the policy objective. Additionally, as practical datasets are usually collected by heterogeneous policies, we model the behavior policies as a Gaussian Mixture and overcome the induced optimization difficulties by leveraging the LogSumExp's lower bound and Jensen's Inequality, giving rise to a closed-form policy improvement operator. We instantiate both one-step and iterative offline RL algorithms with our novel policy improvement operators and empirically demonstrate their effectiveness over state-of-the-art algorithms on the standard D4RL benchmark. Our code is available at https://cfpi-icml23.github.io/.

Text-to-image synthesis has recently seen significant progress thanks to large pretrained language models, large-scale training data, and the introduction of scalable model families such as diffusion and autoregressive models. However, the best-performing models require iterative evaluation to generate a single sample. In contrast, generative adversarial networks (GANs) only need a single forward pass. They are thus much faster, but they currently remain far behind the state-of-the-art in large-scale text-to-image synthesis. This paper aims to identify the necessary steps to regain competitiveness. Our proposed model, StyleGAN-T, addresses the specific requirements of large-scale text-to-image synthesis, such as large capacity, stable training on diverse datasets, strong text alignment, and controllable variation vs. text alignment tradeoff. StyleGAN-T significantly improves over previous GANs and outperforms distilled diffusion models - the previous state-of-the-art in fast text-to-image synthesis - in terms of sample quality and speed.

Data augmentation methods have played an important role in the recent advance of deep learning models, and have become an indispensable component of state-of-the-art models in semi-supervised, self-supervised, and supervised training for vision. Despite incurring no additional latency at test time, data augmentation often requires more epochs of training to be effective. For example, even the simple flips-and-crops augmentation requires training for more than 5 epochs to improve performance, whereas RandAugment requires more than 90 epochs. We propose a general framework called Tied-Augment, which improves the efficacy of data augmentation in a wide range of applications by adding a simple term to the loss that can control the similarity of representations under distortions. Tied-Augment can improve state-of-the-art methods from data augmentation (e.g. RandAugment, mixup), optimization (e.g. SAM), and semi-supervised learning (e.g. FixMatch). For example, Tied-RandAugment can outperform RandAugment by 2.0% on ImageNet. Notably, using Tied-Augment, data augmentation can be made to improve generalization even when training for a few epochs and when fine-tuning. We open source our code at https://github.com/ekurtulus/tied-augment/tree/main.

Deep neural networks often fail catastrophically by relying on spurious correlations. Most prior work assumes a clear dichotomy into spurious and reliable features; however, this is often unrealistic. For example, most of the time we do not want an autonomous car to simply copy the speed of surrounding cars---we don't want our car to run a red light if a neighboring car does so. However, we cannot simply enforce invariance to next-lane speed, since it could provide valuable information about an unobservable pedestrian at a crosswalk. Thus, universally ignoring features that are sometimes (but not always) reliable can lead to non-robust performance. We formalize a new setting called contextual reliability which accounts for the fact that the "right" features to use may vary depending on the context. We propose and analyze a two-stage framework called Explicit Non-spurious feature Prediction (ENP) which first identifies the relevant features to use for a given context, then trains a model to rely exclusively on these features. Our work theoretically and empirically demonstrates the advantages of ENP over existing methods and provides new benchmarks for contextual reliability.

In this paper, we introduce Latent Go-Explore (LGE), a simple and general approach based on the Go-Explore paradigm for exploration in reinforcement learning (RL). Go-Explore was initially introduced with a strong domain knowledge constraint for partitioning the state space into cells. However, in most real-world scenarios, drawing domain knowledge from raw observations is complex and tedious. If the cell partitioning is not informative enough, Go-Explore can completely fail to explore the environment. We argue that the Go-Explore approach can be generalized to any environment without domain knowledge and without cells by exploiting a learned latent representation. Thus, we show that LGE can be flexibly combined with any strategy for learning a latent representation. Our results indicate that LGE, although simpler than Go-Explore, is more robust and outperforms state-of-the-art algorithms in terms of pure exploration on multiple hard-exploration environments including Montezuma's Revenge. The LGE implementation is available as open-source at https://github.com/qgallouedec/lge.

Multi-Agent Reinforcement Learning (MARL) has demonstrated its effectiveness in learning collaboration, but it often struggles with low-quality reward signals and high non-stationarity. In contrast, Evolutionary Algorithm (EA) has shown better convergence, robustness, and signal quality insensitivity. This paper introduces a hybrid framework, Representation Asymmetry and Collaboration Evolution (RACE), which combines EA and MARL for efficient collaboration. RACE maintains a MARL team and a population of EA teams. To enable efficient knowledge sharing and policy exploration, RACE decomposes the policies of different teams controlling the same agent into a shared nonlinear observation representation encoder and individual linear policy representations. To address the partial observation issue, we introduce Value-Aware Mutual Information Maximization to enhance the shared representation with useful information about superior global states. EA evolves the population using novel agent-level crossover and mutation operators, offering diverse experiences for MARL. Concurrently, MARL optimizes its policies and injects them into the population for evolution. The experiments on challenging continuous and discrete tasks demonstrate that RACE significantly improves the basic algorithms, consistently outperforming other algorithms. Our code is available at https://github.com/yeshenpy/RACE.

We formalize the problem of contextual optimization through the lens of Bayesian experimental design and propose CO-BED---a general, model-agnostic framework for designing contextual experiments using information-theoretic principles. After formulating a suitable information-based objective, we employ black-box variational methods to simultaneously estimate it and optimize the designs in a single stochastic gradient scheme. In addition, to accommodate discrete actions within our framework, we propose leveraging continuous relaxation schemes, which can naturally be integrated into our variational objective. As a result, CO-BED provides a general and automated solution to a wide range of contextual optimization problems. We illustrate its effectiveness in a number of experiments, where CO-BED demonstrates competitive performance even when compared to bespoke, model-specific alternatives.

Understanding the effect of a feature vector $x\in \mathbb{R}^d$ on the response value (label) $y\in \mathbb{R}$ is the cornerstone of many statistical learning problems. Ideally, it is desired to understand how a set of collected features combine together and influence the response value, but this problem is notoriously difficult, due to the high-dimensionality of data and limited number of labeled data points, among many others. In this work, we take a new perspective on this problem, and we study the question of assessing the difference of influence that the two given features have on the response value. We first propose a notion of closeness for the influence of features, and show that our definition recovers the familiar notion of the magnitude of coefficients in the parametric model. We then propose a novel method to test for the closeness of influence in general model-free supervised learning problems. Our proposed test can be used with finite number of samples with control on type I error rate, no matter the ground truth conditional law $\mathcal{L}(Y|X)$. We analyze the power of our test for two general learning problems i) linear regression, and ii) binary classification under mixture of Gaussian models, and show that under the proper choice of score function, an internal component of our test, with sufficient number of samples will achieve full statistical power. We evaluate our findings through extensive numerical simulations, specifically we adopt the datamodel framework (Ilyas, et al., 2022) for CIFAR-10 dataset to identify pairs of training samples with different influence on the trained model via optional black box training mechanisms.

Graph neural networks (GNNs) have emerged as a powerful paradigm to learn from relational data mostly through applying the message passing mechanism. However, this approach may exhibit suboptimal performance when applied to graphs possessing various structural issues. In this work, we focus on understanding and alleviating the effect of graph structural noise on GNN performance. To evaluate the graph structural noise in real data, we propose edge signal-to-noise ratio (ESNR), a novel metric evaluating overall edge noise level with respect to data features or labels based on random matrix theory. We have found striking concordance between the proposed ESNR metric and the GNN performance in various simulated and real data. To reduce the effect of the noise, we propose GPS (Graph Propensity Score) graph rewiring, which estimates the edge likelihood for rewiring data graphs based on self-supervised link prediction. We provide a theoretical guarantee for GPS graph rewiring and demonstrate its efficacy by comprehensive benchmarks.

Recent advances to combine structured regression models and deep neural networks for better interpretability, more expressiveness, and statistically valid uncertainty quantification demonstrate the versatility of semi-structured neural networks (SSNs). We show that techniques to properly identify the contributions of the different model components in SSNs, however, lead to suboptimal network estimation, slower convergence, and degenerated or erroneous predictions. In order to solve these problems while preserving favorable model properties, we propose a non-invasive post-hoc orthogonalization (PHO) that guarantees identifiability of model components and provides better estimation and prediction quality. Our theoretical findings are supported by numerical experiments, a benchmark comparison as well as a real-world application to COVID-19 infections.

Two different approaches exist to handle missing values for prediction: either imputation, prior to fitting any predictive algorithms, or dedicated methods able to natively incorporate missing values. While imputation is widely (and easily) use, it is unfortunately biased when low-capacity predictors (such as linear models) are applied afterward. However, in practice, naive imputation exhibits good predictive performance. In this paper, we study the impact of imputation in a high-dimensional linear model with MCAR missing data. We prove that zero imputation performs an implicit regularization closely related to the ridge method, often used in high-dimensional problems. Leveraging on this connection, we establish that the imputation bias is controlled by a ridge bias, which vanishes in high dimension. As a predictor, we argue in favor of the averaged SGD strategy, applied to zero-imputed data. We establish an upper bound on its generalization error, highlighting that imputation is benign in the $d \gg \sqrt{n}$ regime. Experiments illustrate our findings.

Source-free domain adaptation (SFDA) is compelling because it allows adapting an off-the-shelf model to a new domain using only unlabelled data. In this work, we apply existing SFDA techniques to a challenging set of naturally-occurring distribution shifts in bioacoustics, which are very different from the ones commonly studied in computer vision. We find existing methods perform differently relative to each other than observed in vision benchmarks, and sometimes perform worse than no adaptation at all. We propose a new simple method which outperforms the existing methods on our new shifts while exhibiting strong performance on a range of vision datasets. Our findings suggest that existing SFDA methods are not as generalizable as previously thought and that considering diverse modalities can be a useful avenue for designing more robust models.

For many application domains, the integration of machine learning (ML) models into decision making is hindered by the poor explainability and theoretical guarantees of black box models. Although the emerging area of algorithms with predictions offers a way to leverage ML while enjoying worst-case guarantees, existing work usually assumes access to only one predictor. We demonstrate how to more effectively utilize historical datasets and application domain knowledge by intentionally using predictors of different quantities. By leveraging the heterogeneity in our predictors, we are able to achieve improved performance, explainability and computational efficiency over predictor-agnostic methods. Theoretical results are supplemented by large-scale empirical evaluations with production data demonstrating the success of our methods on optimization problems occurring in large distributed computing systems.

Physics-informed Neural Networks (PINNs) have recently achieved remarkable progress in solving Partial Differential Equations (PDEs) in various fields by minimizing a weighted sum of PDE loss and boundary loss. However, there are several critical challenges in the training of PINNs, including the lack of theoretical frameworks and the imbalance between PDE loss and boundary loss. In this paper, we present an analysis of second-order non-homogeneous PDEs, which are classified into three categories and applicable to various common problems. We also characterize the connections between the training loss and actual error, guaranteeing convergence under mild conditions. The theoretical analysis inspires us to further propose MultiAdam, a scale-invariant optimizer that leverages gradient momentum to parameter-wisely balance the loss terms. Extensive experiment results on multiple problems from different physical domains demonstrate that our MultiAdam solver can improve the predictive accuracy by 1-2 orders of magnitude compared with strong baselines.

Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.

A wide variety of model explanation approaches have been proposed in recent years, all guided by very different rationales and heuristics. In this paper, we take a new route and cast interpretability as a statistical inference problem. We propose a general deep probabilistic model designed to produce interpretable predictions. The model’s parameters can be learned via maximum likelihood, and the method can be adapted to any predictor network architecture, and any type of prediction problem. Our model is akin to amortized interpretability methods, where a neural network is used as a selector to allow for fast interpretation at inference time. Several popular interpretability methods are shown to be particular cases of regularized maximum likelihood for our general model. Using our framework, we identify imputation as a common issue of these models. We propose new datasets with ground truth selection which allow for the evaluation of the features importance map and show experimentally that multiple imputation provides more reasonable interpretations.

Graph Neural Networks (GNNs) are able to achieve high classification accuracy on many important real world datasets, but provide no rigorous notion of predictive uncertainty. Quantifying the confidence of GNN models is difficult due to the dependence between datapoints induced by the graph structure. We leverage recent advances in conformal prediction to construct prediction sets for node classification in inductive learning scenarios. We do this by taking an existing approach for conformal classification that relies on exchangeable data and modifying it by appropriately weighting the conformal scores to reflect the network structure. We show through experiments on standard benchmark datasets using popular GNN models that our approach provides tighter and better calibrated prediction sets than a naive application of conformal prediction.

State space models (SSMs) have high performance on long sequence modeling but require sophisticated initialization techniques and specialized implementations for high quality and runtime performance. We study whether a simple alternative can match SSMs in performance and efficiency: directly learning long convolutions over the sequence. We find that a key requirement to achieving high performance is keeping the convolution kernels smooth. We find that simple interventions-such as squashing the kernel weights-result in smooth kernels and recover SSM performance on a range of tasks including the long range arena, image classification, language modeling, and brain data modeling. Next, we develop FlashButterfly, an IO-aware algorithm to improve the runtime performance of long convolutions. FlashButterfly appeals to classic Butterfly decompositions of the convolution to reduce GPU memory IO and increase FLOP utilization. FlashButterfly speeds up convolutions by 2.2$\times$, and allows us to train on Path256, a challenging task with sequence length 64K, where we set state-of-the-art by 29.1 points while training 7.2$\times$ faster than prior work. Lastly, we introduce an extension to FlashButterfly that learns the coefficients of the Butterfly decomposition, increasing expressivity without increasing runtime. Using this extension, we outperform a Transformer on WikiText103 by 0.2 PPL with 30% fewer parameters.

Domain adaptation aims to mitigate distribution shifts among different domains. However, traditional formulations are mostly limited to categorical domains, greatly simplifying nuanced domain relationships in the real world. In this work, we tackle a generalization with taxonomy-structured domains, which formalizes domains with nested, hierarchical similarity structures such as animal species and product catalogs. We build on the classic adversarial framework and introduce a novel taxonomist, which competes with the adversarial discriminator to preserve the taxonomy information. The equilibrium recovers the classic adversarial domain adaptation's solution if given a non-informative domain taxonomy (e.g., a flat taxonomy where all leaf nodes connect to the root node) while yielding non-trivial results with other taxonomies. Empirically, our method achieves state-of-the-art performance on both synthetic and real-world datasets with successful adaptation.

The goal of this paper is to revisit Kernel Principal Component Analysis (KPCA) through dualization of a difference of convex functions. This allows to naturally extend KPCA to multiple objective functions and leads to efficient gradient-based algorithms avoiding the expensive SVD of the Gram matrix. Particularly, we consider objective functions that can be written as Moreau envelopes, demonstrating how to promote robustness and sparsity within the same framework. The proposed method is evaluated on synthetic and realworld benchmarks, showing significant speedup in KPCA training time as well as highlighting the benefits in terms of robustness and sparsity.

We propose a new first-order optimization algorithm --- AcceleratedGradient-OptimisticGradient (AG-OG) Descent Ascent---for separable convex-concave minimax optimization. The main idea of our algorithm is to carefully leverage the structure of the minimax problem, performing Nesterov acceleration on the individual component and optimistic gradient on the coupling component. Equipped with proper restarting, we show that AG-OG achieves the optimal convergence rate (up to a constant) for a variety of settings, including bilinearly coupled strongly convex-strongly concave minimax optimization (bi-SC-SC), bilinearly coupled convex-strongly concave minimax optimization (bi-C-SC), and bilinear games. We also extend our algorithm to the stochastic setting and achieve the optimal convergence rate in both bi-SC-SC and bi-C-SC settings. AG-OG is the first single-call algorithm with optimal convergence rates in both deterministic and stochastic settings for bilinearly coupled minimax optimization problems.

In machine learning applications, it is well known that carefully designed learning rate (step size) schedules can significantly improve the convergence of commonly used first-order optimization algorithms. Therefore how to set step size adaptively becomes an important research question. A popular and effective method is the Polyak step size, which sets step size adaptively for gradient descent or stochastic gradient descent without the need to estimate the smoothness parameter of the objective function. However, there has not been a principled way to generalize the Polyak step size for algorithms with momentum accelerations. This paper presents a general framework to set the learning rate adaptively for first-order optimization methods with momentum, motivated by the derivation of Polyak step size. It is shown that the resulting techniques are much less sensitive to the choice of momentum parameter and may avoid the oscillation of the heavy-ball method on ill-conditioned problems. These adaptive step sizes are further extended to the stochastic settings, which are attractive choices for stochastic gradient descent with momentum. Our methods are demonstrated to be more effective for stochastic gradient methods than prior adaptive step size algorithms in large-scale machine learning tasks.

Smoothness and low dimensional structures play central roles in improving generalization and stability in learning and statistics. This work combines techniques from semi-infinite constrained learning and manifold regularization to learn representations that are globally smooth on a manifold. To do so, it shows that under typical conditions the problem of learning a Lipschitz continuous function on a manifold is equivalent to a dynamically weighted manifold regularization problem. This observation leads to a practical algorithm based on a weighted Laplacian penalty whose weights are adapted using stochastic gradient techniques. It is shown that under mild conditions, this method estimates the Lipschitz constant of the solution, learning a globally smooth solution as a byproduct. Experiments on real world data illustrate the advantages of the proposed method relative to existing alternatives. Our code is available at https://github.com/JuanCervino/smoothbench.

Currently, applying diffusion models in pixel space of high resolution images is difficult. Instead, existing approaches focus on diffusion in lower dimensional spaces (latent diffusion), or have multiple super-resolution levels of generation referred to as cascades. The downside is that these approaches add additional complexity to the diffusion framework. This paper aims to improve denoising diffusion for high resolution images while keeping the model as simple as possible. The paper is centered around the research question: How can one train a standard denoising diffusion models on high resolution images, and still obtain performance comparable to these alternate approaches? The four main findings are: 1) the noise schedule should be adjusted for high resolution images, 2) It is sufficient to scale only a particular part of the architecture, 3) dropout should be added at specific locations in the architecture, and 4) downsampling is an effective strategy to avoid high resolution feature maps. Combining these simple yet effective techniques, we achieve state-of-the-art on image generation among diffusion models without sampling modifiers on ImageNet.

Learning signed distance functions (SDFs) from 3D point clouds is an important task in 3D computer vision. However, without ground truth signed distances, point normals or clean point clouds, current methods still struggle from learning SDFs from noisy point clouds. To overcome this challenge, we propose to learn SDFs via a noise to noise mapping, which does not require any clean point cloud or ground truth supervision for training. Our novelty lies in the noise to noise mapping which can infer a highly accurate SDF of a single object or scene from its multiple or even single noisy point cloud observations. Our novel learning manner is supported by modern Lidar systems which capture multiple noisy observations per second. We achieve this by a novel loss which enables statistical reasoning on point clouds and maintains geometric consistency although point clouds are irregular, unordered and have no point correspondence among noisy observations. Our evaluation under the widely used benchmarks demonstrates our superiority over the state-of-the-art methods in surface reconstruction, point cloud denoising and upsampling. Our code, data, and pre-trained models are available at https://github.com/mabaorui/Noise2NoiseMapping/ .

Visual and linguistic concepts naturally organize themselves in a hierarchy, where a textual concept "dog" entails all images that contain dogs. Despite being intuitive, current large-scale vision and language models such as CLIP do not explicitly capture such hierarchy. We propose MERU, a contrastive model that yields hyperbolic representations of images and text. Hyperbolic spaces have suitable geometric properties to embed tree-like data, so MERU can better capture the underlying hierarchy in image-text datasets. Our results show that MERU learns a highly interpretable and structured representation space while being competitive with CLIP's performance on standard multi-modal tasks like image classification and image-text retrieval.

Human dexterity is a hallmark of motor control behaviors. Our hands can rapidly synthesize new behaviors despite the complexity (multi-articular and multi-joints, with 23 joints controlled by more than 40 muscles) of mosculoskeletal control. In this work, we take inspiration from how human dexterity builds on a diversity of prior experiences, instead of being acquired through a single task. Motivated by this observation, we set out to develop agents that can build upon previous experience to quickly acquire new (previously unattainable) behaviors. Specifically, our approach leverages multi-task learning to implicitly capture a task-agnostic behavioral priors (MyoDex) for human-like dexterity, using a physiologically realistic human hand model -- MyoHand. We demonstrate MyoDex's effectiveness in few-shot generalization as well as positive transfer to a large repertoire of unseen dexterous manipulation tasks. MyoDex can solve approximately 3x more tasks and it can accelerate the achievement of solutions by about 4x in comparison to a distillation baseline. While prior work has synthesized single musculoskeletal control behaviors, MyoDex is the first generalizable manipulation prior that catalyzes the learning of dexterous physiological control across a large variety of contact-rich behaviors.

A key component of model-based reinforcement learning (RL) is a dynamics model that predicts the outcomes of actions. Errors in this predictive model can degrade the performance of model-based controllers, and complex Markov decision processes (MDPs) can present exceptionally difficult prediction problems. To mitigate this issue, we propose predictable MDP abstraction (PMA): instead of training a predictive model on the original MDP, we train a model on a transformed MDP with a learned action space that only permits predictable, easy-to-model actions, while covering the original state-action space as much as possible. As a result, model learning becomes easier and more accurate, which allows robust, stable model-based planning or model-based RL. This transformation is learned in an unsupervised manner, before any task is specified by the user. Downstream tasks can then be solved with model-based control in a zero-shot fashion, without additional environment interactions. We theoretically analyze PMA and empirically demonstrate that PMA leads to significant improvements over prior unsupervised model-based RL approaches in a range of benchmark environments. Our code and videos are available at https://seohong.me/projects/pma/

Reinforcement learning algorithms typically struggle in the absence of a dense, well-shaped reward function. Intrinsically motivated exploration methods address this limitation by rewarding agents for visiting novel states or transitions, but these methods offer limited benefits in large environments where most discovered novelty is irrelevant for downstream tasks. We describe a method that uses background knowledge from text corpora to shape exploration. This method, called ELLM (Exploring with LLMs) rewards an agent for achieving goals suggested by a language model prompted with a description of the agent's current state. By leveraging large-scale language model pretraining, ELLM guides agents toward human-meaningful and plausibly useful behaviors without requiring a human in the loop. We evaluate ELLM in the Crafter game environment and the Housekeep robotic simulator, showing that ELLM-trained agents have better coverage of common-sense behaviors during pretraining and usually match or improve performance on a range of downstream tasks.

In Federated Learning (FL) and many other distributed training frameworks, collaborators can hold their private data locally and only share the network weights trained with the local data after multiple iterations. Gradient inversion is a family of privacy attacks that recovers data from its generated gradients. Seemingly, FL can provide a degree of protection against gradient inversion attacks on weight updates, since the gradient of a single step is concealed by the accumulation of gradients over multiple local iterations. In this work, we propose a principled way to extend gradient inversion attacks to weight updates in FL, thereby better exposing weaknesses in the presumed privacy protection inherent in FL. In particular, we propose a surrogate model method based on the characteristic of two-dimensional gradient flow and low-rank property of local updates. Our method largely boosts the ability of gradient inversion attacks on weight updates containing many iterations and achieves state-of-the-art (SOTA) performance. Additionally, our method runs up to $100\times$ faster than the SOTA baseline in the common FL scenario. Our work re-evaluates and highlights the privacy risk of sharing network weights. Our code is available at https://github.com/JunyiZhu-AI/surrogate_model_extension.

In the privacy-utility tradeoff of a model trained on benchmark language and vision tasks, remarkable improvements have been widely reported when the model is pretrained on public data. Some gain is expected as these models inherit the benefits of transfer learning, which is the standard motivation in non-private settings. However, the stark contrast in the gain of pretraining between non-private and private machine learning suggests that the gain in the latter is rooted in a fundamentally different cause. To explain this phenomenon, we hypothesize that the non-convex loss landscape of a model training necessitates the optimization algorithm to go through two phases. In the first, the algorithm needs to select a good ``basin'' in the loss landscape. In the second, the algorithm solves an easy optimization within that basin. The former is a harder problem to solve with private data, while the latter is harder to solve with public data due to a distribution shift or data scarcity. Guided by this intuition, we provide theoretical constructions that provably demonstrate the separation between private training with and without public pretraining. Further, systematic experiments on CIFAR10 and Librispeech provide supporting evidence for our hypothesis.

Deep neural networks perform well on classification tasks where data streams are i.i.d. and labeled data is abundant. Challenges emerge with non-stationary training data streams such as continual learning. One powerful approach that has addressed this challenge involves pre-training of large encoders on volumes of readily available data, followed by task-specific tuning. Given a new task, however, updating the weights of these encoders is challenging as a large number of weights needs to be fine-tuned, and as a result, they forget information about the previous tasks. In the present work, we propose a model architecture to address this issue, building upon a discrete bottleneck containing pairs of separate and learnable key-value codes. Our paradigm will be to encode; process the representation via a discrete bottleneck; and decode. Here, the input is fed to the pre-trained encoder, the output of the encoder is used to select the nearest keys, and the corresponding values are fed to the decoder to solve the current task. The model can only fetch and re-use a sparse number of these key-value pairs during inference, enabling localized and context-dependent model updates. We theoretically investigate the ability of the discrete key-value bottleneck to minimize the effect of learning under distribution shifts and show that it reduces the complexity of the hypothesis class. We empirically verify the proposed method under challenging class-incremental learning scenarios and show that the proposed model --- without any task boundaries --- reduces catastrophic forgetting across a wide variety of pre-trained models, outperforming relevant baselines on this task.

Compact representation of multimedia signals using implicit neural representations (INRs) has advanced significantly over the past few years, and recent works address their applications to video. Existing studies on video INR have focused on network architecture design as all video information is contained within network parameters. Here, we propose a new paradigm in efficient INR for videos based on the idea of strong lottery ticket (SLT) hypothesis (Zhou et al., 2019), which demonstrates the possibility of finding an accurate subnetwork mask, called supermask, for a randomly initialized classification network without weight training. Specifically, we train multiple supermasks with a hierarchical structure for a randomly initialized image-wise video representation model without weight updates. Different from a previous approach employing hierarchical supermasks (Okoshi et al., 2022), a trainable scale parameter for each mask is used instead of multiplying by the same fixed scale for all levels. This simple modification widens the parameter search space to sufficiently explore various sparsity patterns, leading the proposed algorithm to find stronger subnetworks. Moreover, extensive experiments on popular UVG benchmark show that random subnetworks obtained from our framework achieve higher reconstruction and visual quality than fully trained models with similar encoding sizes. Our study is the first to demonstrate the existence of SLTs in video INR models and propose an efficient method for finding them.

Foundation models are redefining how AI systems are built. Practitioners now follow a standard procedure to build their machine learning solutions: from a pre-trained foundation model, they fine-tune the weights on the target task of interest. So, the Internet is swarmed by a handful of foundation models fine-tuned on many diverse tasks: these individual fine-tunings exist in isolation without benefiting from each other. In our opinion, this is a missed opportunity, as these specialized models contain rich and diverse features. In this paper, we thus propose model ratatouille, a new strategy to recycle the multiple fine-tunings of the same foundation model on diverse auxiliary tasks. Specifically, we repurpose these auxiliary weights as initializations for multiple parallel fine-tunings on the target task; then, we average all fine-tuned weights to obtain the final model. This recycling strategy aims at maximizing the diversity in weights by leveraging the diversity in auxiliary tasks. Empirically, it improves the state of the art on the reference DomainBed benchmark for out-of-distribution generalization. Looking forward, this work contributes to the emerging paradigm of updatable machine learning where, akin to open-source software development, the community collaborates to reliably update machine learning models.

Many recent machine learning tasks focus to develop models that can generalize to unseen distributions. Domain generalization (DG) has become one of the key topics in various fields. Several literatures show that DG can be arbitrarily hard without exploiting target domain information. To address this issue, test-time adaptive (TTA) methods are proposed. Existing TTA methods require offline target data or extra sophisticated optimization procedures during the inference stage. In this work, we adopt **N**on-**P**arametric **C**lassifier to perform the test-time **Ada**ptation (**AdaNPC**). In particular, we construct a memory that contains the feature and label pairs from training domains. During inference, given a test instance, AdaNPC first recalls $k$ closed samples from the memory to vote for the prediction, and then the test feature and predicted label are added to the memory. In this way, the sample distribution in the memory can be gradually changed from the training distribution towards the test distribution with very little extra computation cost. We theoretically justify the rationality behind the proposed method. Besides, we test our model on extensive numerical experiments. AdaNPC significantly outperforms competitive baselines on various DG benchmarks. In particular, when the adaptation target is a series of domains, the adaptation accuracy of AdaNPC is $50$% higher than advanced TTA methods.

Recent end-to-end multi-object detectors simplify the inference pipeline by removing hand-crafted processes such as non-maximum suppression (NMS). However, during training, they still heavily rely on heuristics and hand-crafted processes which deteriorate the reliability of the predicted confidence score. In this paper, we propose a novel framework to train an end-to-end multi-object detector consisting of only two terms: negative log-likelihood (NLL) and a regularization term. In doing so, the multi-object detection problem is treated as density estimation of the ground truth bounding boxes utilizing a regularized mixture density model. The proposed end-to-end multi-object Detection with a Regularized Mixture Model (D-RMM) is trained by minimizing the NLL with the proposed regularization term, maximum component maximization (MCM) loss, preventing duplicate predictions. Our method reduces the heuristics of the training process and improves the reliability of the predicted confidence score. Moreover, our D-RMM outperforms the previous end-to-end detectors on MS COCO dataset. Code is available at https://github.com/lhj815/D-RMM.

Optimal transport (OT) has gained popularity due to its various applications in fields such as machine learning, statistics, and signal processing. However, the balanced mass requirement limits its performance in practical problems. To address these limitations, variants of the OT problem, including unbalanced OT, Optimal partial transport (OPT), and Hellinger Kantorovich (HK), have been proposed. In this paper, we propose the Linear optimal partial transport (LOPT) embedding, which extends the (local) linearization technique on OT and HK to the OPT problem. The proposed embedding allows for faster computation of OPT distance between pairs of positive measures. Besides our theoretical contributions, we demonstrate the LOPT embedding technique in point-cloud interpolation and PCA analysis. Our code is available at https://github.com/Baio0/LinearOPT.

Selecting hyperparameters in deep learning greatly impacts its effectiveness but requires manual effort and expertise. Recent works show that Bayesian model selection with Laplace approximations can allow to optimize such hyperparameters just like standard neural network parameters using gradients and on the training data. However, estimating a single hyperparameter gradient requires a pass through the entire dataset, limiting the scalability of such algorithms. In this work, we overcome this issue by introducing lower bounds to the linearized Laplace approximation of the marginal likelihood. In contrast to previous estimators, these bounds are amenable to stochastic-gradient-based optimization and allow to trade off estimation accuracy against computational complexity. We derive them using the function-space form of the linearized Laplace, which can be estimated using the neural tangent kernel. Experimentally, we show that the estimators can significantly accelerate gradient-based hyperparameter optimization.

Curriculum learning (CL)- training using samples that are generated and presented in a meaningful order - was introduced in the machine learning context around a decade ago. While CL has been extensively used and analysed empirically, there has been very little mathematical justification for its advantages. We introduce a CL model for learning the class of k-parities on d bits of a binary string with a neural network trained by stochastic gradient descent (SGD). We show that a wise choice of training examples, involving two or more product distributions, allows to reduce significantly the computational cost of learning this class of functions, compared to learning under the uniform distribution. We conduct experiments to support our analysis. Furthermore, we show that for another class of functions - namely the `Hamming mixtures' - CL strategies involving a bounded number of product distributions are not beneficial.

Oceanographers are interested in predicting ocean currents and identifying divergences in a current vector field based on sparse observations of buoy velocities. Since we expect current dynamics to be smooth but highly non-linear, Gaussian processes (GPs) offer an attractive model. But we show that applying a GP with a standard stationary kernel directly to buoy data can struggle at both current prediction and divergence identification -- due to some physically unrealistic prior assumptions. To better reflect known physical properties of currents, we propose to instead put a standard stationary kernel on the divergence and curl-free components of a vector field obtained through a Helmholtz decomposition. We show that, because this decomposition relates to the original vector field just via mixed partial derivatives, we can still perform inference given the original data with only a small constant multiple of additional computational expense. We illustrate the benefits of our method on synthetic and real oceans data.

Communication-reduction techniques are a popular way to improve scalability in data-parallel training of deep neural networks (DNNs). The recent emergence of large language models such as GPT has created the need for new approaches to exploit data-parallelism. Among these, fully-sharded data parallel (FSDP) training is highly popular, yet it still encounters scalability bottlenecks. One reason is that applying compression techniques to FSDP is challenging: as the vast majority of the communication involves the model's weights, direct compression alters convergence and leads to accuracy loss. We present QSDP, a variant of FSDP which supports both gradient and weight quantization with theoretical guarantees, is simple to implement and has essentially no overheads. To derive QSDP we prove that a natural modification of SGD achieves convergence even when we only maintain quantized weights, and thus the domain over which we train consists of quantized points and is, therefore, highly non-convex. We validate this approach by training GPT-family models with up to 1.3 billion parameters on a multi-node cluster. Experiments show that QSDP preserves model accuracy, while completely removing the communication bottlenecks of FSDP, providing end-to-end speedups of up to 2.2x.

The high computational and memory requirements of large language model (LLM) inference make it feasible only with multiple high-end accelerators. Motivated by the emerging demand for latency-insensitive tasks with batched processing, this paper initiates the study of high-throughput LLM inference using limited resources, such as a single commodity GPU. We present FlexGen, a high-throughput generation engine for running LLMs with limited GPU memory. FlexGen can be flexibly configured under various hardware resource constraints by aggregating memory and computation from the GPU, CPU, and disk. By solving a linear programming problem, it searches for efficient patterns to store and access tensors. FlexGen further compresses the weights and the attention cache to 4 bits with negligible accuracy loss. These techniques enable FlexGen to have a larger space of batch size choices and thus significantly increase maximum throughput. As a result, when running OPT-175B on a single 16GB GPU, FlexGen achieves significantly higher throughput compared to state-of-the-art offloading systems, reaching a generation throughput of 1 token/s for the first time with an effective batch size of 144. On the HELM benchmark, FlexGen can benchmark a 30B model with a 16GB GPU on 7 representative sub-scenarios in 21 hours. The code is available at https://github.com/FMInference/FlexGen.

Identifying a small molecule from its mass spectrum is the primary open problem in computational metabolomics. This is typically cast as information retrieval: an unknown spectrum is matched against spectra predicted computationally from a large database of chemical structures. However, current approaches to spectrum prediction model the output space in ways that force a tradeoff between capturing high resolution mass information and tractable learning. We resolve this tradeoff by casting spectrum prediction as a mapping from an input molecular graph to a probability distribution over chemical formulas. We further discover that a large corpus of mass spectra can be closely approximated using a fixed vocabulary constituting only 2% of all observed formulas. This enables efficient spectrum prediction using an architecture similar to graph classification - GrAFF-MS - achieving significantly lower prediction error and greater retrieval accuracy than previous approaches.

Contrastive learning (CL) has emerged as a powerful technique for representation learning, with or without label supervision. However, supervised CL is prone to collapsing representations of subclasses within a class by not capturing all their features, and unsupervised CL may suppress harder class-relevant features by focusing on learning easy class-irrelevant features; both significantly compromise representation quality. Yet, there is no theoretical understanding of class collapse or feature suppression at test time. We provide the first unified theoretically rigorous framework to determine which features are learnt by CL. Our analysis indicate that, perhaps surprisingly, bias of (stochastic) gradient descent towards finding simpler solutions is a key factor in collapsing subclass representations and suppressing harder class-relevant features. Moreover, we present increasing embedding dimensionality and improving the quality of data augmentations as two theoretically motivated solutions to feature suppression. We also provide the first theoretical explanation for why employing supervised and unsupervised CL together yields higher-quality representations, even when using commonly-used stochastic gradient methods.

In model-based reinforcement learning (MBRL), policy gradients can be estimated either by derivative-free RL methods, such as likelihood ratio gradients (LR), or by backpropagating through a differentiable model via reparameterization gradients (RP). Instead of using one or the other, the Total Propagation (TP) algorithm in prior work showed that a combination of LR and RP estimators averaged using inverse variance weighting (IVW) can achieve orders of magnitude improvement over either method. However, IVW-based composite estimators have not yet been applied in modern RL tasks, as it is unclear if they can be implemented scalably. We propose a scalable method, Total Propagation X (TPX) that improves over TP by changing the node used for IVW, and employing coordinate wise weighting. We demonstrate the scalability of TPX by applying it to the state of the art visual MBRL algorithm Dreamer. The experiments showed that Dreamer fails with long simulation horizons, while our TPX works reliably for only a fraction of additional computation. One key advantage of TPX is its ease of implementation, which will enable experimenting with IVW on many tasks beyond MBRL.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients.

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width are proportionally large and propose a closed-form expression for the Bayes-optimal test error, for regression and classification tasks. We further compute closed-form expressions for the test errors of ridge regression, kernel and random features regression. We find, in particular, that optimally regularized ridge regression, as well as kernel regression, achieve Bayes-optimal performances, while the logistic loss yields a near-optimal test error for classification. We further show numerically that when the number of samples grows faster than the dimension, ridge and kernel methods become suboptimal, while neural networks achieve test error close to zero from quadratically many samples.

When training neural networks, it has been widely observed that a large step size is essential in stochastic gradient descent (SGD) for obtaining superior models. However, the effect of large step sizes on the success of SGD is not well understood theoretically. Several previous works have attributed this success to the stochastic noise present in SGD. However, we show through a novel set of experiments that the stochastic noise is not sufficient to explain good non-convex training, and that instead the effect of a large learning rate itself is essential for obtaining best performance.We demonstrate the same effects also in the noise-less case, i.e. for full-batch GD. We formally prove that GD with large step size ---on certain non-convex function classes --- follows a different trajectory than GD with a small step size, which can lead to convergence to a global minimum instead of a local one. Our settings provide a framework for future analysis which allows comparing algorithms based on behaviors that can not be observed in the traditional settings.

We consider solving partial differential equations (PDEs) with Fourier neural operators (FNOs), which operate in the frequency domain. Since the laws of physics do not depend on the coordinate system used to describe them, it is desirable to encode such symmetries in the neural operator architecture for better performance and easier learning. While encoding symmetries in the physical domain using group theory has been studied extensively, how to capture symmetries in the frequency domain is under-explored. In this work, we extend group convolutions to the frequency domain and design Fourier layers that are equivariant to rotations, translations, and reflections by leveraging the equivariance property of the Fourier transform. The resulting $G$-FNO architecture generalizes well across input resolutions and performs well in settings with varying levels of symmetry. Our code is publicly available as part of the AIRS library (https://github.com/divelab/AIRS).

This paper presents a novel generative model for Computer Aided Design (CAD) that 1) represents high-level design concepts of a CAD model as a three-level hierarchical tree of neural codes, from global part arrangement down to local curve geometry; and 2) controls the generation or completion of CAD models by specifying the target design using a code tree. Concretely, a novel variant of a vector quantized VAE with "masked skip connection" extracts design variations as neural codebooks at three levels. Two-stage cascaded auto-regressive transformers learn to generate code trees from incomplete CAD models and then complete CAD models following the intended design. Extensive experiments demonstrate superior performance on conventional tasks such as unconditional generation while enabling novel interaction capabilities on conditional generation tasks. The code is available at https://github.com/samxuxiang/hnc-cad.

Layout design is an important task in various design fields, including user interfaces, document, and graphic design. As this task requires tedious manual effort by designers, prior works have attempted to automate this process using generative models, but commonly fell short of providing intuitive user controls and achieving design objectives. In this paper, we build a conditional latent diffusion model, PLay, that generates parametrically conditioned layouts in vector graphic space from user-specified guidelines, which are commonly used by designers for representing their design intents in current practices. Our method outperforms prior works across three datasets on metrics including FID and FD-VG, and in user test. Moreover, it brings a novel and interactive experience to professional layout design processes.

Topic models have been prevalent for decades with various applications. However, existing topic models commonly suffer from the notorious topic collapsing: discovered topics semantically collapse towards each other, leading to highly repetitive topics, insufficient topic discovery, and damaged model interpretability. In this paper, we propose a new neural topic model, Embedding Clustering Regularization Topic Model (ECRTM). Besides the existing reconstruction error, we propose a novel Embedding Clustering Regularization (ECR), which forces each topic embedding to be the center of a separately aggregated word embedding cluster in the semantic space. This enables each produced topic to contain distinct word semantics, which alleviates topic collapsing. Regularized by ECR, our ECRTM generates diverse and coherent topics together with high-quality topic distributions of documents. Extensive experiments on benchmark datasets demonstrate that ECRTM effectively addresses the topic collapsing issue and consistently surpasses state-of-the-art baselines in terms of topic quality, topic distributions of documents, and downstream classification tasks.

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

Graph Neural Networks (GNNs) have become important machine learning tools for graph analysis, and its explainability is crucial for safety, fairness, and robustness. Layer-wise relevance propagation for GNNs (GNN-LRP) evaluates the relevance of walks to reveal important information flows in the network, and provides higher-order explanations, which have been shown to be superior to the lower-order, i.e., node-/edge-level, explanations. However, identifying relevant walks by GNN-LRP requires exponential computational complexity with respect to the network depth, which we will remedy in this paper. Specifically, we propose polynomial-time algorithms for finding top-$K$ relevant walks, which drastically reduces the computation and thus increases the applicability of GNN-LRP to large-scale problems. Our proposed algorithms are based on the max-product algorithm---a common tool for finding the maximum likelihood configurations in probabilistic graphical models---and can find the most relevant walks exactly at the neuron level and approximately at the node level. Our experiments demonstrate the performance of our algorithms at scale and their utility across application domains, i.e., on epidemiology, molecular, and natural language benchmarks. We provide our codes under github.com/xiong-ping/rel_walk_gnnlrp.

Graph transformers have emerged as a promising architecture for a variety of graph learning and representation tasks. Despite their successes, though, it remains challenging to scale graph transformers to large graphs while maintaining accuracy competitive with message-passing networks. In this paper, we introduce Exphormer, a framework for building powerful and scalable graph transformers. Exphormer consists of a sparse attention mechanism based on two mechanisms: virtual global nodes and expander graphs, whose mathematical characteristics, such as spectral expansion, pseduorandomness, and sparsity, yield graph transformers with complexity only linear in the size of the graph, while allowing us to prove desirable theoretical properties of the resulting transformer models. We show that incorporating Exphormer into the recently-proposed GraphGPS framework produces models with competitive empirical results on a wide variety of graph datasets, including state-of-the-art results on three datasets. We also show that Exphormer can scale to datasets on larger graphs than shown in previous graph transformer architectures.

Learning 3D graph with spatial position as well as node attributes has been recently actively studied, for its utility in different applications e.g. 3D molecules. Quantum computing is known a promising direction for its potential theoretical supremacy for large-scale graph and combinatorial problem as well as the increasing evidence for the availability to physical quantum devices in the near term. In this paper, for the first time to our best knowledge, we propose a quantum 3D embedding ansatz that learns the latent representation of 3D structures from the Hilbert space composed of the Bloch sphere of each qubit. Specifically, the 3D Cartesian coordinates of nodes are converted into rotation and torsion angles and then encode them into the form of qubits. Moreover, Parameterized Quantum Circuit (PQC) is applied to serve as the trainable layers and the output of the PQC is adopted as the final node embedding. Experimental results on two downstream tasks, molecular property prediction and 3D molecular geometries generation, demonstrate the effectiveness of our model. We show the capacity and capability of our model with the evaluation on the QM9 dataset (134k molecules) with very few parameters, and its potential to be executed on a real quantum device.

Dictionary learning, which approximates data samples by a set of shared atoms, is a fundamental task in representation learning. However, dictionary learning over graphs, namely graph dictionary learning (GDL), is much more challenging than vectorial data as graphs lie in disparate metric spaces. The sparse literature on GDL formulates the problem from the reconstructive view and often learns linear graph embeddings with a high computational cost. In this paper, we propose a Fused Gromov-Wasserstein (FGW) Mixture Model named FraMe to address the GDL problem from the generative view. Equipped with the graph generation function based on the radial basis function kernel and FGW distance, FraMe generates nonlinear embedding spaces, which, as we theoretically proved, provide a good approximation of the original graph spaces. A fast solution is further proposed on top of the expectation-maximization algorithm with guaranteed convergence. Extensive experiments demonstrate the effectiveness of the obtained node and graph embeddings, and our algorithm achieves significant improvements over the state-of-the-art methods.

Mutual information-based reinforcement learning (RL) has been proposed as a promising framework for retrieving complex skills autonomously without a task-oriented reward function through mutual information (MI) maximization or variational empowerment. However, learning complex skills is still challenging, due to the fact that the order of training skills can largely affect sample efficiency. Inspired by this, we recast variational empowerment as curriculum learning in goal-conditioned RL with an intrinsic reward function, which we name Variational Curriculum RL (VCRL). From this perspective, we propose a novel approach to unsupervised skill discovery based on information theory, called Value Uncertainty Variational Curriculum (VUVC). We prove that, under regularity conditions, VUVC accelerates the increase of entropy in the visited states compared to the uniform curriculum. We validate the effectiveness of our approach on complex navigation and robotic manipulation tasks in terms of sample efficiency and state coverage speed. We also demonstrate that the skills discovered by our method successfully complete a real-world robot navigation task in a zero-shot setup and that incorporating these skills with a global planner further increases the performance.

This paper investigates conservative exploration in reinforcement learning where the performance of the learning agent is guaranteed to be above a certain threshold throughout the learning process. It focuses on the tabular episodic Markov Decision Process (MDP) setting that has finite states and actions. With the knowledge of an existing safe baseline policy, an algorithms termed as StepMix is proposed to balance the exploitation and exploration while ensuring that the conservative constraint is never violated in each episode with high probability. StepMix features a unique design of a mixture policy that adaptively and smoothly interpolates between the baseline policy and the optimistic policy. Theoretical analysis shows that StepMix achieves near-optimal regret order as in the constraint-free setting, indicating that obeying the stringent episode-wise conservative constraint does not compromise the learning performance. Besides, a randomization based EpsMix algorithm is also proposed and shown the achieve the same performance as StepMix. The algorithm design and theoretical analysis are further extended to the setting where the baseline policy is not given a priori but must be learned from an offline dataset, and it is proved that similar conservative guarantee and regret can be achieved if the offline dataset is sufficiently large. Experiment results corroborate the theoretical analysis and demonstrate the effectiveness of the proposed conservative exploration strategies.

Despite the great interest in the bandit problem, designing efficient algorithms for complex models remains challenging, as there is typically no analytical way to quantify uncertainty. In this paper, we propose Multiplier Bootstrap-based Exploration (MBE), a novel exploration strategy that is applicable to any reward model amenable to weighted loss minimization. We prove both instance-dependent and instance-independent rate-optimal regret bounds for MBE in sub-Gaussian multi-armed bandits. With extensive simulation and real-data experiments, we show the generality and adaptivity of MBE.

Bayesian inference provides a principled framework for learning from complex data and reasoning under uncertainty. It has been widely applied in machine learning tasks such as medical diagnosis, drug design, and policymaking. In these common applications, data can be highly sensitive. Differential privacy (DP) offers data analysis tools with powerful worst-case privacy guarantees and has been developed as the leading approach in privacy-preserving data analysis. In this paper, we study Metropolis-Hastings (MH), one of the most fundamental MCMC methods, for large-scale Bayesian inference under differential privacy. While most existing private MCMC algorithms sacrifice accuracy and efficiency to obtain privacy, we provide the first exact and fast DP MH algorithm, using only a minibatch of data in most iterations. We further reveal, for the first time, a three-way trade-off among privacy, scalability (i.e. the batch size), and efficiency (i.e. the convergence rate), theoretically characterizing how privacy affects the utility and computational cost in Bayesian inference. We empirically demonstrate the effectiveness and efficiency of our algorithm in various experiments.

We study graph data augmentation by mixup, which has been used successfully on images. A key operation of mixup is to compute a convex combination of a pair of inputs. This operation is straightforward for grid-like data, such as images, but challenging for graph data. The key difficulty lies in the fact that different graphs typically have different numbers of nodes, and thus there lacks a node-level correspondence between graphs. In this work, we propose S-Mixup, a simple yet effective mixup method for graph classification by soft alignments. Specifically, given a pair of graphs, we explicitly obtain node-level correspondence via computing a soft assignment matrix to match the nodes between two graphs. Based on the soft assignments, we transform the adjacency and node feature matrices of one graph, so that the transformed graph is aligned with the other graph. In this way, any pair of graphs can be mixed directly to generate an augmented graph. We conduct systematic experiments to show that S-Mixup can improve the performance and generalization of graph neural networks (GNNs) on various graph classification tasks. In addition, we show that S-Mixup can increase the robustness of GNNs against noisy labels. Our code is publicly available as part of the DIG package (https://github.com/divelab/DIG).

Deep neural networks (DNNs), despite their ability to generalize with over-capacity networks, often rely heavily on the malignant bias as shortcuts instead of task-related information for discriminative tasks. This can lead to poor performance on real-world inputs, particularly when the majority of the sample is biased. To address the highly biased issue, recent studies either exploit auxiliary information which is rarely obtainable in practice or sift handful bias-free samples to emphasize them for debiasing. However, these methods are not always guaranteed to work due to unmet presumptions. In this paper, we propose Contrastive Debiasing via Generative Bias-transformation (CDvG) which is capable of operating without explicitly exploiting bias labels and bias-free samples. Motivated by our observation that not only discriminative models but also image translation models tend to focus on the malignant bias, CDvG employs an image translation model to transform the bias to another mode of bias while preserving task-relevant information. Through contrastive learning, the bias-transformed views are set against each other to learn bias-invariant representations. Our method shows a better debiasing effect when bias is more malignant as opposed to previous methods, and can also be integrated with the methods that focus on bias-free samples in a plug-and-play manner for further improvement. Experimental results on diverse datasets demonstrate that the proposed method outperforms the state-of-the-art, especially when bias-free samples are extremely scarce or absent.

Backdoor (Trojan) attack is a common threat to deep neural networks, where samples from one or more source classes embedded with a backdoor trigger will be misclassified to adversarial target classes. Existing methods for detecting whether a classifier is backdoor attacked are mostly designed for attacks with a single adversarial target (e.g., all-to-one attack). To the best of our knowledge, without supervision, no existing methods can effectively address the more general X2X attack with an arbitrary number of source classes, each paired with an arbitrary target class. In this paper, we propose UMD, the first Unsupervised Model Detection method that effectively detects X2X backdoor attacks via a joint inference of the adversarial (source, target) class pairs. In particular, we first define a novel transferability statistic to measure and select a subset of putative backdoor class pairs based on a proposed clustering approach. Then, these selected class pairs are jointly assessed based on an aggregation of their reverse-engineered trigger size for detection inference, using a robust and unsupervised anomaly detector we proposed. We conduct comprehensive evaluations on CIFAR-10, GTSRB, and Imagenette dataset, and show that our unsupervised UMD outperforms SOTA detectors (even with supervision) by 17%, 4%, and 8%, respectively, in terms of the detection accuracy against diverse X2X attacks. We also show the strong detection performance of UMD against several strong adaptive attacks.

With the success of large language models (LLMs) of code and their use as code assistants (e.g. Codex used in GitHub Copilot), techniques for introducing domain-specific knowledge in the prompt design process become important. In this work, we propose a framework called Repo-Level Prompt Generator that learns to generate example-specific prompts using prompt proposals. The prompt proposals take context from the entire repository, thereby incorporating both the structure of the repository and the context from other relevant files (e.g. imports, parent class files). Our technique doesn't require any access to the weights of the LLM, making it applicable in cases where we only have black-box access to the LLM. We conduct experiments on the task of single-line code auto-completion using code repositories taken from Google Code archives. We demonstrate that an oracle constructed from our prompt proposals gives a relative improvement of 36% over Codex, showing the quality of these proposals. Further, we show that when we train a model to predict a prompt proposal, we can achieve significant performance gains over Codex and other baselines. We release our code, data, and trained checkpoints at: https://github.com/shrivastavadisha/repolevelprompt_generation.

Unsupervised domain adaptation (UDA) enables the transfer of models trained on source domains to unlabeled target domains. However, transferring complex time series models presents challenges due to the dynamic temporal structure variations across domains. This leads to feature shifts in the time and frequency representations. Additionally, the label distributions of tasks in the source and target domains can differ significantly, posing difficulties in addressing label shifts and recognizing labels unique to the target domain. Effectively transferring complex time series models remains a formidable problem. We present RAINCOAT, the first model for both closed-set and universal domain adaptation on complex time series. RAINCOAT addresses feature and label shifts by considering both temporal and frequency features, aligning them across domains, and correcting for misalignments to facilitate the detection of private labels. Additionally, RAINCOAT improves transferability by identifying label shifts in target domains. Our experiments with 5 datasets and 13 state-of-the-art UDA methods demonstrate that RAINCOAT can improve transfer learning performance by up to 16.33% and can handle both closed-set and universal domain adaptation.

In this paper, we aim to optimize a contrastive loss with individualized temperatures in a principled manner. The common practice of using a global temperature parameter $\tau$ ignores the fact that ``not all semantics are created equal", meaning that different anchor data may have different numbers of samples with similar semantics, especially when data exhibits long-tails. First, we propose a new robust contrastive loss inspired by distributionally robust optimization (DRO), providing us an intuition about the effect of $\tau$ and a mechanism for automatic temperature individualization. Then, we propose an efficient stochastic algorithm for optimizing the robust contrastive loss with a provable convergence guarantee without using large mini-batch sizes. Theoretical and experimental results show that our algorithm automatically learns a suitable $\tau$ for each sample. Specifically, samples with frequent semantics use large temperatures to keep local semantic structures, while samples with rare semantics use small temperatures to induce more separable features. Our method not only outperforms prior strong baselines (e.g., SimCLR, CLIP) on unimodal and bimodal tasks with larger improvements on imbalanced data but also is less sensitive to hyper-parameters. To our best knowledge, this is the first methodical approach to optimizing a contrastive loss with individualized temperatures. Our proposed algorithms are implemented in the LibAUC library at https://libauc.org.

We introduce a boosting algorithm to pre-process data for fairness. Starting from an initial fair but inaccurate distribution, our approach shifts towards better data fitting while still ensuring a minimal fairness guarantee. To do so, it learns the sufficient statistics of an exponential family with boosting-compliant convergence. Importantly, we are able to theoretically prove that the learned distribution will have a representation rate and statistical rate data fairness guarantee. Unlike recent optimization based pre-processing methods, our approach can be easily adapted for continuous domain features. Furthermore, when the weak learners are specified to be decision trees, the sufficient statistics of the learned distribution can be examined to provide clues on sources of (un)fairness. Empirical results are present to display the quality of result on real-world data.

In this paper, we use Prior-data Fitted Networks (PFNs) as a flexible surrogate for Bayesian Optimization (BO). PFNs are neural processes that are trained to approximate the posterior predictive distribution (PPD) through in-context learning on any prior distribution that can be efficiently sampled from. We describe how this flexibility can be exploited for surrogate modeling in BO. We use PFNs to mimic a naive Gaussian process (GP), an advanced GP, and a Bayesian Neural Network (BNN). In addition, we show how to incorporate further information into the prior, such as allowing hints about the position of optima (user priors), ignoring irrelevant dimensions, and performing non-myopic BO by learning the acquisition function. The flexibility underlying these extensions opens up vast possibilities for using PFNs for BO. We demonstrate the usefulness of PFNs for BO in a large-scale evaluation on artificial GP samples and three different hyperparameter optimization testbeds: HPO-B, Bayesmark, and PD1. We publish code alongside trained models at https://github.com/automl/PFNs4BO.

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning geometrical and invariant temporal properties of the system in question (like attractors). However, training reconstruction algorithms like recurrent neural networks (RNNs) on such systems by gradient-descent based techniques faces severe challenges. This is mainly due to exploding gradients caused by the exponential divergence of trajectories in chaotic systems. Moreover, for (scientific) interpretability we wish to have as low dimensional reconstructions as possible, preferably in a model which is mathematically tractable. Here we report that a surprisingly simple modification of teacher forcing leads to provably strictly all-time bounded gradients in training on chaotic systems, and, when paired with a simple architectural rearrangement of a tractable RNN design, piecewise-linear RNNs (PLRNNs), allows for faithful reconstruction in spaces of at most the dimensionality of the observed system. We show on several DS that with these amendments we can reconstruct DS better than current SOTA algorithms, in much lower dimensions. Performance differences were particularly compelling on real world data with which most other methods severely struggled. This work thus led to a simple yet powerful DS reconstruction algorithm which is highly interpretable at the same time.

TD-learning is a foundation reinforcement learning (RL) algorithm for value prediction. Critical to the accuracy of value predictions is the quality of state representations. In this work, we consider the question: how does end-to-end TD-learning impact the representation over time? Complementary to prior work, we provide a set of analysis that sheds further light on the representation dynamics under TD-learning. We first show that when the environments are reversible, end-to-end TD-learning strictly decreases the value approximation error over time. Under further assumptions on the environments, we can connect the representation dynamics with spectral decomposition over the transition matrix. This latter finding establishes fitting multiple value functions from randomly generated rewards as a useful auxiliary task for representation learning, as we empirically validate on both tabular and Atari game suites.

We investigate the extent to which offline demonstration data can improve online learning. It is natural to expect some improvement, but the question is how, and by how much? We show that the degree of improvement must depend on the quality of the demonstration data. To generate portable insights, we focus on Thompson sampling (TS) applied to a multi-armed bandit as a prototypical online learning algorithm and model. The demonstration data is generated by an expert with a given competence level, a notion we introduce. We propose an informed TS algorithm that utilizes the demonstration data in a coherent way through Bayes' rule and derive a prior-dependent Bayesian regret bound. This offers insight into how pretraining can greatly improve online performance and how the degree of improvement increases with the expert's competence level. We also develop a practical, approximate informed TS algorithm through Bayesian bootstrapping and show substantial empirical regret reduction through experiments.

We propose a new method for count-based exploration in high-dimensional state spaces. Unlike previous work which relies on density models, we show that counts can be derived by averaging samples from the Rademacher distribution (or coin flips). This insight is used to set up a simple supervised learning objective which, when optimized, yields a state's visitation count. We show that our method is significantly more effective at deducing ground-truth visitation counts than previous work; when used as an exploration bonus for a model-free reinforcement learning algorithm, it outperforms existing approaches on most of 9 challenging exploration tasks, including the Atari game Montezuma's Revenge.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

In this paper, we present a Conformal Prediction method that computes prediction sets in a one-shot Federated Learning (FL) setting. More specifically, we introduce a novel quantile-of-quantiles estimator and prove that for any distribution, it is possible to compute prediction sets with desired coverage in only one round of communication. To mitigate privacy issues, we also describe a locally differentially private version of our estimator. Finally, over a wide range of experiments, we show that our method returns prediction sets with coverage and length very similar to those obtained in a centralized setting. These results demonstrate that our method is well-suited for one-shot Federated Learning.

In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and sharper dependencies on other salient problem parameters. Moreover, existing approaches to federated Q-learning adopt an equally-weighted averaging of local Q-estimates, which can be highly sub-optimal in the asynchronous setting since the local trajectories can be highly heterogeneous due to different local behavior policies. Existing sample complexity scales inverse proportionally to the minimum entry of the stationary state-action occupancy distributions over all agents, requiring that every agent covers the entire state-action space. Instead, we propose a novel importance averaging algorithm, giving larger weights to more frequently visited state-action pairs. The improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents collectively cover the entire state-action space, unveiling the blessing of heterogeneity.

Generalization is one of the most fundamental challenges in deep learning, aiming to predict model performances on unseen data. Empirically, such predictions usually rely on a validation set, while recent works showed that an unlabeled validation set also works. Without validation sets, it is extremely difficult to obtain non-vacuous generalization bounds, which leads to a weaker task of finding generalization measures that monotonically relate to generalization error. In this paper, we propose a new generalization measure REF Complexity (RElative Fitting degree between signal and noise), motivated by the intuition that a given model-algorithm pair may generalize well if it fits signal (e.g., true labels) fast while fitting noise (e.g., random labels) slowly. Empirically, REF Complexity monotonically relates to test accuracy in real-world datasets without accessing additional validation sets, achieving -0.988 correlation on CIFAR-10 and -0.960 correlation on CIFAR-100. We further theoretically verify the utility of REF Complexity under three different cases, including convex and smooth regimes with stochastic gradient descent, smooth regimes (not necessarily convex) with stochastic gradient Langevin dynamics, and linear regimes with gradient descent. The code is available at https://github.com/962086838/REF-complexity.

A big convergence of model architectures across language, vision, speech, and multimodal is emerging. However, under the same name ''Transformers'', the above areas use different implementations for better performance, e.g., Post-LayerNorm for BERT, and Pre-LayerNorm for GPT and vision Transformers. We call for the development of Foundation Transformer for true general-purpose modeling, which serves as a go-to architecture for various tasks and modalities with guaranteed training stability. In this work, we introduce a Transformer variant, named Magneto, to fulfill the goal. Specifically, we propose Sub-LayerNorm for good expressivity, and the initialization strategy theoretically derived from DeepNet for stable scaling up. Extensive experiments demonstrate its superior performance and better stability than the de facto Transformer variants designed for various applications, including language modeling (i.e., BERT, and GPT), machine translation, vision pretraining (i.e., BEiT), speech recognition, and multimodal pretraining (i.e., BEiT-3).

To deal with the challenge of high cost of annotating all relevant labels for each example in multi-label learning, single-positive multi-label learning (SPMLL) has been studied in recent years, where each example is annotated with only one positive label. By adopting pseudo-label generation, i.e., assigning pseudo-label to each example by various strategies, existing methods have empirically validated that SPMLL would significantly reduce the amount of supervision with a tolerable damage in classification performance. However, there is no existing method that can provide a theoretical guarantee for learning from pseudo-label on SPMLL. In this paper, the conditions of the effectiveness of learning from pseudo-label for SPMLL are shown and the learnability of pseudo-label-based methods is proven. Furthermore, based on the theoretical guarantee of pseudo-label for SPMLL, we propose a novel SPMLL method named MIME, i.e., Mutual label enhancement for sIngle-positive Multi-label lEarning and prove that the generated pseudo-label by MIME approximately converges to the fully-supervised case. Experiments on four image datasets and five MLL datasets show the effectiveness of our methods over several existing SPMLL approaches.

In this paper, we consider the problem of Iterative Machine Teaching (IMT), where the teacher provides examples to the learner iteratively such that the learner can achieve fast convergence to a target model. However, existing IMT algorithms are solely based on parameterized families of target models. They mainly focus on convergence in the parameter space, resulting in difficulty when the target models are defined to be functions without dependency on parameters. To address such a limitation, we study a more general task -- Nonparametric Iterative Machine Teaching (NIMT), which aims to teach nonparametric target models to learners in an iterative fashion. Unlike parametric IMT that merely operates in the parameter space, we cast NIMT as a functional optimization problem in the function space. To solve it, we propose both random and greedy functional teaching algorithms. We obtain the iterative teaching dimension (ITD) of the random teaching algorithm under proper assumptions, which serves as a uniform upper bound of ITD in NIMT. Further, the greedy teaching algorithm has a significantly lower ITD, which reaches a tighter upper bound of ITD in NIMT. Finally, we verify the correctness of our theoretical findings with extensive experiments in nonparametric scenarios.

Cutting out an object and estimating its opacity mask, known as image matting, is a key task in image and video editing. Due to the highly ill-posed issue, additional inputs, typically user-defined trimaps or scribbles, are usually needed to reduce the uncertainty. Although effective, it is either time consuming or only suitable for experienced users who know where to place the strokes. In this work, we propose a decomposed-uncertainty-guided matting (dugMatting) algorithm, which explores the explicitly decomposed uncertainties to efficiently and effectively improve the results. Basing on the characteristic of these uncertainties, the epistemic uncertainty is reduced in the process of guiding interaction (which introduces prior knowledge), while the aleatoric uncertainty is reduced in modeling data distribution (which introduces statistics for both data and possible noise). The proposed matting framework relieves the requirement for users to determine the interaction areas by using simple and efficient labeling. Extensively quantitative and qualitative results validate that the proposed method significantly improves the original matting algorithms in terms of both efficiency and efficacy.

In recent years, increasing attention has been directed to leveraging pre-trained vision models for motor control. While existing works mainly emphasize the importance of this pre-training phase, the arguably equally important role played by downstream policy learning during control-specific fine-tuning is often neglected. It thus remains unclear if pre-trained vision models are consistent in their effectiveness under different control policies. To bridge this gap in understanding, we conduct a comprehensive study on 14 pre-trained vision models using 3 distinct classes of policy learning methods, including reinforcement learning (RL), imitation learning through behavior cloning (BC), and imitation learning with a visual reward function (VRF). Our study yields a series of intriguing results, including the discovery that the effectiveness of pre-training is highly dependent on the choice of the downstream policy learning algorithm. We show that conventionally accepted evaluation based on RL methods is highly variable and therefore unreliable, and further advocate for using more robust methods like VRF and BC. To facilitate more universal evaluations of pre-trained models and their policy learning methods in the future, we also release a benchmark of 21 tasks across 3 different environments alongside our work.

Data-driven optimization uses contextual information and machine learning algorithms to find solutions to decision problems with uncertain parameters. While a vast body of work is dedicated to interpreting machine learning models in the classification setting, explaining decision pipelines involving learning algorithms remains unaddressed. This lack of interpretability can block the adoption of data-driven solutions as practitioners may not understand or trust the recommended decisions. We bridge this gap by introducing a counterfactual explanation methodology tailored to explain solutions to data-driven problems. We introduce two classes of explanations and develop methods to find nearest explanations of random forest and nearest-neighbor predictors. We demonstrate our approach by explaining key problems in operations management such as inventory management and routing.

We consider the task of evaluating policies of algorithmic resource allocation through randomized controlled trials (RCTs). Such policies are tasked with optimizing the utilization of limited intervention resources, with the goal of maximizing the benefits derived. Evaluation of such allocation policies through RCTs proves difficult, notwithstanding the scale of the trial, because the individuals’ outcomes are inextricably interlinked through resource constraints controlling the policy decisions. Our key contribution is to present a new estimator leveraging our proposed novel concept, that involves retrospective reshuffling of participants across experimental arms at the end of an RCT. We identify conditions under which such reassignments are permissible and can be leveraged to construct counterfactual trials, whose outcomes can be accurately ascertained, for free. We prove theoretically that such an estimator is more accurate than common estimators based on sample means -- we show that it returns an unbiased estimate and simultaneously reduces variance. We demonstrate the value of our approach through empirical experiments on synthetic, semisynthetic as well as real case study data and show improved estimation accuracy across the board.

Population-based search has recently emerged as a possible alternative to Reinforcement Learning (RL) for black-box neural architecture search (NAS). It performs well in practice even though it is not theoretically well understood. In particular, whereas traditional population-based search methods such as evolutionary algorithms (EAs) draw much power from crossover operations, it is difficult to take advantage of them in NAS. The main obstacle is believed to be the permutation problem: The mapping between genotype and phenotype in traditional graph representations is many-to-one, leading to a disruptive effect of standard crossover. This paper presents the first theoretical analysis of the behaviors of mutation, crossover and RL in black-box NAS, and proposes a new crossover operator based on the shortest edit path (SEP) in graph space. The SEP crossover is shown theoretically to overcome the permutation problem, and as a result, have a better expected improvement compared to mutation, standard crossover and RL. Further, it empirically outperform these other methods on state-of-the-art NAS benchmarks. The SEP crossover therefore allows taking full advantage of population-based search in NAS, and the underlying theory can serve as a foundation for deeper understanding of black-box NAS methods in general.

We study the domain adaptation problem with label shift in this work. Under the label shift context, the marginal distribution of the label varies across the training and testing datasets, while the conditional distribution of features given the label is the same. Traditional label shift adaptation methods either suffer from large estimation errors or require cumbersome post-prediction calibrations. To address these issues, we first propose a moment-matching framework for adapting the label shift based on the geometry of the influence function. Under such a framework, we propose a novel method named $\underline{\mathrm{E}}$fficient $\underline{\mathrm{L}}$abel $\underline{\mathrm{S}}$hift $\underline{\mathrm{A}}$daptation (ELSA), in which the adaptation weights can be estimated by solving linear systems. Theoretically, the ELSA estimator is $\sqrt{n}$-consistent ($n$ is the sample size of the source data) and asymptotically normal. Empirically, we show that ELSA can achieve state-of-the-art estimation performances without post-prediction calibrations, thus, gaining computational efficiency.

We consider the reinforcement learning (RL) problem with general utilities which consists in maximizing a function of the state-action occupancy measure. Beyond the standard cumulative reward RL setting, this problem includes as particular cases constrained RL, pure exploration and learning from demonstrations among others. For this problem, we propose a simpler single-loop parameter-free normalized policy gradient algorithm. Implementing a recursive momentum variance reduction mechanism, our algorithm achieves $\tilde{\mathcal{O}}(\epsilon^{-3})$ and $\tilde{\mathcal{O}}(\epsilon^{-2})$ sample complexities for $\epsilon$-first-order stationarity and $\epsilon$-global optimality respectively, under adequate assumptions. We further address the setting of large finite state action spaces via linear function approximation of the occupancy measure and show a $\tilde{\mathcal{O}}(\epsilon^{-4})$ sample complexity for a simple policy gradient method with a linear regression subroutine.

In many applications of online decision making, the environment is non-stationary and it is therefore crucial to use bandit algorithms that handle changes. Most existing approaches are designed to protect against non-smooth changes, constrained only by total variation or Lipschitzness over time, where they guarantee $T^{2/3}$ regret. However, in practice environments are often changing *smoothly*, so such algorithms may incur higher-than-necessary regret in these settings and do not leverage information on the *rate of change*. In this paper, we study a non-stationary two-arm bandit problem where we assume an arm's mean reward is a $\beta$-Hölder function over (normalized) time, meaning it is $(\beta-1)$-times Lipschitz-continuously differentiable. We show the first *separation* between the smooth and non-smooth regimes by presenting a policy with $T^{3/5}$ regret for $\beta=2$. We complement this result by a $T^{\frac{\beta+1}{2\beta+1}}$ lower bound for any integer $\beta\ge 1$, which matches our upper bound for $\beta=2$.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an $\epsilon$-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make a significant progress on minimizing simple regret in both data-rich ($T\ge n$) and data-poor regime ($T \le n$) where $n$ is the number of arms and $T$ is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm where we bound the probability of returning an arm whose mean reward is not within $\epsilon$ from the best (i.e., not $\epsilon$-good) for *any* choice of $\epsilon>0$, although $\epsilon$ is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of $\sqrt{n/T}$ up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an $\epsilon$-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

We study the top-$k$ selection problem under the differential privacy model: $m$ items are rated according to votes of a set of clients. We consider a setting in which algorithms can retrieve data via a sequence of accesses, each either a random access or a sorted access; the goal is to minimize the total number of data accesses. Our algorithm requires only $O(\sqrt{mk})$ expected accesses: to our knowledge, this is the first sublinear data-access upper bound for this problem. Our analysis also shows that the well-known exponential mechanism requires only $O(\sqrt{m})$ expected accesses. Accompanying this, we develop the first lower bounds for the problem, in three settings: only random accesses; only sorted accesses; a sequence of accesses of either kind. We show that, to avoid $\Omega(m)$ access cost, supporting *both* kinds of access is necessary, and that in this case our algorithm's access cost is optimal.

The notion of omnipredictors (Gopalan, Kalai, Reingold, Sharan and Wieder ITCS 2022), suggested a new paradigm for loss minimization. Rather than learning a predictor based on a known loss function, omnipredictors can easily be post-processed to minimize any one of a rich family of loss functions compared with the loss of hypotheses in a class $\mathcal C$. It has been shown that such omnipredictors exist and are implied (for all convex and Lipschitz loss functions) by the notion of multicalibration from the algorithmic fairness literature. In this paper, we introduce omnipredictors for constrained optimization and study their complexity and implications. The notion that we introduce allows the learner to be unaware of the loss function that will be later assigned *as well as the constraints that will be later imposed*, as long as the subpopulations that are used to define these constraints are known. We show how to obtain omnipredictors for constrained optimization problems, relying on appropriate variants of multicalibration. We also investigate the implications of this notion when the constraints used are so-called group fairness notions.

Differential privacy (DP) is by far the most widely accepted framework for mitigating privacy risks in machine learning. However, exactly how small the privacy parameter $\epsilon$ needs to be to protect against certain privacy risks in practice is still not well-understood. In this work, we study data reconstruction attacks for discrete data and analyze it under the framework of multiple hypothesis testing. For a learning algorithm satisfying $(\alpha, \epsilon)$-Renyi DP, we utilize different variants of the celebrated Fano's inequality to upper bound the attack advantage of a data reconstruction adversary. Our bound can be numerically computed to relate the parameter $\epsilon$ to the desired level of privacy protection in practice, and complements the empirical evidence for the effectiveness of DP against data reconstruction attacks even at relatively large values of $\epsilon$.

Two-point zeroth order methods are important in many applications of zeroth-order optimization arising in robotics, wind farms, power systems, online optimization, and adversarial robustness to black-box attacks in deep neural networks, where the problem can be high-dimensional and/or time-varying. Furthermore, such problems may be nonconvex and contain saddle points. While existing works have shown that zeroth-order methods utilizing $\Omega(d)$ function valuations per iteration (with $d$ denoting the problem dimension) can escape saddle points efficiently, it remains an open question if zeroth-order methods based on two-point estimators can escape saddle points. In this paper, we show that by adding an appropriate isotropic perturbation at each iteration, a zeroth-order algorithm based on $2m$ (for any $1 \leq m \leq d$) function evaluations per iteration can not only find $\epsilon$-second order stationary points polynomially fast, but do so using only $\tilde{O}(\frac{d}{m\epsilon^{2}\bar{\psi}})$ function evaluations, where $\bar{\psi} \geq \tilde{\Omega}(\sqrt{\epsilon})$ is a parameter capturing the extent to which the function of interest exhibits the strict saddle property.

The concept class of low-degree polynomial threshold functions (PTFs) plays a fundamental role in machine learning. In this paper, we study PAC learning of $K$-sparse degree-$d$ PTFs on $\mathbb{R}^n$, where any such concept depends only on $K$ out of $n$ attributes of the input. Our main contribution is a new algorithm that runs in time $({nd}/{\epsilon})^{O(d)}$ and under the Gaussian marginal distribution, PAC learns the class up to error rate $\epsilon$ with $O(\frac{K^{4d}}{\epsilon^{2d}} \cdot \log^{5d} n)$ samples even when an $\eta \leq O(\epsilon^d)$ fraction of them are corrupted by the nasty noise of Bshouty et al. (2002), possibly the strongest corruption model. Prior to this work, attribute-efficient robust algorithms are established only for the special case of sparse homogeneous halfspaces. Our key ingredients are: 1) a structural result that translates the attribute sparsity to a sparsity pattern of the Chow vector under the basis of Hermite polynomials, and 2) a novel attribute-efficient robust Chow vector estimation algorithm which uses exclusively a restricted Frobenius norm to either certify a good approximation or to validate a sparsity-induced degree-$2d$ polynomial as a filter to detect corrupted samples.

This paper studies the prediction of a target $\mathbf{z}$ from a pair of random variables $(\mathbf{x},\mathbf{y})$, where the ground-truth predictor is additive $\mathbb{E}[\mathbf{z} \mid \mathbf{x},\mathbf{y}] = f_\star(\mathbf{x}) +g_{\star}(\mathbf{y})$. We study the performance of empirical risk minimization (ERM) over functions $f+g$, $f \in \mathcal{F}$ and $g \in \mathcal{G}$, fit on a given training distribution, but evaluated on a test distribution which exhibits covariate shift. We show that, when the class $\mathcal{F}$ is "simpler" than $\mathcal{G}$ (measured, e.g., in terms of its metric entropy), our predictor is more resilient to *heterogenous covariate shifts* in which the shift in $\mathbf{x}$ is much greater than that in $\mathbf{y}$. These results rely on a novel Hölder style inequality for the Dudley integral which may be of independent interest. Moreover, we corroborate our theoretical findings with experiments demonstrating improved resilience to shifts in "simpler" features across numerous domains.

We consider a contextual combinatorial bandit problem where in each round a learning agent selects a subset of arms and receives feedback on the selected arms according to their scores. The score of an arm is an unknown function of the arm's feature. Approximating this unknown score function with deep neural networks, we propose algorithms: Combinatorial Neural UCB ($\texttt{CN-UCB}$) and Combinatorial Neural Thompson Sampling ($\texttt{CN-TS}$). We prove that $\texttt{CN-UCB}$ achieves $\tilde{\mathcal{O}}(\tilde{d} \sqrt{T})$ or $\tilde{\mathcal{O}}(\sqrt{\tilde{d} T K})$ regret, where $\tilde{d}$ is the effective dimension of a neural tangent kernel matrix, $K$ is the size of a subset of arms, and $T$ is the time horizon. For $\texttt{CN-TS}$, we adapt an optimistic sampling technique to ensure the optimism of the sampled combinatorial action, achieving a worst-case (frequentist) regret of $\tilde{\mathcal{O}}(\tilde{d} \sqrt{TK})$. To the best of our knowledge, these are the first combinatorial neural bandit algorithms with regret performance guarantees. In particular, $\texttt{CN-TS}$ is the first Thompson sampling algorithm with the worst-case regret guarantees for the general contextual combinatorial bandit problem. The numerical experiments demonstrate the superior performances of our proposed algorithms.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) shows that even if a learner is given linear features in $\mathbb{R}^d$ that approximate the rewards in a bandit or RL with a uniform error of $\varepsilon$, searching for an $O(\varepsilon)$-optimal action requires pulling at least $\Omega(\exp(d))$ queries. Furthermore, Lattimore et al. (2020) show that a degraded $O(\varepsilon\sqrt{d})$-optimal solution can be learned within $\operatorname{poly}(d/\varepsilon)$ queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break $\varepsilon\sqrt{d}$ barrier. In this paper, we address this question by showing that algorithms can obtain $O(\varepsilon)$-optimal actions by querying $\tilde{O}(\exp(m\varepsilon))$ actions, where $m$ is the sparsity parameter, removing the $\exp(d)$-dependence. We further show (with an information-theoretical lower bound) that this is the best possible if one demands an error $ m^{\delta}\varepsilon$ for $0<\delta<1$. We further show that $\operatorname{poly}(m/\varepsilon)$ bounds are possible when the linear features are "good''. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are ``useful'' for bandit and reinforcement learning with misspecification.

Differential private optimization for nonconvex smooth objective is considered. In the previous work, the best known utility bound is $\widetilde O(\sqrt{d}/(n\varepsilon_\mathrm{DP}))$ in terms of the squared full gradient norm, which is achieved by Differential Private Gradient Descent (DP-GD) as an instance, where $n$ is the sample size, $d$ is the problem dimensionality and $\varepsilon_\mathrm{DP}$ is the differential privacy parameter. To improve the best known utility bound, we propose a new differential private optimization framework called DIFF2 (DIFFerential private optimization via gradient DIFFerences) that constructs a differential private global gradient estimator with possibly quite small variance based on communicated gradient differences rather than gradients themselves. It is shown that DIFF2 with a gradient descent subroutine achieves the utility of $\widetilde O(d^{2/3}/(n\varepsilon_\mathrm{DP})^{4/3})$, which can be significantly better than the previous one in terms of the dependence on the sample size $n$. To the best of our knowledge, this is the first fundamental result to improve the standard utility $\widetilde O(\sqrt{d}/(n\varepsilon_\mathrm{DP}))$ for nonconvex objectives. Additionally, a more computational and communication efficient subroutine is combined with DIFF2 and its theoretical analysis is also given. Numerical experiments are conducted to validate the superiority of DIFF2 framework.

Self-distillation (SD) is the process of first training a "teacher" model and then using its predictions to train a "student" model that has the *same* architecture. Specifically, the student's loss is $\big(\xi*\ell(\text{teacher's predictions}, \text{ student's predictions}) + (1-\xi)*\ell(\text{given labels}, \text{ student's predictions})\big)$, where $\ell$ is the loss function and $\xi$ is some parameter $\in [0,1]$. SD has been empirically observed to provide performance gains in several settings. In this paper, we theoretically characterize the effect of SD in two supervised learning problems with *noisy labels*. We first analyze SD for regularized linear regression and show that in the high label noise regime, the optimal value of $\xi$ that minimizes the expected error in estimating the ground truth parameter is surprisingly greater than 1. Empirically, we show that $\xi > 1$ works better than $\xi \leq 1$ even with the cross-entropy loss for several classification datasets when 50% or 30% of the labels are corrupted. Further, we quantify when optimal SD is better than optimal regularization. Next, we analyze SD in the case of logistic regression for binary classification with random label corruption and quantify the range of label corruption in which the student outperforms the teacher (w.r.t. accuracy). To our knowledge, this is the first result of its kind for the cross-entropy loss.

We consider random walks on discrete state spaces, such as general undirected graphs, where the random walkers are designed to approximate a target quantity over the network topology via sampling and neighborhood exploration in the form of Markov chain Monte Carlo (MCMC) procedures. Given any Markov chain corresponding to a target probability distribution, we design a *self-repellent random walk* (SRRW) which is less likely to transition to nodes that were highly visited in the past, and more likely to transition to seldom visited nodes. For a class of SRRWs parameterized by a positive real $\alpha$, we prove that the empirical distribution of the process converges almost surely to the the target (stationary) distribution of the underlying Markov chain kernel. We then provide a central limit theorem and derive the exact form of the arising asymptotic co-variance matrix, which allows us to show that the SRRW with a stronger repellence (larger $\alpha$) always achieves a smaller asymptotic covariance, in the sense of Loewner ordering of co-variance matrices. Especially for SRRW-driven MCMC algorithms, we show that the decrease in the asymptotic sampling variance is of the order $O(1/\alpha)$, eventually going down to zero. Finally, we provide numerical simulations complimentary to our theoretical results, also empirically testing a version of SRRW with $\alpha$ increasing in time to combine the benefits of smaller asymptotic variance due to large $\alpha$, with empirically observed faster mixing properties of SRRW with smaller $\alpha$.

Decentralized Stochastic Gradient Descent (SGD) is an emerging neural network training approach that enables multiple agents to train a model collaboratively and simultaneously. Rather than using a central parameter server to collect gradients from all the agents, each agent keeps a copy of the model parameters and communicates with a small number of other agents to exchange model updates. Their communication, governed by the communication topology and gossip weight matrices, facilitates the exchange of model updates. The state-of-the-art approach uses the dynamic one-peer exponential-2 topology, achieving faster training times and improved scalability than the ring, grid, torus, and hypercube topologies. However, this approach requires a power-of-2 number of agents, which is impractical at scale. In this paper, we remove this restriction and propose Decentralized SGD with Communication-optimal Exact Consensus Algorithm (DSGD-CECA), which works for any number of agents while still achieving state-of-the-art properties. In particular, DSGD-CECA incurs a unit per-iteration communication overhead and an $\tilde{O}(n^3)$ transient iteration complexity. Our proof is based on newly discovered properties of gossip weight matrices and a novel approach to combine them with DSGD's convergence analysis. Numerical experiments show the efficiency of DSGD-CECA.

A well-known limitation of existing molecular generative models is that the generated molecules highly resemble those in the training set. To generate truly novel molecules that may have even better properties for de novo drug discovery, more powerful exploration in the chemical space is necessary. To this end, we propose Molecular Out-Of-distribution Diffusion(MOOD), a score-based diffusion scheme that incorporates out-of-distribution (OOD) control in the generative stochastic differential equation (SDE) with simple control of a hyperparameter, thus requires no additional costs. Since some novel molecules may not meet the basic requirements of real-world drugs, MOOD performs conditional generation by utilizing the gradients from a property predictor that guides the reverse-time diffusion process to high-scoring regions according to target properties such as protein-ligand interactions, drug-likeness, and synthesizability. This allows MOOD to search for novel and meaningful molecules rather than generating unseen yet trivial ones. We experimentally validate that MOOD is able to explore the chemical space beyond the training distribution, generating molecules that outscore ones found with existing methods, and even the top 0.01% of the original training pool. Our code is available at https://github.com/SeulLee05/MOOD.

In this work, we initiate the idea of using denoising diffusion models to learn priors for online decision making problems. We specifically focus on bandit meta-learning, aiming to learn a policy that performs well across bandit tasks of a same class. To this end, we train a diffusion model that learns the underlying task distribution and combine Thompson sampling with the learned prior to deal with new tasks at test time. Our posterior sampling algorithm carefully balances between the learned prior and the noisy observations that come from the learner's interaction with the environment. To capture realistic bandit scenarios, we propose a novel diffusion model training procedure that trains from incomplete and noisy data, which could be of independent interest. Finally, our extensive experiments clearly demonstrate the potential of the proposed approach.

Deep graph generative modeling has proven capable of learning the distribution of complex, multi-scale structures characterizing real-world graphs. However, one of the main limitations of existing methods is their large output space, which limits generation scalability and hinders accurate modeling of the underlying distribution. To overcome these limitations, we propose a novel approach that significantly reduces the output space of existing graph generative models. Specifically, starting from the observation that many real-world graphs have low graph bandwidth, we restrict graph bandwidth during training and generation. Our strategy improves both generation scalability and quality without increasing architectural complexity or reducing expressiveness. Our approach is compatible with existing graph generative methods, and we describe its application to both autoregressive and one-shot models. We extensively validate our strategy on synthetic and real datasets, including molecular graphs. Our experiments show that, in addition to improving generation efficiency, our approach consistently improves generation quality and reconstruction accuracy. The implementation is made available.

Variational auto-encoders are powerful probabilistic models in generative tasks but suffer from generating low-quality samples which are caused by the holes in the prior. We propose the Coupled Variational Auto-Encoder (C-VAE), which formulates the VAE problem as one of Optimal Transport (OT) between the prior and data distributions. The C-VAE allows greater flexibility in priors and natural resolution of the prior hole problem by enforcing coupling between the prior and the data distribution and enables flexible optimization through the primal, dual, and semi-dual formulations of entropic OT. Simulations on synthetic and real data show that the C-VAE outperforms alternatives including VAE, WAE, and InfoVAE in fidelity to the data, quality of the latent representation, and in quality of generated samples.

Recent score-based diffusion models (SBDMs) show promising results in unpaired image-to-image translation (I2I). However, existing methods, either energy-based or statistically-based, provide no explicit form of the interfered intermediate generative distributions. This work presents a new score-decomposed diffusion model (SDDM) on manifolds to explicitly optimize the tangled distributions during image generation. SDDM derives manifolds to make the distributions of adjacent time steps separable and decompose the score function or energy guidance into an image "denoising" part and a content "refinement" part. To refine the image in the same noise level, we equalize the refinement parts of the score function and energy guidance, which permits multi-objective optimization on the manifold. We also leverage the block adaptive instance normalization module to construct manifolds with lower dimensions but still concentrated with the perturbed reference image. SDDM outperforms existing SBDM-based methods with much fewer diffusion steps on several I2I benchmarks.

Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.

The success of deep learning is greatly attributed to stochastic gradient descent (SGD), yet it remains unclear how SGD finds well-generalized models. We demonstrate that SGD has an implicit regularization effect on the logit-weight Jacobian norm of neural networks. This regularization effect is weighted with the impurity of the probability output, and thus it is active in a certain phase of training. Moreover, based on these findings, we propose a novel optimization method that explicitly regularizes the Jacobian norm, which leads to similar performance as other state-of-the-art sharpness-aware optimization methods.

Many problems in science and engineering involve optimizing an expensive black-box function over a high-dimensional space. In the offline model-based optimization (MBO) setting, we assume access to a fixed, offline dataset for pretraining and a small budget for online function evaluations. Prior approaches seek to utilize the offline data to approximate the function or its inverse but are not sufficiently accurate far from the data distribution. We propose BONET, a generative framework for pretraining a novel model-based optimizer using offline datasets. In BONET, we train an autoregressive model on fixed-length trajectories derived from an offline dataset. We design a sampling strategy to synthesize trajectories from offline data using a simple heuristic of rolling out monotonic transitions from low-fidelity to high-fidelity samples. Empirically, we instantiate BONET using a causally masked Transformer (Radford et al., 2019) and evaluate it on Design-Bench (Trabucco et al., 2022), where we rank the best on average, outperforming state-of-the-art baselines.

Learning unnormalized statistical models (e.g., energy-based models) is computationally challenging due to the complexity of handling the partition function. To eschew this complexity, noise-contrastive estimation (NCE) has been proposed by formulating the objective as the logistic loss of the real data and the artificial noise. However, as found in previous works, NCE may perform poorly in many tasks due to its flat loss landscape and slow convergence. In this paper, we study a direct approach for optimizing the negative log-likelihood of unnormalized models from the perspective of compositional optimization. To tackle the partition function, a noise distribution is introduced such that the log partition function can be written as a compositional function whose inner function can be estimated with stochastic samples. Hence, the objective can be optimized by stochastic compositional optimization algorithms. Despite being a simple method, we demonstrate that it is more favorable than NCE by (1) establishing a fast convergence rate and quantifying its dependence on the noise distribution through the variance of stochastic estimators; (2) developing better results for one-dimensional Gaussian mean estimation by showing our objective has a much favorable loss landscape and hence our method enjoys faster convergence; (3) demonstrating better performance on multiple applications, including density estimation, out-of-distribution detection, and real image generation.

In practical federated learning (FL) systems, the communication cost between the clients and the central server can often be a bottleneck. In this paper, we focus on biased gradient compression in non-convex FL problems. In the classical distributed learning, the method of error feedback (EF) is a common technique to remedy the downsides of biased gradient compression, but the performance of EF in FL still lacks systematic investigation. In this work, we study a compressed FL scheme with error feedback, named Fed-EF, with two variants depending on the global model optimizer. While directly applying biased compression in FL leads to poor convergence, we show that Fed-EF is able to match the convergence rate of the full-precision FL counterpart with a linear speedup w.r.t. the number of clients. Experiments verify that Fed-EF achieves the same performance as the full-precision FL approach, at the substantially reduced communication cost. Moreover, we develop a new analysis of the EF under partial participation (PP), an important scenario in FL. Under PP, the convergence rate of Fed-EF exhibits an extra slow-down factor due to a so-called ``stale error compensation'' effect, which is also justified in our experiments. Our results provide insights on a theoretical limitation of EF, and possible directions for improvements.

Recently, diffusion model shines as a promising backbone for the sequence modeling paradigm in offline reinforcement learning(RL). However, these works mostly lack the generalization ability across tasks with reward or dynamics change. To tackle this challenge, in this paper we propose a task-oriented conditioned diffusion planner for offline meta-RL(MetaDiffuser), which considers the generalization problem as conditional trajectory generation task with contextual representation. The key is to learn a context conditioned diffusion model which can generate task-oriented trajectories for planning across diverse tasks. To enhance the dynamics consistency of the generated trajectories while encouraging trajectories to achieve high returns, we further design a dual-guided module in the sampling process of the diffusion model. The proposed framework enjoys the robustness to the quality of collected warm-start data from the testing task and the flexibility to incorporate with different task representation method. The experiment results on MuJoCo benchmarks show that MetaDiffuser outperforms other strong offline meta-RL baselines, demonstrating the outstanding conditional generation ability of diffusion architecture.

We propose an efficient method to ground pretrained text-only language models to the visual domain, enabling them to process arbitrarily interleaved image-and-text data, and generate text interleaved with retrieved images. Our method leverages the abilities of language models learnt from large scale text-only pretraining, such as in-context learning and free-form text generation. We keep the language model frozen, and finetune input and output linear layers to enable cross-modality interactions. This allows our model to process arbitrarily interleaved image-and-text inputs, and generate free-form text interleaved with retrieved images. We achieve strong zero-shot performance on grounded tasks such as contextual image retrieval and multimodal dialogue, and showcase compelling interactive abilities. Our approach works with any off-the-shelf language model and paves the way towards an effective, general solution for leveraging pretrained language models in visually grounded settings.

Machine learning models often perform poorly on subgroups that are underrepresented in the training data. Yet, little is understood on the variation in mechanisms that cause subpopulation shifts, and how algorithms generalize across such diverse shifts at scale. In this work, we provide a fine-grained analysis of subpopulation shift. We first propose a unified framework that dissects and explains common shifts in subgroups. We then establish a comprehensive benchmark of 20 state-of-the-art algorithms evaluated on 12 real-world datasets in vision, language, and healthcare domains. With results obtained from training over 10,000 models, we reveal intriguing observations for future progress in this space. First, existing algorithms only improve subgroup robustness over certain types of shifts but not others. Moreover, while current algorithms rely on group-annotated validation data for model selection, we find that a simple selection criterion based on worst-class accuracy is surprisingly effective even without any group information. Finally, unlike existing works that solely aim to improve worst-group accuracy (WGA), we demonstrate the fundamental tradeoff between WGA and other important metrics, highlighting the need to carefully choose testing metrics. Code and data are available at: https://github.com/YyzHarry/SubpopBench.

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

Data valuation—quantifying the contribution of individual data sources to certain predictive behaviors of a model—is of great importance to enhancing the transparency of machine learning and designing incentive systems for data sharing. Existing work has focused on evaluating data sources with the shared feature or sample space. How to valuate fragmented data sources of which each only contains partial features and samples remains an open question. We start by presenting a method to calculate the counterfactual of removing a fragment from the aggregated data matrix. Based on the counterfactual calculation, we further propose 2D-Shapley, a theoretical framework for fragmented data valuation that uniquely satisfies some appealing axioms in the fragmented data context. 2D-Shapley empowers a range of new use cases, such as selecting useful data fragments, providing interpretation for sample-wise data values, and fine-grained data issue diagnosis.

Identifying prognostic genes associated with patient survival is an important goal in cancer genomics, as this information could inform treatment approaches and improve patient outcomes. However, the identification of prognostic genes is complicated by the high dimensionality of genetic data, which makes their identification computationally intensive. Furthermore, most cancer genomics studies lack appropriate low-risk groups against which to compare. To address these issues, we present a framework that identifies candidate prognostic genes by integrating representation learning and statistical analysis approaches. Specifically, we propose a collaborative filtering-derived mechanism to represent patients in order of their survival risk, facilitating their dichotomization. We also propose a mechanism that allows embedded gene vectors to be polarized on the extremities of, or centered on, both reference axes to facilitate recommendations. Restricting our analysis to a few representative genes within each cluster allowed for the efficient identification of prognostic genes. Finally, we demonstrate the potential of this proposed framework for identifying prognostic genes.

We propose a new method to ensure neural ordinary differential equations (ODEs) satisfy output specifications by using invariance set propagation. Our approach uses a class of control barrier functions to transform output specifications into constraints on the parameters and inputs of the learning system. This setup allows us to achieve output specification guarantees simply by changing the constrained parameters/inputs both during training and inference. Moreover, we demonstrate that our invariance set propagation through data-controlled neural ODEs not only maintains generalization performance but also creates an additional degree of robustness by enabling causal manipulation of the system's parameters/inputs. We test our method on a series of representation learning tasks, including modeling physical dynamics and convexity portraits, as well as safe collision avoidance for autonomous vehicles.

Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically discover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training.

Learning heuristics for vehicle routing problems (VRPs) has gained much attention due to the less reliance on hand-crafted rules. However, existing methods are typically trained and tested on the same task with a fixed size and distribution (of nodes), and hence suffer from limited generalization performance. This paper studies a challenging yet realistic setting, which considers generalization across both size and distribution in VRPs. We propose a generic meta-learning framework, which enables effective training of an initialized model with the capability of fast adaptation to new tasks during inference. We further develop a simple yet efficient approximation method to reduce the training overhead. Extensive experiments on both synthetic and benchmark instances of the traveling salesman problem (TSP) and capacitated vehicle routing problem (CVRP) demonstrate the effectiveness of our method. The code is available at: https://github.com/RoyalSkye/Omni-VRP.

Sparse reward remains a valuable and challenging problem in multi-agent reinforcement learning (MARL). This paper addresses this issue from a new perspective, i.e., lazy agents. We empirically illustrate how lazy agents damage learning from both exploration and exploitation. Then, we propose a novel MARL framework called Lazy Agents Avoidance through Influencing External States (LAIES). Firstly, we examine the causes and types of lazy agents in MARL using a causal graph of the interaction between agents and their environment. Then, we mathematically define the concept of fully lazy agents and teams by calculating the causal effect of their actions on external states using the do-calculus process. Based on definitions, we provide two intrinsic rewards to motivate agents, i.e., individual diligence intrinsic motivation (IDI) and collaborative diligence intrinsic motivation (CDI). IDI and CDI employ counterfactual reasoning based on the external states transition model (ESTM) we developed. Empirical results demonstrate that our proposed method achieves state-of-the-art performance on various tasks, including the sparse-reward version of StarCraft multi-agent challenge (SMAC) and Google Research Football (GRF). Our code is open-source and available at https://github.com/liuboyin/LAIES.

Macro-AUC is the arithmetic mean of the class-wise AUCs in multi-label learning and is commonly used in practice. However, its theoretical understanding is far lacking. Toward solving it, we characterize the generalization properties of various learning algorithms based on the corresponding surrogate losses w.r.t. Macro-AUC. We theoretically identify a critical factor of the dataset affecting the generalization bounds: the label-wise class imbalance. Our results on the imbalance-aware error bounds show that the widely-used univariate loss-based algorithm is more sensitive to the label-wise class imbalance than the proposed pairwise and reweighted loss-based ones, which probably implies its worse performance. Moreover, empirical results on various datasets corroborate our theory findings. To establish it, technically, we propose a new (and more general) McDiarmid-type concentration inequality, which may be of independent interest.

There is extensive interest in metric learning methods for image retrieval. Many metric learning loss functions focus on learning a correct ranking of training samples, but strongly overfit semantically inconsistent labels and require a large amount of data. To address these shortcomings, we propose a new metric learning method, called contextual loss, which optimizes contextual similarity in addition to cosine similarity. Our contextual loss implicitly enforces semantic consistency among neighbors while converging to the correct ranking. We empirically show that the proposed loss is more robust to label noise, and is less prone to overfitting even when a large portion of train data is withheld. Extensive experiments demonstrate that our method achieves a new state-of-the-art across four image retrieval benchmarks and multiple different evaluation settings. Code is available at: https://github.com/Chris210634/metric-learning-using-contextual-similarity

In this work, we propose a novel prior learning method for advancing generalization and uncertainty estimation in deep neural networks. The key idea is to exploit scalable and structured posteriors of neural networks as informative priors with generalization guarantees. Our learned priors provide expressive probabilistic representations at large scale, like Bayesian counterparts of pre-trained models on ImageNet, and further produce non-vacuous generalization bounds. We also extend this idea to a continual learning framework, where the favorable properties of our priors are desirable. Major enablers are our technical contributions: (1) the sums-of-Kronecker-product computations, and (2) the derivations and optimizations of tractable objectives that lead to improved generalization bounds. Empirically, we exhaustively show the effectiveness of this method for uncertainty estimation and generalization.

Score-based diffusion models learn to reverse a stochastic differential equation that maps data to noise. However, for complex tasks, numerical error can compound and result in highly unnatural samples. Previous work mitigates this drift with thresholding, which projects to the natural data domain (such as pixel space for images) after each diffusion step, but this leads to a mismatch between the training and generative processes. To incorporate data constraints in a principled manner, we present Reflected Diffusion Models, which instead reverse a reflected stochastic differential equation evolving on the support of the data. Our approach learns the perturbed score function through a generalized score matching loss and extends key components of standard diffusion models including diffusion guidance, likelihood-based training, and ODE sampling. We also bridge the theoretical gap with thresholding: such schemes are just discretizations of reflected SDEs. On standard image benchmarks, our method is competitive with or surpasses the state of the art without architectural modifications and, for classifier-free guidance, our approach enables fast exact sampling with ODEs and produces more faithful samples under high guidance weight.

We develop a principled approach to end-to-end learning in stochastic optimization. First, we show that the standard end-to-end learning algorithm admits a Bayesian interpretation and trains a posterior Bayes action map. Building on the insights of this analysis, we then propose new end-to-end learning algorithms for training decision maps that output solutions of empirical risk minimization and distributionally robust optimization problems, two dominant modeling paradigms in optimization under uncertainty. Numerical results for a synthetic newsvendor problem illustrate the key differences between alternative training schemes. We also investigate an economic dispatch problem based on real data to showcase the impact of the neural network architecture of the decision maps on their test performance.

Existing machine learning methods for causal inference usually estimate quantities expressed via the mean of potential outcomes (e.g., average treatment effect). However, such quantities do not capture the full information about the distribution of potential outcomes. In this work, we estimate the density of potential outcomes after interventions from observational data. For this, we propose a novel, fully-parametric deep learning method called Interventional Normalizing Flows. Specifically, we combine two normalizing flows, namely (i) a nuisance flow for estimating nuisance parameters and (ii) a target flow for parametric estimation of the density of potential outcomes. We further develop a tractable optimization objective based on a one-step bias correction for efficient and doubly robust estimation of the target flow parameters. As a result, our Interventional Normalizing Flows offer a properly normalized density estimator. Across various experiments, we demonstrate that our Interventional Normalizing Flows are expressive and highly effective, and scale well with both sample size and high-dimensional confounding. To the best of our knowledge, our Interventional Normalizing Flows are the first proper fully-parametric, deep learning method for density estimation of potential outcomes.

Two main challenges in Reinforcement Learning (RL) are designing appropriate reward functions and ensuring the safety of the learned policy. To address these challenges, we present a theoretical framework for Inverse Reinforcement Learning (IRL) in constrained Markov decision processes. From a convex-analytic perspective, we extend prior results on reward identifiability and generalizability to both the constrained setting and a more general class of regularizations. In particular, we show that identifiability up to potential shaping (Cao et al., 2021) is a consequence of entropy regularization and may generally no longer hold for other regularizations or in the presence of safety constraints. We also show that to ensure generalizability to new transition laws and constraints, the true reward must be identified up to a constant. Additionally, we derive a finite sample guarantee for the suboptimality of the learned rewards, and validate our results in a gridworld environment.

In many human-centric applications for Machine Learning instances will adapt to a classifier after its deployment. The field of strategic classification deals with this issue by aiming for a classifier that balances the trade-off between correctness and robustness to manipulation. This task is made harder if the underlying manipulation structure (i.e. the set of manipulations available at every instance) is unknown to the learner. We propose a novel batch-learning setting in which we use unlabeled data from previous rounds to estimate the manipulation structure. We show that in this batch-learning setting it is possible to learn a close-to-optimal classifier in terms of the strategic loss even without knowing the feasible manipulations beforehand. In line with recent advances in the strategic classification literature, we do not assume a best-response from agents but only require that observed manipulations are feasible.

Diffusion models have found widespread adoption in various areas. However, their sampling process is slow because it requires hundreds to thousands of network evaluations to emulate a continuous process defined by differential equations. In this work, we use neural operators, an efficient method to solve the probability flow differential equations, to accelerate the sampling process of diffusion models. Compared to other fast sampling methods that have a sequential nature, we are the first to propose a parallel decoding method that generates images with only one model forward pass. We propose diffusion model sampling with neural operator (DSNO) that maps the initial condition, i.e., Gaussian distribution, to the continuous-time solution trajectory of the reverse diffusion process. To model the temporal correlations along the trajectory, we introduce temporal convolution layers that are parameterized in the Fourier space into the given diffusion model backbone. We show our method achieves state-of-the-art FID of 3.78 for CIFAR-10 and 7.83 for ImageNet-64 in the one-model-evaluation setting.

Recent approaches build on implicit neural representations (INRs) to propose generative models over function spaces. However, they are computationally costly when dealing with inference tasks, such as missing data imputation, or directly cannot tackle them. In this work, we propose a novel deep generative model, named VaMoH. VaMoH combines the capabilities of modeling continuous functions using INRs and the inference capabilities of Variational Autoencoders (VAEs). In addition, VaMoH relies on a normalizing flow to define the prior, and a mixture of hypernetworks to parametrize the data log-likelihood. This gives VaMoH a high expressive capability and interpretability. Through experiments on a diverse range of data types, such as images, voxels, and climate data, we show that VaMoH can effectively learn rich distributions over continuous functions. Furthermore, it can perform inference-related tasks, such as conditional super-resolution generation and in-painting, as well or better than previous approaches, while being less computationally demanding.

While the successes of transformers across many domains are indisputable, accurate understanding of the learning mechanics is still largely lacking. Their capabilities have been probed on benchmarks which include a variety of structured and reasoning tasks---but mathematical understanding is lagging substantially behind. Recent lines of work have begun studying representational aspects of this question: that is, the size/depth/complexity of attention-based networks to perform certain tasks. However, there is no guarantee the learning dynamics will converge to the constructions proposed. In our paper, we provide fine-grained mechanistic understanding of how transformers learn ``semantic structure'', understood as capturing co-occurrence structure of words. Precisely, we show, through a combination of mathematical analysis and experiments on Wikipedia data and synthetic data modeled by Latent Dirichlet Allocation (LDA), that the embedding layer and the self-attention layer encode the topical structure. In the former case, this manifests as higher average inner product of embeddings between same-topic words. In the latter, it manifests as higher average pairwise attention between same-topic words. The mathematical results involve several assumptions to make the analysis tractable, which we verify on data, and might be of independent interest as well.

Being able to provide explanations for a model's decision has become a central requirement for the development, deployment, and adoption of machine learning models. However, we are yet to understand what explanation methods can and cannot do. How do upstream factors such as data, model prediction, hyperparameters, and random initialization influence downstream explanations? While previous work raised concerns that explanations (E) may have little relationship with the prediction (Y), there is a lack of conclusive study to quantify this relationship. Our work borrows tools from causal inference to systematically assay this relationship. More specifically, we study the relationship between E and Y by measuring the treatment effect when intervening on their causal ancestors, i.e., on hyperparameters and inputs used to generate saliency-based Es or Ys. Our results suggest that the relationships between E and Y is far from ideal. In fact, the gap between 'ideal' case only increase in higher-performing models --- models that are likely to be deployed. Our work is a promising first step towards providing a quantitative measure of the relationship between E and Y, which could also inform the future development of methods for E with a quantitative metric.

High-quality machine learning models are dependent on access to high-quality training data. When the data are not already available, it is tedious and costly to obtain them. Data markets help with identifying valuable training data: model consumers pay to train a model, the market uses that budget to identify data and train the model (the budget allocation problem), and finally the market compensates data providers according to their data contribution (revenue allocation problem). For example, a bank could pay the data market to access data from other financial institutions to train a fraud detection model. Compensating data contributors requires understanding data’s contribution to the model; recent efforts to solve this revenue allocation problem based on the Shapley value are inefficient to lead to practical data markets. In this paper, we introduce a new algorithm to solve budget allocation and revenue allocation problems simultaneously in linear time. The new algorithm employs an adaptive sampling process that selects data from those providers who are contributing the most to the model. Better data means that the algorithm accesses those providers more often, and more frequent accesses corresponds to higher compensation. Furthermore, the algorithm can be deployed in both centralized and federated scenarios, boosting its applicability. We provide theoretical guarantees for the algorithm that show the budget is used efficiently and the properties of revenue allocation are similar to Shapley’s. Finally, we conduct an empirical evaluation to show the performance of the algorithm in practical scenarios and when compared to other baselines. Overall, we believe that the new algorithm paves the way for the implementation of practical data markets.

Robustness to adversarial attacks is typically evaluated with adversarial accuracy. While essential, this metric does not capture all aspects of robustness and in particular leaves out the question of how many perturbations can be found for each point. In this work, we introduce an alternative approach, adversarial sparsity, which quantifies how difficult it is to find a successful perturbation given both an input point and a constraint on the direction of the perturbation. We show that sparsity provides valuable insight into neural networks in multiple ways: for instance, it illustrates important differences between current state-of-the-art robust models them that accuracy analysis does not, and suggests approaches for improving their robustness. When applying broken defenses effective against weak attacks but not strong ones, sparsity can discriminate between the totally ineffective and the partially effective defenses. Finally, with sparsity we can measure increases in robustness that do not affect accuracy: we show for example that data augmentation can by itself increase adversarial robustness, without using adversarial training.

We study offline multi-agent reinforcement learning (RL) in Markov games, where the goal is to learn an approximate equilibrium---such as Nash equilibrium and (Coarse) Correlated Equilibrium---from an offline dataset pre-collected from the game. Existing works consider relatively restricted tabular or linear models and handle each equilibria separately. In this work, we provide the first framework for sample-efficient offline learning in Markov games under general function approximation, handling all 3 equilibria in a unified manner. By using Bellman-consistent pessimism, we obtain interval estimation for policies' returns, and use both the upper and the lower bounds to obtain a relaxation on the gap of a candidate policy, which becomes our optimization objective. Our results generalize prior works and provide several additional insights. Importantly, we require a data coverage condition that improves over the recently proposed ``unilateral concentrability''. Our condition allows selective coverage of deviation policies that optimally trade-off between their greediness (as approximate best responses) and coverage, and we show scenarios where this leads to significantly better guarantees. As a new connection, we also show how our algorithmic framework can subsume seemingly different solution concepts designed for the special case of two-player zero-sum games.

Understanding when reinforcement learning algorithms can make successful off-policy predictions---and when the may fail to do so--remains an open problem. Typically, model-free algorithms for reinforcement learning are analyzed under a condition called Bellman completeness when they operate off-policy with function approximation, unless additional conditions are met. However, Bellman completeness is a requirement that is much stronger than realizability and that is deemed to be too strong to hold in practice. In this work, we relax this structural assumption and analyze the statistical complexity of off-policy reinforcement learning when only realizability holds for the prescribed function class. We establish finite-sample guarantees for off-policy reinforcement learning that are free of the approximation error term known as inherent Bellman error, and that depend on the interplay of three factors. The first two are well known: they are the metric entropy of the function class and the concentrability coefficient that represents the cost of learning off-policy. The third factor is new, and it measures the violation of Bellman completeness, namely the mis-alignment between the chosen function class and its image through the Bellman operator. Our analysis directly applies to the solution found by temporal difference algorithms when they converge.

Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers that take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender repeatedly faces one or more receivers with unknown and adversarially selected types. First, we show how to obtain a tight $\tilde O(T^{1/2})$ regret bound in the case in which the sender faces a single receiver and has bandit feedback, improving over the best previously known bound of $\tilde O(T^{4/5})$. Then, we provide the first no-regret guarantees for the multi-receiver setting under bandit feedback. Finally, we show how to design no-regret algorithms with polynomial per-iteration running time by exploiting type reporting, thereby circumventing known complexity results on online Bayesian persuasion. We provide efficient algorithms guaranteeing a $O(T^{1/2})$ regret upper bound both in the single- and multi-receiver scenario when type reporting is allowed.

We study the problems of *distributed online and bandit convex optimization* against an adaptive adversary. We aim to minimize the average regret on $M$ machines working in parallel over $T$ rounds with $R$ intermittent communications. Assuming the underlying cost functions are convex and can be generated adaptively, our results show that *collaboration is not beneficial when the machines have access to the first-order gradient information at the queried points*. This is in contrast to the case for stochastic functions, where each machine samples the cost functions from a fixed distribution. Furthermore, we delve into the more challenging setting of *federated online optimization with bandit (zeroth-order) feedback*, where the machines can only access values of the cost functions at the queried points. The key finding here is *identifying the high-dimensional regime where collaboration is beneficial and may even lead to a linear speedup in the number of machines*. We further illustrate our findings through federated adversarial linear bandits by developing novel distributed single and two-point feedback algorithms. Our work is the first attempt towards a systematic understanding of federated online optimization with limited feedback, and it attains tight regret bounds in the intermittent communication setting for both first and zeroth-order feedback. Our results thus bridge the gap between stochastic and adaptive settings in federated online optimization.

Does the dominant approach to learn representations (as a side effect of optimizing an expected cost for a single training distribution) remain a good approach when we are dealing with multiple distributions? Our thesis is that such scenarios are better served by representations that are richer than those obtained with a single optimization episode. We support this thesis with simple theoretical arguments and with experiments utilizing an apparently näive ensembling technique: concatenating the representations obtained from multiple training episodes using the same data, model, algorithm, and hyper-parameters, but different random seeds. These independently trained networks perform similarly. Yet, in a number of scenarios involving new distributions, the concatenated representation performs substantially better than an equivalently sized network trained with a single training run. This proves that the representations constructed by multiple training episodes are in fact different. Although their concatenation carries little additional information about the training task under the training distribution, it becomes substantially more informative when tasks or distributions change. Meanwhile, a single training episode is unlikely to yield such a redundant representation because the optimization process has no reason to accumulate features that do not incrementally improve the training performance.

Recent efforts at explaining the interplay of memorization and generalization in deep overparametrized networks have posited that neural networks memorize ``hard'' examples in the final few layers of the model. Memorization refers to the ability to correctly predict on atypical examples of the training set. In this work, we show that rather than being confined to individual layers, memorization is a phenomenon confined to a small set of neurons in various layers of the model. First, via three experimental sources of converging evidence, we find that most layers are redundant for the memorization of examples and the layers that contribute to example memorization are, in general, not the final layers. The three sources are gradient accounting (measuring the contribution to the gradient norms from memorized and clean examples), layer rewinding (replacing specific model weights of a converged model with previous training checkpoints), and retraining (training rewound layers only on clean examples). Second, we ask a more generic question: can memorization be localized anywhere in a model? We discover that memorization is often confined to a small number of neurons or channels (around 5) of the model. Based on these insights we propose a new form of dropout---example-tied dropout that enables us to direct the memorization of examples to an aprior determined set of neurons. By dropping out these neurons, we are able to reduce the accuracy on memorized examples from 100% to 3%, while also reducing the generalization gap.

Training data is always finite, making it unclear how to generalise to unseen situations. But, animals do generalise, wielding Occam's razor to select a parsimonious explanation of their observations. How they do this is called their inductive bias, and it is implicitly built into the operation of animals' neural circuits. This relationship between an observed circuit and its inductive bias is a useful explanatory window for neuroscience, allowing design choices to be understood normatively. However, it is generally very difficult to map circuit structure to inductive bias. Here, we present a neural network tool to bridge this gap. The tool meta-learns the inductive bias by learning functions that a neural circuit finds easy to generalise, since easy-to-generalise functions are exactly those the circuit chooses to explain incomplete data. In systems with analytically known inductive bias, i.e. linear and kernel regression, our tool recovers it. Generally, we show it can flexibly extract inductive biases from supervised learners, including spiking neural networks, and show how it could be applied to real animals. Finally, we use our tool to interpret recent connectomic data illustrating our intended use: understanding the role of circuit features through the resulting inductive bias.

In this paper, we conduct an empirical study of the feature learning process in deep classifiers. Recent research has identified a training phenomenon called Neural Collapse (NC), in which the top-layer feature embeddings of samples from the same class tend to concentrate around their means, and the top layer's weights align with those features. Our study aims to investigate if these properties extend to intermediate layers. We empirically study the evolution of the covariance and mean of representations across different layers and show that as we move deeper into a trained neural network, the within-class covariance decreases relative to the between-class covariance. Additionally, we find that in the top layers, where the between-class covariance is dominant, the subspace spanned by the class means aligns with the subspace spanned by the most significant singular vector components of the weight matrix in the corresponding layer. Finally, we discuss the relationship between NC and Associative Memories (Willshaw et. al. 1969).

We showcase important features of the dynamics of the Stochastic Gradient Descent (SGD) in the training of neural networks. We present empirical observations that commonly used large step sizes (i) may lead the iterates to jump from one side of a valley to the other causing loss stabilization, and (ii) this stabilization induces a hidden stochastic dynamics that biases it implicitly toward simple predictors. Furthermore, we show empirically that the longer large step sizes keep SGD high in the loss landscape valleys, the better the implicit regularization can operate and find sparse representations. Notably, no explicit regularization is used: the regularization effect comes solely from the SGD dynamics influenced by the large step sizes schedule. Therefore, these observations unveil how, through the step size schedules, both gradient and noise drive together the SGD dynamics through the loss landscape of neural networks. We justify these findings theoretically through the study of simple neural network models as well as qualitative arguments inspired from stochastic processes. This analysis allows us to shed new light on some common practices and observed phenomena when training deep networks.

Reconstructing natural images from fMRI recordings is a challenging task of great importance in neuroscience. The current architectures are bottlenecked because they fail to effectively capture the hierarchical processing of visual stimuli that takes place in the human brain. Motivated by that fact, we introduce a novel neural network architecture for the problem of neural decoding. Our architecture uses Hierarchical Variational Autoencoders (HVAEs) to learn meaningful representations of natural images and leverages their latent space hierarchy to learn voxel-to-image mappings. By mapping the early stages of the visual pathway to the first set of latent variables and the higher visual cortex areas to the deeper layers in the latent hierarchy, we are able to construct a latent variable neural decoding model that replicates the hierarchical visual information processing. Our model achieves better reconstructions compared to the state of the art and our ablation study indicates that the hierarchical structure of the latent space is responsible for that performance.

Labels are typically sparse in real-world time series due to the high annotation cost. Recently, consistency regularization techniques have been used to generate artificial labels from unlabeled augmented instances. To fully exploit the sequential characteristic of time series in consistency regularization, we propose a novel method of data augmentation called context-attached augmentation, which adds preceding and succeeding instances to a target instance to form its augmented instance. Unlike the existing augmentation techniques that modify a target instance by directly perturbing its attributes, the context-attached augmentation generates instances augmented with varying contexts while maintaining the target instance. Based on our augmentation method, we propose a context consistency regularization framework, which first adds different contexts to a target instance sampled from a given time series and then shares unitary reliability-based cross-window labels across the augmented instances to maintain consistency. We demonstrate that the proposed framework outperforms the existing state-of-the-art consistency regularization frameworks through comprehensive experiments on real-world time-series datasets.

The proliferation of pretrained models, as a result of advancements in pretraining techniques, has led to the emergence of a vast zoo of publicly available models. Effectively utilizing these resources to obtain models with robust out-of-distribution generalization capabilities for downstream tasks has become a crucial area of research. Previous research has primarily focused on identifying the most powerful models within the model zoo, neglecting to fully leverage the diverse inductive biases contained within. This paper argues that the knowledge contained in weaker models is valuable and presents a method for leveraging the diversity within the model zoo to improve out-of-distribution generalization capabilities. Specifically, we investigate the behaviors of various pretrained models across different domains of downstream tasks by characterizing the variations in their encoded representations in terms of two dimensions: diversity shift and correlation shift. This characterization enables us to propose a new algorithm for integrating diverse pretrained models, not limited to the strongest models, in order to achieve enhanced out-of-distribution generalization performance. Our proposed method demonstrates state-of-the-art empirical results on a variety of datasets, thus validating the benefits of utilizing diverse knowledge.

Federated Semi-supervised Learning (FedSSL) has emerged as a new paradigm for allowing distributed clients to collaboratively train a machine learning model over scarce labeled data and abundant unlabeled data. However, existing works for FedSSL rely on a closed-world assumption that all local training data and global testing data are from seen classes observed in the labeled dataset. It is crucial to go one step further: adapting FL models to an open-world setting, where unseen classes exist in the unlabeled data. In this paper, we propose a novel Federatedopen-world Semi-Supervised Learning (FedoSSL) framework, which can solve the key challenge in distributed and open-world settings, i.e., the biased training process for heterogeneously distributed unseen classes. Specifically, since the advent of a certain unseen class depends on a client basis, the locally unseen classes (exist in multiple clients) are likely to receive differentiated superior aggregation effects than the globally unseen classes (exist only in one client). We adopt an uncertainty-aware suppressed loss to alleviate the biased training between locally unseen and globally unseen classes. Besides, we enable a calibration module supplementary to the global aggregation to avoid potential conflicting knowledge transfer caused by inconsistent data distribution among different clients. The proposed FedoSSL can be easily adapted to state-of-the-art FL methods, which is also validated via extensive experiments on benchmarks and real-world datasets (CIFAR-10, CIFAR-100 and CINIC-10).

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

Anytime neural networks (AnytimeNNs) are a promising solution to adaptively adjust the model complexity at runtime under various hardware resource constraints. However, the manually-designed AnytimeNNs are biased by designers' prior experience and thus provide sub-optimal solutions. To address the limitations of existing hand-crafted approaches, we first model the training process of AnytimeNNs as a discrete-time Markov chain (DTMC) and use it to identify the paths that contribute the most to the training of AnytimeNNs. Based on this new DTMC-based analysis, we further propose TIPS, a framework to automatically design AnytimeNNs under various hardware constraints. Our experimental results show that TIPS can improve the convergence rate and test accuracy of AnytimeNNs. Compared to the existing AnytimeNNs approaches, TIPS improves the accuracy by 2%-6.6% on multiple datasets and achieves SOTA accuracy-FLOPs tradeoffs.

Precision and Recall are two prominent metrics of generative performance, which were proposed to separately measure the fidelity and diversity of generative models. Given their central role in comparing and improving generative models, understanding their limitations are crucially important. To that end, in this work, we identify a critical flaw in the common approximation of these metrics using k-nearest-neighbors, namely, that the very interpretations of fidelity and diversity that are assigned to Precision and Recall can fail in high dimensions, resulting in very misleading conclusions. Specifically, we empirically and theoretically show that as the number of dimensions grows, two model distributions with supports at equal point-wise distance from the support of the real distribution, can have vastly different Precision and Recall regardless of their respective distributions, hence an emergent asymmetry in high dimensions. Based on our theoretical insights, we then provide simple yet effective modifications to these metrics to construct symmetric metrics regardless of the number of dimensions. Finally, we provide experiments on real-world datasets to illustrate that the identified flaw is not merely a pathological case, and that our proposed metrics are effective in alleviating its impact.

We present IRNeXt, a simple yet effective convolutional network architecture for image restoration. Recently, Transformer models have dominated the field of image restoration due to the powerful ability of modeling long-range pixels interactions. In this paper, we excavate the potential of the convolutional neural network (CNN) and show that our CNN-based model can receive comparable or better performance than Transformer models with low computation overhead on several image restoration tasks. By re-examining the characteristics possessed by advanced image restoration algorithms, we discover several key factors leading to the performance improvement of restoration models. This motivates us to develop a novel network for image restoration based on cheap convolution operators. Comprehensive experiments demonstrate that IRNeXt delivers state-of-the-art performance among numerous datasets on a range of image restoration tasks with low computational complexity, including image dehazing, single-image defocus/motion deblurring, image deraining, and image desnowing. https://github.com/c-yn/IRNeXt.

Language models (LMs) are increasingly being used in open-ended contexts, where the opinions they reflect in response to subjective queries can have a profound impact, both on user satisfaction, and shaping the views of society at large. We put forth a quantitative framework to investigate the opinions reflected by LMs -- by leveraging high-quality public opinion polls. Using this framework, we create OpinionQA, a dataset for evaluating the alignment of LM opinions with those of 60 US demographic groups over topics ranging from abortion to automation. Across topics, we find substantial misalignment between the views reflected by current LMs and those of US demographic groups: on par with the Democrat-Republican divide on climate change. Notably, this misalignment persists even after explicitly steering the LMs towards particular groups. Our analysis not only confirms prior observations about the left-leaning tendencies of some human feedback-tuned LMs, but also surfaces groups whose opinions are poorly reflected by current LMs (e.g., 65+ and widowed individuals).

We analyze Elman-type recurrent neural networks (RNNs) and their training in the mean-field regime. Specifically, we show convergence of gradient descent training dynamics of the RNN to the corresponding mean-field formulation in the large width limit. We also show that the fixed points of the limiting infinite-width dynamics are globally optimal, under some assumptions on the initialization of the weights. Our results establish optimality for feature-learning with wide RNNs in the mean-field regime.

We rigorously quantify the improvement in the sample complexity of variational divergence estimations for group-invariant distributions. In the cases of the Wasserstein-1 metric and the Lipschitz-regularized $\alpha$-divergences, the reduction of sample complexity is proportional to an ambient-dimension-dependent power of the group size. For the maximum mean discrepancy (MMD), the improvement of sample complexity is more nuanced, as it depends on not only the group size but also the choice of kernel. Numerical simulations verify our theories.

In recent years, particle-based variational inference (ParVI) methods such as Stein variational gradient descent (SVGD) have grown in popularity as scalable methods for Bayesian inference. Unfortunately, the properties of such methods invariably depend on hyperparameters such as the learning rate, which must be carefully tuned by the practitioner in order to ensure convergence to the target measure at a suitable rate. In this paper, we introduce a suite of new particle-based methods for scalable Bayesian inference based on coin betting, which are entirely learning-rate free. We illustrate the performance of our approach on a range of numerical examples, including several high-dimensional models and datasets, demonstrating comparable performance to other ParVI algorithms with no need to tune a learning rate.

Neural pruning, which involves identifying the optimal sparse subnetwork, is a key technique for reducing the complexity and improving the efficiency of deep neural networks. To address the challenge of solving neural pruning at a specific sparsity level directly, we investigate the evolution of optimal subnetworks with continuously increasing sparsity, which can provide insight into how to transform an unpruned dense model into an optimal subnetwork with any desired level of sparsity. In this paper, we proposed a novel pruning framework, coined Sparsity-indexed ODE (SpODE) that provides explicit guidance on how to best preserve model performance while ensuring an infinitesimal increase in model sparsity. On top of this, we develop a pruning algorithm, termed Pruning via Sparsity-indexed ODE (PSO), that enables effective pruning via traveling along the SpODE path. Empirical experiments show that PSO achieves either better or comparable performance compared to state-of-the-art baselines across various pruning settings.

Activation compressed training provides a solution towards reducing the memory cost of training deep neural networks (DNNs). However, state-of-the-art work combines a search of quantization bit-width with the training, which makes the procedure complicated and less transparent. To this end, we propose a simple and effective method to compress DNN training. Our method is motivated by an instructive observation: DNN backward propagation mainly utilizes the low-frequency component (LFC) of the activation maps, while the majority of memory is for caching the high-frequency component (HFC) during the training. This indicates the HFC of activation maps is highly redundant and compressible, which inspires our proposed Dual Activation Precision (DIVISION). During the training, DIVISION preserves a high-precision copy of LFC and compresses the HFC into a light-weight copy with low numerical precision. This can significantly reduce the memory cost while maintaining a competitive model accuracy. Experiment results show DIVISION has better comprehensive performance than state-of-the-art methods, including over 10x compression of activation maps and competitive training throughput, without loss of model accuracy. The source code is available at https://github.com/guanchuwang/division.

Solving large-scale multistage stochastic programming (MSP) problems poses a significant challenge as commonly used stagewise decomposition algorithms, including stochastic dual dynamic programming (SDDP), face growing time complexity as the subproblem size and problem count increase. Traditional approaches approximate the value functions as piecewise linear convex functions by incrementally accumulating subgradient cutting planes from the primal and dual solutions of stagewise subproblems. Recognizing these limitations, we introduce TranSDDP, a novel Transformer-based stagewise decomposition algorithm. This innovative approach leverages the structural advantages of the Transformer model, implementing a sequential method for integrating subgradient cutting planes to approximate the value function. Through our numerical experiments, we affirm TranSDDP's effectiveness in addressing MSP problems. It efficiently generates a piecewise linear approximation for the value function, significantly reducing computation time while preserving solution quality, thus marking a promising progression in the treatment of large-scale multistage stochastic programming problems.

Federated bilevel optimization has attracted increasing attention due to emerging machine learning and communication applications. The biggest challenge lies in computing the gradient of the upper-level objective function (i.e., hypergradient) in the federated setting due to the nonlinear and distributed construction of a series of global Hessian matrices. In this paper, we propose a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation (AggITD). AggITD is simple to implement and significantly reduces the communication cost by conducting the federated hypergradient estimation and the lower-level optimization simultaneously. We show that the proposed AggITD-based algorithm achieves the same sample complexity as existing approximate implicit differentiation (AID)-based approaches with much fewer communication rounds in the presence of data heterogeneity. Our results also shed light on the great advantage of ITD over AID in the federated/distributed hypergradient estimation. This differs from the comparison in the non-distributed bilevel optimization, where ITD is less efficient than AID. Our extensive experiments demonstrate the great effectiveness and communication efficiency of the proposed method.

This work develops analysis and algorithms for solving a class of bilevel optimization problems where the lower-level (LL) problems have linear constraints. Most of the existing approaches for constrained bilevel problems rely on value function-based approximate reformulations, which suffer from issues such as non-convex and non-differentiable constraints. In contrast, in this work, we develop an implicit gradient-based approach, which is easy to implement, and is suitable for machine learning applications. We first provide an in-depth understanding of the problem, by showing that the implicit objective for such problems is in general non-differentiable. However, if we add some small (linear) perturbation to the LL objective, the resulting implicit objective becomes differentiable almost surely. This key observation opens the door for developing (deterministic and stochastic) gradient-based algorithms similar to the state-of-the-art ones for unconstrained bi-level problems. We show that when the implicit function is assumed to be strongly-convex, convex, and weakly-convex, the resulting algorithms converge with guaranteed rate. Finally, we experimentally corroborate the theoretical findings and evaluate the performance of the proposed framework on numerical and adversarial learning problems.

Paging is a prototypical problem in the area of online algorithms. It has also played a central role in the development of learning-augmented algorithms. Previous work on learning-augmented paging has investigated predictions on (i) when the current page will be requested again (reoccurrence predictions), (ii) the current state of the cache in an optimal algorithm (state predictions), (iii) all requests until the current page gets requested again, and (iv) the relative order in which pages are requested. We study learning-augmented paging from the new perspective of requiring the least possible amount of predicted information. More specifically, the predictions obtained alongside each page request are limited to one bit only. We develop algorithms satisfy all three desirable properties of learning-augmented algorithms -- that is, they are consistent, robust and smooth -- despite being limited to a one-bit prediction per request. We also present lower bounds establishing that our algorithms are essentially best possible.

The noise transition matrix plays a central role in the problem of learning with noisy labels. Among many other reasons, a large number of existing solutions rely on the knowledge of it. Identifying and estimating the transition matrix without ground truth labels is a critical and challenging task. When label noise transition depends on each instance, the problem of identifying the instance-dependent noise transition matrix becomes substantially more challenging. Despite recently proposed solutions for learning from instance-dependent noisy labels, the literature lacks a unified understanding of when such a problem remains identifiable. The goal of this paper is to characterize the identifiability of the label noise transition matrix. Building on Kruskal's identifiability results, we are able to show the necessity of multiple noisy labels in identifying the noise transition matrix at the instance level. We further instantiate the results to explain the successes of the state-of-the-art solutions and how additional assumptions alleviated the requirement of multiple noisy labels. Our result reveals that disentangled features improve identification. This discovery led us to an approach that improves the estimation of the transition matrix using properly disentangled features. Code is available at https://github.com/UCSC-REAL/Identifiability.

Semi-supervised semantic segmentation involves assigning pixel-wise labels to unlabeled images at training time. This is useful in a wide range of real-world applications where collecting pixel-wise labels is not feasible in time or cost. Current approaches to semi-supervised semantic segmentation work by predicting pseudo-labels for each pixel from a class-wise probability distribution output by a model. If this predicted probability distribution is incorrect, however, it leads to poor segmentation results which can have knock-on consequences in safety critical systems, like medical images or self-driving cars. It is, therefore, important to understand what a model does not know, which is mainly achieved by uncertainty quantification. Recently, neural processes (NPs) have been explored in semi-supervised image classification, and they have been a computationally efficient and effective method for uncertainty quantification. In this work, we move one step forward by adapting NPs to semi-supervised semantic segmentation, resulting in a new model called NP-SemiSeg. We experimentally evaluated NP-SemiSeg on the public benchmarks PASCAL VOC 2012 and Cityscapes, with different training settings, and the results verify its effectiveness.

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning probability measures to the spatial domain, which allows us to treat collocation grids probabilistically as random variables to be marginalised out. Adapting this spatial statistics view, we solve forward and inverse problems for parametric PDEs in a way that leads to the construction of Gaussian process models of solution fields. The implementation of these random grids poses a unique set of challenges for inverse physics informed deep learning frameworks and we propose a new architecture called Grid Invariant Convolutional Networks (GICNets) to overcome these challenges. We further show how to incorporate noisy data in a principled manner into our physics informed model to improve predictions for problems where data may be available but whose measurement location does not coincide with any fixed mesh or grid. The proposed method is tested on a nonlinear Poisson problem, Burgers equation, and Navier-Stokes equations, and we provide extensive numerical comparisons. We demonstrate significant computational advantages over current physics informed neural learning methods for parametric PDEs while improving the predictive capabilities and flexibility of these models.

The size of deep neural networks has grown exponentially in recent years. Unfortunately, hardware devices have not kept pace with the rapidly increasing memory requirements. To cope with this, researchers have proposed various techniques including spilling, rematerialization, reduced precision training, model pruning, and so on. However, these approaches suffer from various limitations, such as increasing training time, affecting model accuracy, or requiring extensive manual modifications to the neural networks. We present MODeL, an algorithm that optimizes the lifetime and memory location of the tensors used to train neural networks. Our method automatically reduces the memory usage of existing neural networks without any of the drawbacks of other techniques. We formulate the problem as a joint integer linear program (ILP). We present several techniques to simplify the encoding of the problem, and enable our approach to scale to the size of state-of-the-art neural networks using an off-the-shelf ILP solver. We experimentally demonstrate that MODeL only takes seconds to allow the training of neural networks using 30% less memory on average.

We focus on addressing the dense backward propagation issue for training efficiency of N:M fine-grained sparsity that preserves at most N out of M consecutive weights and achieves practical speedups supported by the N:M sparse tensor core. Therefore, we present a novel method of Bi-directional Masks (Bi-Mask) with its two central innovations in: 1) Separate sparse masks in the two directions of forward and backward propagation to obtain training acceleration. It disentangles the forward and backward weight sparsity and overcomes the very dense gradient computation. 2) An efficient weight row permutation method to maintain performance. It picks up the permutation candidate with the most eligible N:M weight blocks in the backward to minimize the gradient gap between traditional unidirectional masks and our bi-directional masks. Compared with existing uni-directional scenario that applies a transposable mask and enables backward acceleration, our Bi-Mask is experimentally demonstrated to be more superior in performance. Also, our Bi-Mask performs on par with or even better than methods that fail to achieve backward acceleration. Project of this paper is available at https://github.com/zyxxmu/Bi-Mask.

Training graph neural networks (GNNs) is extremely time consuming because sparse graph-based operations are hard to be accelerated by community hardware. Prior art successfully reduces the computation cost of dense matrix based operations (e.g., convolution and linear) via sampling-based approximation. However, unlike dense matrices, sparse matrices are stored in the irregular data format such that each row/column may have different number of non-zero entries. Thus, compared to the dense counterpart, approximating sparse operations has two unique challenges (1) we cannot directly control the efficiency of approximated sparse operation since the computation is only executed on non-zero entries; (2) sampling sparse matrices is much more inefficient due to the irregular data format. To address the issues, our key idea is to control the accuracy-efficiency trade off by optimizing computation resource allocation layer-wisely and epoch-wisely. For the first challenge, we customize the computation resource to different sparse operations, while limit the total used resource below a certain budget. For the second challenge, we cache previous sampled sparse matrices to reduce the epoch-wise sampling overhead. Finally, we propose a switching mechanisms to improve the generalization of GNNs trained with approximated operations. To this end, we propose Randomized Sparse Computation. In practice, rsc can achieve up to 11.6X speedup for a single sparse operation and 1.6X end-to-end wall-clock time speedup with almost no accuracy drop.

This paper presents Ske2Grid, a new representation learning framework for improved skeleton-based action recognition. In Ske2Grid, we define a regular convolution operation upon a novel grid representation of human skeleton, which is a compact image-like grid patch constructed and learned through three novel designs. Specifically, we propose a graph-node index transform (GIT) to construct a regular grid patch through assigning the nodes in the skeleton graph one by one to the desired grid cells. To ensure that GIT is a bijection and enrich the expressiveness of the grid representation, an up-sampling transform (UPT) is learned to interpolate the skeleton graph nodes for filling the grid patch to the full. To resolve the problem when the one-step UPT is aggressive and further exploit the representation capability of the grid patch with increasing spatial size, a progressive learning strategy (PLS) is proposed which decouples the UPT into multiple steps and aligns them to multiple paired GITs through a compact cascaded design learned progressively. We construct networks upon prevailing graph convolution networks and conduct experiments on six mainstream skeleton-based action recognition datasets. Experiments show that our Ske2Grid significantly outperforms existing GCN-based solutions under different benchmark settings, without bells and whistles. Code and models are available at https://github.com/OSVAI/Ske2Grid.

Popular deep-learning models in the field of image classification suffer from catastrophic forgetting---models will forget previously acquired skills when learning new ones. Generative replay (GR), which typically consists of a generator and a classifier, is an efficient way to mitigate catastrophic forgetting. However, conventional GR methods only focus on a single instruction relationship (generator-to-classifier), where the generator synthesizes samples for previous tasks to instruct the training of the classifier, while ignoring the ways in which the classifier can benefit the generator. In addition, most generative replay methods typically reuse the generated samples to update the generator, which causes the samples regenerated by the generator deviating from the distribution of previous tasks. To overcome these two issues, we propose a novel approach, called deep diffusion-based generative replay (DDGR), which adopts a diffusion model as the generator and calculates an instruction-operator through the classifier to instruct the generation of samples. Extensive experiments in class incremental (CI) and class incremental with repetition (CIR) settings demonstrate the advantages of DDGR. Our code is available at https://github.com/xiaocangshengGR/DDGR.

This paper addresses a regression problem in which output label values are the results of sensing the magnitude of a phenomenon. A low value of such labels can mean either that the actual magnitude of the phenomenon was low or that the sensor made an incomplete observation. This leads to a bias toward lower values in labels and the resultant learning because labels may have lower values due to incomplete observations, even if the actual magnitude of the phenomenon was high. Moreover, because an incomplete observation does not provide any tags indicating incompleteness, we cannot eliminate or impute them. To address this issue, we propose a learning algorithm that explicitly models incomplete observations corrupted with an asymmetric noise that always has a negative value. We show that our algorithm is unbiased as if it were learned from uncorrupted data that does not involve incomplete observations. We demonstrate the advantages of our algorithm through numerical experiments.

We propose causal isotonic calibration, a novel nonparametric method for calibrating predictors of heterogeneous treatment effects. Furthermore, we introduce cross-calibration, a data-efficient variant of calibration that eliminates the need for hold-out calibration sets. Cross-calibration leverages cross-fitted predictors and generates a single calibrated predictor using all available data. Under weak conditions that do not assume monotonicity, we establish that both causal isotonic calibration and cross-calibration achieve fast doubly-robust calibration rates, as long as either the propensity score or outcome regression is estimated accurately in a suitable sense. The proposed causal isotonic calibrator can be wrapped around any black-box learning algorithm, providing robust and distribution-free calibration guarantees while preserving predictive performance.

Composition is a key feature of differential privacy. Well-known advanced composition theorems allow one to query a private database quadratically more times than basic privacy composition would permit. However, these results require that the privacy parameters of all algorithms be fixed before interacting with the data. To address this, Rogers et al. introduced fully adaptive composition, wherein both algorithms and their privacy parameters can be selected adaptively. They defined two probabilistic objects to measure privacy in adaptive composition: privacy filters, which provide differential privacy guarantees for composed interactions, and privacy odometers, time-uniform bounds on privacy loss. There are substantial gaps between advanced composition and existing filters and odometers. First, existing filters place stronger assumptions on the algorithms being composed. Second, these odometers and filters suffer from large constants, making them impractical. We construct filters that match the rates of advanced composition, including constants, despite allowing for adaptively chosen privacy parameters. En route we also derive a privacy filter for approximate zCDP. We also construct several general families of odometers. These odometers match the tightness of advanced composition at an arbitrary, preselected point in time, or at all points in time simultaneously, up to a doubly-logarithmic factor. We obtain our results by leveraging advances in martingale concentration. In sum, we show that fully adaptive privacy is obtainable at almost no loss.

Many deep generative models are defined as a push-forward of a Gaussian measure by a continuous generator, such as Generative Adversarial Networks (GANs) or Variational Auto-Encoders (VAEs). This work explores the latent space of such deep generative models. A key issue with these models is their tendency to output samples outside of the support of the target distribution when learning disconnected distributions. We investigate the relationship between the performance of these models and the geometry of their latent space. Building on recent developments in geometric measure theory, we prove a sufficient condition for optimality in the case where the dimension of the latent space is larger than the number of modes. Through experiments on GANs, we demonstrate the validity of our theoretical results and gain new insights into the latent space geometry of these models. Additionally, we propose a truncation method that enforces a simplicial cluster structure in the latent space and improves the performance of GANs.

Data used for analytics and machine learning often take the form of tables with categorical entries. We introduce a family of lossless compression algorithms for such data that proceed in four steps: (i) Estimate latent variables associated to rows and columns; (ii) Partition the table in blocks according to the row/column latents; (iii) Apply a sequential (e.g. Lempel-Ziv) coder to each of the blocks; (iv) Append a compressed encoding of the latents. We evaluate this approach on several benchmark datasets, and study optimal compression in a probabilistic model for tabular data, whereby latent values are independent and table entries are conditionally independent given the latent values. We prove that the model has a well defined entropy rate and satisfies an asymptotic equipartition property. We also prove that classical compression schemes such as Lempel-Ziv and finite-state encoders do not achieve this rate. On the other hand, the latent estimation strategy outlined above achieves the optimal rate.

We study a new framework of learning mixture models via automatic clustering called PRESTO, wherein we optimize a joint objective function on the model parameters and the partitioning, with each model tailored to perform well on its specific cluster. In contrast to prior work, we do not assume any generative model for the data. We convert our training problem to a joint parameter estimation cum a subset selection problem, subject to a matroid span constraint. This allows us to reduce our problem into a constrained set function minimization problem, where the underlying objective is monotone and approximately submodular. We then propose a new joint discrete-continuous optimization algorithm that achieves a bounded approximation guarantee for our problem. We show that PRESTO outperforms several alternative methods. Finally, we study PRESTO in the context of resource-efficient deep learning, where we train smaller resource-constrained models on each partition and show that it outperforms existing data partitioning and model pruning/knowledge distillation approaches, which in contrast to PRESTO, require large initial (teacher) models.

We study a new connection between a technical measure called $\mu$-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of $\mu$-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal $\mu$-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Hamiltonian Monte Carlo (HMC) is a powerful algorithm to sample latent variables from Bayesian models. The advent of probabilistic programming languages (PPLs) frees users from writing inference algorithms and lets users focus on modeling. However, many models are difficult for HMC to solve directly, and often require tricks like model reparameterization. We are motivated by the fact that many of those models could be simplified by marginalization. We propose to use automatic marginalization as part of the sampling process using HMC in a graphical model extracted from a PPL, which substantially improves sampling from real-world hierarchical models.

Temperature scaling is a popular technique for tuning the sharpness of a model distribution. It is used extensively for sampling likely generations and calibrating model uncertainty, and even features as a controllable parameter to many large language models in deployment. However, autoregressive models rely on myopic temperature scaling that greedily optimizes the next token. To address this, we propose *Long Horizon Temperature Scaling* (LHTS), a novel approach for sampling from temperature-scaled *joint* distributions. LHTS is compatible with all likelihood-based models, and optimizes for the long-horizon likelihood of samples. We derive a temperature-dependent LHTS objective, and show that fine-tuning a model on a range of temperatures produces a single model capable of generation with a controllable long-horizon temperature parameter. We experiment with LHTS on image diffusion models and character/language autoregressive models, demonstrating its advantages over myopic temperature scaling in likelihood and sample quality, and showing improvements in accuracy of a multiple choice analogy by $10$%.

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

Latent variable models are powerful tools for modeling complex phenomena involving in particular partially observed data, unobserved variables or underlying complex unknown structures. Inference is often difficult due to the latent structure of the model. To deal with parameter estimation in the presence of latent variables, well-known efficient methods exist, such as gradient-based and EM-type algorithms, but with practical and theoretical limitations. In this paper, we propose as an alternative for parameter estimation an efficient preconditioned stochastic gradient algorithm. Our method includes a preconditioning step based on a positive definite Fisher information matrix estimate. We prove convergence results for the proposed algorithm under mild assumptions for very general latent variables models. We illustrate through relevant simulations the performance of the proposed methodology in a nonlinear mixed effects model and in a stochastic block model.

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). We show that when the underlying true reward is linear, under both Bradley-Terry-Luce (BTL) model (pairwise comparison) and Plackett-Luce (PL) model ($K$-wise comparison), MLE converges under certain semi-norm for the family of linear reward. On the other hand, when training a policy based on the learned reward model, we show that MLE fails while a pessimistic MLE provides policies with good performance under certain coverage assumption. We also show that under the PL model, both the true MLE and a different MLE which splits the $K$-wise comparison into pairwise comparisons converge, while the true MLE is asymptotically more efficient. Our results validate the empirical success of the existing RLHF algorithms, and provide new insights for algorithm design. Our analysis can also be applied for the problem of online RLHF and inverse reinforcement learning.

Annealed Importance Sampling (AIS) synthesizes weighted samples from an intractable distribution given its unnormalized density function. This algorithm relies on a sequence of interpolating distributions bridging the target to an initial tractable distribution such as the well-known geometric mean path of unnormalized distributions which is assumed to be suboptimal in general. In this paper, we prove that the geometric annealing corresponds to the distribution path that minimizes the KL divergence between the current particle distribution and the desired target when the feasible change in the particle distribution is constrained. Following this observation, we derive the constant rate discretization schedule for this annealing sequence, which adjusts the schedule to the difficulty of moving samples between the initial and the target distributions. We further extend our results to $f$-divergences and present the respective dynamics of annealing sequences based on which we propose the Constant Rate AIS (CR-AIS) algorithm and its efficient implementation for $\alpha$-divergences. We empirically show that CR-AIS performs well on multiple benchmark distributions while avoiding the computationally expensive tuning loop in existing Adaptive AIS.

The top-$k$ operator returns a $k$-sparse vector, where the non-zero values correspond to the $k$ largest values of the input. Unfortunately, because it is a discontinuous function, it is difficult to incorporate in neural networks trained end-to-end with backpropagation. Recent works have considered differentiable relaxations, based either on regularization or perturbation techniques. However, to date, no approach is fully differentiable and sparse. In this paper, we propose new differentiable and sparse top-$k$ operators. We view the top-$k$ operator as a linear program over the permutahedron, the convex hull of permutations. We then introduce a $p$-norm regularization term to smooth out the operator, and show that its computation can be reduced to isotonic optimization. Our framework is significantly more general than the existing one and allows for example to express top-$k$ operators that select values in magnitude. On the algorithmic side, in addition to pool adjacent violator (PAV) algorithms, we propose a new GPU/TPU-friendly Dykstra algorithm to solve isotonic optimization problems. We successfully use our operators to prune weights in neural networks, to fine-tune vision transformers, and as a router in sparse mixture of experts.

Radial basis function neural networks (RBFNN) are well-known for their capability to approximate any continuous function on a closed bounded set with arbitrary precision given enough hidden neurons. In this paper, we introduce the first algorithm to construct coresets for RBFNNs, i.e., small weighted subsets that approximate the loss of the input data on any radial basis function network and thus approximate any function defined by an RBFNN on the larger input data. In particular, we construct coresets for radial basis and Laplacian loss functions. We then use our coresets to obtain a provable data subset selection algorithm for training deep neural networks. Since our coresets approximate every function, they also approximate the gradient of each weight in a neural network, which is a particular function on the input. We then perform empirical evaluations on function approximation and dataset subset selection on popular network architectures and data sets, demonstrating the efficacy and accuracy of our coreset construction.

We consider online scheduling on unrelated (heterogeneous) machines in a speed-oblivious setting, where an algorithm is unaware of the exact job-dependent processing speeds. We show strong impossibility results for clairvoyant and non-clairvoyant algorithms and overcome them in models inspired by practical settings: (i) we provide competitive learning-augmented algorithms, assuming that (possibly erroneous) predictions on the speeds are given, and (ii) we provide competitive algorithms for the speed-ordered model, where a single global order of machines according to their unknown job-dependent speeds is known. We prove strong theoretical guarantees and evaluate our findings on a representative heterogeneous multi-core processor. These seem to be the first empirical results for scheduling algorithms with predictions that are evaluated in a non-synthetic hardware environment.

Language modeling on large-scale datasets improves performance of various downstream tasks. The validation pre-training loss is often used as the evaluation metric for language models since the pre-training loss tends to be well-correlated with downstream performance (which is itself hard to evaluate comprehensively). Contrary to the conventional wisdom, this paper shows that 1) pre-training loss cannot fully explain downstream performance and 2) flatness of the model is well-correlated with downstream performance where pre-training loss is not. We identify three ways to produce models with the same pre-training loss but different downstream performance: continue pre-training after convergence, increasing the model size, and changing the pre-training algorithms. These experiments demonstrate the existence of implicit bias of pre-training algorithms---among models with the same minimal pre-training loss, they implicitly prefer more transferable ones. Toward understanding this implicit bias, we prove that SGD with standard mini-batch noise implicitly prefers flatter minima of pre-training loss in language models, and empirically observe a strong correlation between flatness (measured by the trace of Hessian) and downstream performance among models with the same pre-training loss. We also prove in a synthetic language setting that among models with the minimal pre-training loss, the flattest model transfers to downstream tasks.

With growing attention to tabular data these days, the attempt to apply a synthetic table to various tasks has been expanded toward various scenarios. Owing to the recent advances in generative modeling, fake data generated by tabular data synthesis models become sophisticated and realistic. However, there still exists a difficulty in modeling discrete variables (columns) of tabular data. In this work, we propose to process continuous and discrete variables separately (but being conditioned on each other) by two diffusion models. The two diffusion models are co-evolved during training by reading conditions from each other. In order to further bind the diffusion models, moreover, we introduce a contrastive learning method with a negative sampling method. In our experiments with 11 real-world tabular datasets and 8 baseline methods, we prove the efficacy of the proposed method, called $\texttt{CoDi}$. Our code is available at https://github.com/ChaejeongLee/CoDi.

Symbolic regression (SR) is the problem of learning a symbolic expression from numerical data. Recently, deep neural models trained on procedurally-generated synthetic datasets showed competitive performance compared to more classical Genetic Programming (GP) ones. Unlike their GP counterparts, these neural approaches are trained to generate expressions from datasets given as context. This allows them to produce accurate expressions in a single forward pass at test time. However, they usually do not benefit from search abilities, which result in low performance compared to GP on out-of-distribution datasets. In this paper, we propose a novel method which provides the best of both worlds, based on a Monte-Carlo Tree Search procedure using a context-aware neural mutation model, which is initially pre-trained to learn promising mutations, and further refined from successful experiences in an online fashion. The approach demonstrates state-of-the-art performance on the well-known SRBench benchmark.

Clustering aims to group unlabelled samples based on their similarities and is widespread in high-dimensional data analysis. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The theoretical analysis and experiments illustrate the superiority of HCHC.

Despite the emergence of principled methods for domain adaptation under label shift, their sensitivity to shifts in class conditional distributions is precariously under explored. Meanwhile, popular deep domain adaptation heuristics tend to falter when faced with label proportions shifts. While several papers modify these heuristics in attempts to handle label proportions shifts, inconsistencies in evaluation standards, datasets, and baselines make it difficult to gauge the current best practices. In this paper, we introduce RLSbench, a large-scale benchmark for *relaxed label shift*, consisting of $>$500 distribution shift pairs spanning vision, tabular, and language modalities, with varying label proportions. Unlike existing benchmarks, which primarily focus on shifts in class-conditional $p(x|y)$, our benchmark also focuses on label marginal shifts. First, we assess 13 popular domain adaptation methods, demonstrating more widespread failures under label proportion shifts than were previously known. Next, we develop an effective two-step meta-algorithm that is compatible with most domain adaptation heuristics: (i) *pseudo-balance* the data at each epoch; and (ii) adjust the final classifier with target label distribution estimate. The meta-algorithm improves existing domain adaptation heuristics under large label proportion shifts, often by 2--10% accuracy points, while conferring minimal effect ($<$0.5%) when label proportions do not shift. We hope that these findings and the availability of RLSbench will encourage researchers to rigorously evaluate proposed methods in relaxed label shift settings. Code is publicly available at https://github.com/acmi-lab/RLSbench.

Consider the problem of exploration in sparse-reward or reward-free environments, such as in Montezuma's Revenge. In the curiosity-driven paradigm, the agent is rewarded for how much each realized outcome differs from their predicted outcome. But using predictive error as intrinsic motivation is fragile in stochastic environments, as the agent may become trapped by high-entropy areas of the state-action space, such as a "noisy TV". In this work, we study a natural solution derived from structural causal models of the world: Our key idea is to learn representations of the future that capture precisely the unpredictable aspects of each outcome---which we use as additional input for predictions, such that intrinsic rewards only reflect the predictable aspects of world dynamics. First, we propose incorporating such hindsight representations into models to disentangle "noise" from "novelty", yielding Curiosity in Hindsight: a simple and scalable generalization of curiosity that is robust to stochasticity. Second, we instantiate this framework for the recently introduced BYOL-Explore algorithm as our prime example, resulting in the noise-robust BYOL-Hindsight. Third, we illustrate its behavior under a variety of different stochasticities in a grid world, and find improvements over BYOL-Explore in hard-exploration Atari games with sticky actions. Notably, we show state-of-the-art results in exploring Montezuma's Revenge with sticky actions, while preserving performance in the non-sticky setting.

Conventional recommender systems are required to train the recommendation model using a centralized database. However, due to data privacy concerns, this is often impractical when multi-parties are involved in recommender system training. Federated learning appears as an excellent solution to the data isolation and privacy problem. Recently, Graph neural network (GNN) is becoming a promising approach for federated recommender systems. However, a key challenge is to conduct embedding propagation while preserving the privacy of the graph structure. Few studies have been conducted on the federated GNN-based recommender system. Our study proposes the first vertical federated GNN-based recommender system, called VerFedGNN. We design a framework to transmit: (i) the summation of neighbor embeddings using random projection, and (ii) gradients of public parameter perturbed by ternary quantization mechanism. Empirical studies show that VerFedGNN has competitive prediction accuracy with existing privacy preserving GNN frameworks while enhanced privacy protection for users' interaction information.

Modern deep learning models with great expressive power can be trained to overfit the training data but still generalize well. This phenomenon is referred to as benign overfitting. Recently, a few studies have attempted to theoretically understand benign overfitting in neural networks. However, these works are either limited to neural networks with smooth activation functions or to the neural tangent kernel regime. How and when benign overfitting can occur in ReLU neural networks remains an open problem. In this work, we seek to answer this question by establishing algorithm-dependent risk bounds for learning two-layer ReLU convolutional neural networks with label-flipping noise. We show that, under mild conditions, the neural network trained by gradient descent can achieve near-zero training loss and Bayes optimal test risk. Our result also reveals a sharp transition between benign and harmful overfitting under different conditions on data distribution in terms of test risk. Experiments on synthetic data back up our theory.

Deep Q-learning based algorithms have been applied successfully in many decision making problems, while their theoretical foundations are not as well understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU neural network parameterization, and find the sample complexity guarantees for the algorithm. Our approach estimates the Q-function in each iteration using a convex optimization problem. We show that this approach achieves a sample complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal. This result holds for a countable state-spaces and does not require any assumptions such as a linear or low rank structure on the MDP.

We consider the problem of learning the best possible policy from a fixed dataset, known as offline Reinforcement Learning (RL). A common taxonomy of existing offline RL works is policy regularization, which typically constrains the learned policy by distribution or support of the behavior policy. However, distribution and support constraints are overly conservative since they both force the policy to choose similar actions as the behavior policy when considering particular states. It will limit the learned policy's performance, especially when the behavior policy is sub-optimal. In this paper, we find that regularizing the policy towards the nearest state-action pair can be more effective and thus propose Policy Regularization with Dataset Constraint (PRDC). When updating the policy in a given state, PRDC searches the entire dataset for the nearest state-action sample and then restricts the policy with the action of this sample. Unlike previous works, PRDC can guide the policy with proper behaviors from the dataset, allowing it to choose actions that do not appear in the dataset along with the given state. It is a softer constraint but still keeps enough conservatism from out-of-distribution actions. Empirical evidence and theoretical analysis show that PRDC can alleviate offline RL's fundamentally challenging value overestimation issue with a bounded performance gap. Moreover, on a set of locomotion and navigation tasks, PRDC achieves state-of-the-art performance compared with existing methods. Code is available at https://github.com/LAMDA-RL/PRDC

We study a class of reinforcement learning problems where the reward signals for policy learning are generated by a discriminator that is dependent on and jointly optimized with the policy. This interdependence between the policy and the discriminator leads to an unstable learning process because reward signals from an immature discriminator are noisy and impede policy learning, and conversely, an under-optimized policy impedes discriminator learning. We call this learning setting $\textit{Internally Rewarded Reinforcement Learning}$ (IRRL) as the reward is not provided directly by the environment but $\textit{internally}$ by the discriminator. In this paper, we formally formulate IRRL and present a class of problems that belong to IRRL. We theoretically derive and empirically analyze the effect of the reward function in IRRL and based on these analyses propose the clipped linear reward function. Experimental results show that the proposed reward function can consistently stabilize the training process by reducing the impact of reward noise, which leads to faster convergence and higher performance compared with baselines in diverse tasks.

We analyze Newton's method with lazy Hessian updates for solving general possibly non-convex optimization problems. We propose to reuse a previously seen Hessian for several iterations while computing new gradients at each step of the method. This significantly reduces the overall arithmetic complexity of second-order optimization schemes. By using the cubic regularization technique, we establish fast global convergence of our method to a second-order stationary point, while the Hessian does not need to be updated each iteration. For convex problems, we justify global and local superlinear rates for lazy Newton steps with quadratic regularization, which is easier to compute. The optimal frequency for updating the Hessian is once every $d$ iterations, where $d$ is the dimension of the problem. This provably improves the total arithmetic complexity of second-order algorithms by a factor $\sqrt{d}$.

Contextual dynamic pricing is a problem of setting prices based on current contextual information and previous sales history to maximize revenue. A popular approach is to postulate a distribution of customer valuation as a function of contextual information and the baseline valuation. A semi-parametric setting, where the context effect is parametric and the baseline is nonparametric, is of growing interest due to its flexibility. A challenge is that customer valuation is almost never observable in practice and is instead *type-I interval censored* by the offered price. To address this challenge, we propose a novel semi-parametric contextual pricing algorithm for stochastic contexts, called the epoch-based Cox proportional hazards Contextual Pricing (CoxCP) algorithm. To our best knowledge, our work is the first to employ the Cox model for customer valuation. The CoxCP algorithm has a high-probability regret upper bound of $\tilde{O}( T^{\frac{2}{3}}d )$, where $T$ is the length of horizon and $d$ is the dimension of context. In addition, if the baseline is known, the regret bound can improve to $O( d \log T )$ under certain assumptions. We demonstrate empirically the proposed algorithm performs better than existing semi-parametric contextual pricing algorithms when the model assumptions of all algorithms are correct.

How do large language models (LLMs) develop and evolve over the course of training? How do these patterns change as models scale? To answer these questions, we introduce Pythia, a suite of 16 LLMs all trained on public data seen in the exact same order and ranging in size from 70M to 12B parameters. We provide public access to 154 checkpoints for each one of the 16 models, alongside tools to download and reconstruct their exact training dataloaders for further study. We intend Pythia to facilitate research in many areas, and we present several case studies including novel results in memorization, term frequency effects on few-shot performance, and reducing gender bias. We demonstrate that this highly controlled setup can be used to yield novel insights toward LLMs and their training dynamics. Trained models, analysis code, training code, and training data can be found at https://github.com/EleutherAI/pythia.

In some medical imaging tasks and other settings where only small parts of the image are informative for the classification task, traditional CNNs can sometimes struggle to generalise. Manually annotated Regions of Interest (ROI) are often used to isolate the most informative parts of the image. However, these are expensive to collect and may vary significantly across annotators. To overcome these issues, we propose a framework that employs saliency maps to obtain soft spatial attention masks that modulate the image features at different scales. We refer to our method as *Adversarial Counterfactual Attention* (ACAT). ACAT increases the baseline classification accuracy of lesions in brain CT scans from $71.39 \%$ to $72.55 \%$ and of COVID-19 related findings in lung CT scans from $67.71 \%$ to $70.84 \%$ and exceeds the performance of competing methods. We investigate the best way to generate the saliency maps employed in our architecture and propose a way to obtain them from adversarially generated counterfactual images. They are able to isolate the area of interest in brain and lung CT scans without using any manual annotations. In the task of localising the lesion location out of 6 possible regions, they obtain a score of $65.05 \%$ on brain CT scans, improving the score of $61.29 \%$ obtained with the best competing method.

Early stopping based on hold-out data is a popular regularization technique designed to mitigate overfitting and increase the predictive accuracy of neural networks. Models trained with early stopping often provide relatively accurate predictions, but they generally still lack precise statistical guarantees unless they are further calibrated using independent hold-out data. This paper addresses the above limitation with conformalized early stopping: a novel method that combines early stopping with conformal calibration while efficiently recycling the same hold-out data. This leads to models that are both accurate and able to provide exact predictive inferences without multiple data splits nor overly conservative adjustments. Practical implementations are developed for different learning tasks---outlier detection, multi-class classification, regression---and their competitive performance is demonstrated on real data.

Artificial neural networks are being proposed as models of parts of the brain. The networks are compared to recordings of biological neurons, and good performance in reproducing neural responses is considered to support the model's validity. A key question is how much this system identification approach tells us about brain computation. Does it validate one model architecture over another? We evaluate the most commonly used comparison techniques, such as a linear encoding model and centered kernel alignment, to correctly identify a model by replacing brain recordings with known ground truth models. System identification performance is quite variable; it also depends significantly on factors independent of the ground truth architecture, such as stimuli images. In addition, we show the limitations of using functional similarity scores in identifying higher-level architectural motifs.

Embodied AI agents that search for objects in large environments such as households often need to make efficient decisions by predicting object locations based on partial information. We pose this as a new type of link prediction problem: link prediction on partially observable dynamic graphs Our graph is a representation of a scene in which rooms and objects are nodes, and their relationships are encoded in the edges; only parts of the changing graph are known to the agent at each timestep. This partial observability poses a challenge to existing link prediction approaches, which we address. We propose a novel state representation -- Scene Graph Memory (SGM) -- with captures the agent’s accumulated set of observations, as well as a neural net architecture called a Node Edge Predictor (NEP) that extracts information from the SGM to search efficiently. We evaluate our method in the Dynamic House Simulator, a new benchmark that creates diverse dynamic graphs following the semantic patterns typically seen at homes, and show that NEP can be trained to predict the locations of objects in a variety of environments with diverse object movement dynamics, outperforming baselines both in terms of new scene adaptability and overall accuracy. The codebase and more can be found www.scenegraphmemory.com.

Policies often fail at test-time due to distribution shifts---changes in the state and reward that occur when an end user deploys the policy in environments different from those seen in training. Data augmentation can help models be more robust to such shifts by varying specific concepts in the state, e.g. object color, that are task-irrelevant and should not impact desired actions. However, designers training the agent don't often know which concepts are irrelevant a priori. We propose a human-in-the-loop framework to leverage feedback from the end user to quickly identify and augment task-irrelevant visual state concepts. Our framework generates counterfactual demonstrations that allow users to quickly isolate shifted state concepts and identify if they should not impact the desired task, and can therefore be augmented using existing actions. We present experiments validating our full pipeline on discrete and continuous control tasks with real human users. Our method better enables users to (1) understand agent failure, (2) improve sample efficiency of demonstrations required for finetuning, and (3) adapt the agent to their desired reward.

Without explicit feedback, humans can rapidly learn the meaning of words. Children can acquire a new word after just a few passive exposures, a process known as fast mapping. This word learning capability is believed to be the most fundamental building block of multimodal understanding and reasoning. Despite recent advancements in multimodal learning, a systematic and rigorous evaluation is still missing for human-like word learning in machines. To fill in this gap, we introduce the MachinE Word Learning (MEWL) benchmark to assess how machines learn word meaning in grounded visual scenes. MEWL covers human's core cognitive toolkits in word learning: cross-situational reasoning, bootstrapping, and pragmatic learning. Specifically, MEWL is a few-shot benchmark suite consisting of nine tasks for probing various word learning capabilities. These tasks are carefully designed to be aligned with the children's core abilities in word learning and echo the theories in the developmental literature. By evaluating multimodal and unimodal agents' performance with a comparative analysis of human performance, we notice a sharp divergence in human and machine word learning. We further discuss these differences between humans and machines and call for human-like few-shot word learning in machines.

Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.

Counterfactual explanations have been widely studied in explainability, with a range of application dependent methods prominent in fairness, recourse and model understanding. The major shortcoming associated with these methods, however, is their inability to provide explanations beyond the local or instance-level. While many works touch upon the notion of a global explanation, typically suggesting to aggregate masses of local explanations in the hope of ascertaining global properties, few provide frameworks that are both reliable and computationally tractable. Meanwhile, practitioners are requesting more efficient and interactive explainability tools. We take this opportunity to propose Global & Efficient Counterfactual Explanations (GLOBE-CE), a flexible framework that tackles the reliability and scalability issues associated with current state-of-the-art, particularly on higher dimensional datasets and in the presence of continuous features. Furthermore, we provide a unique mathematical analysis of categorical feature translations, utilising it in our method. Experimental evaluation with publicly available datasets and user studies demonstrate that GLOBE-CE performs significantly better than the current state-of-the-art across multiple metrics (e.g., speed, reliability).

To bridge the gaps between topology-aware Graph Neural Networks (GNNs) and inference-efficient Multi-Layer Perceptron (MLPs), GLNN proposes to distill knowledge from a well-trained teacher GNN into a student MLP. Despite their great progress, comparatively little work has been done to explore the reliability of different knowledge points (nodes) in GNNs, especially their roles played during distillation. In this paper, we first quantify the knowledge reliability in GNN by measuring the invariance of their information entropy to noise perturbations, from which we observe that different knowledge points (1) show different distillation speeds (temporally); (2) are differentially distributed in the graph (spatially). To achieve reliable distillation, we propose an effective approach, namely Knowledge-inspired Reliable Distillation (KRD), that models the probability of each node being an informative and reliable knowledge point, based on which we sample a set of additional reliable knowledge points as supervision for training student MLPs. Extensive experiments show that KRD improves over the vanilla MLPs by 12.62% and outperforms its corresponding teacher GNNs by 2.16% averaged over 7 datasets and 3 GNN architectures. Codes are publicly available at: https://github.com/LirongWu/RKD.

Contrastive learning (CL) continuously achieves significant breakthroughs across multiple domains. However, the most common InfoNCE-based methods suffer from some dilemmas, such as uniformity-tolerance dilemma (UTD) and gradient reduction, both of which are related to a $\mathcal{P}_{ij}$ term. It has been identified that UTD can lead to unexpected performance degradation. We argue that the fixity of temperature is to blame for UTD. To tackle this challenge, we enrich the CL loss family by presenting a Model-Aware Contrastive Learning (MACL) strategy, whose temperature is adaptive to the magnitude of alignment that reflects the basic confidence of the instance discrimination task, then enables CL loss to adjust the penalty strength for hard negatives adaptively. Regarding another dilemma, the gradient reduction issue, we derive the limits of an involved gradient scaling factor, which allows us to explain from a unified perspective why some recent approaches are effective with fewer negative samples, and summarily present a gradient reweighting to escape this dilemma. Extensive remarkable empirical results in vision, sentence, and graph modality validate our approach's general improvement for representation learning and downstream tasks.

We attack the state-of-the-art Go-playing AI system KataGo by training adversarial policies against it, achieving a >97% win rate against KataGo running at superhuman settings. Our adversaries do not win by playing Go well. Instead, they trick KataGo into making serious blunders. Our attack transfers zero-shot to other superhuman Go-playing AIs, and is comprehensible to the extent that human experts can implement it without algorithmic assistance to consistently beat superhuman AIs. The core vulnerability uncovered by our attack persists even in KataGo agents adversarially trained to defend against our attack. Our results demonstrate that even superhuman AI systems may harbor surprising failure modes. Example games are available https://goattack.far.ai/.

Artificial agents have traditionally been trained to maximize reward, which may incentivize power-seeking and deception, analogous to how next-token prediction in language models (LMs) may incentivize toxicity. So do agents naturally learn to be Machiavellian? And how do we measure these behaviors in general-purpose models such as GPT-4? Towards answering these questions, we introduce Machiavelli, a benchmark of 134 Choose-Your-Own-Adventure games containing over half a million rich, diverse scenarios that center on social decision-making. Scenario labeling is automated with LMs, which are more performant than human annotators. We mathematize dozens of harmful behaviors and use our annotations to evaluate agents' tendencies to be power-seeking, cause disutility, and commit ethical violations. We observe some tension between maximizing reward and behaving ethically. To improve this trade-off, we investigate LM-based methods to steer agents towards less harmful behaviors. Our results show that agents can both act competently and morally, so concrete progress can currently be made in machine ethics--designing agents that are Pareto improvements in both safety and capabilities.

Diffusion models have demonstrated their powerful generative capability in many tasks, with great potential to serve as a paradigm for offline reinforcement learning. However, the quality of the diffusion model is limited by the insufficient diversity of training data, which hinders the performance of planning and the generalizability to new tasks. This paper introduces AdaptDiffuser, an evolutionary planning method with diffusion that can self-evolve to improve the diffusion model hence a better planner, not only for seen tasks but can also adapt to unseen tasks. AdaptDiffuser enables the generation of rich synthetic expert data for goal-conditioned tasks using guidance from reward gradients. It then selects high-quality data via a discriminator to finetune the diffusion model, which improves the generalization ability to unseen tasks. Empirical experiments on two benchmark environments and two carefully designed unseen tasks in KUKA industrial robot arm and Maze2D environments demonstrate the effectiveness of AdaptDiffuser. For example, AdaptDiffuser not only outperforms the previous art Diffuser by 20.8% on Maze2D and 7.5% on MuJoCo locomotion, but also adapts better to new tasks, e.g., KUKA pick-and-place, by 27.9% without requiring additional expert data. More visualization results and demo videos could be found on our project page.

Although Nesterov's accelerated gradient method (AGM) has been studied from various perspectives, it remains unclear why the most popular forms of AGMs must handle convex and strongly convex objective functions separately. To address this inconsistency, we propose a novel unified framework for Lagrangians, ordinary differential equation (ODE) models, and algorithms. As a special case, our new simple momentum algorithm, which we call the unified AGM, seamlessly bridges the gap between the two most popular forms of Nesterov's AGM and has a superior convergence guarantee compared to existing algorithms for non-strongly convex objective functions. This property is beneficial in practice when considering ill-conditioned $\mu$-strongly convex objective functions (with small $\mu$). Furthermore, we generalize this algorithm and the corresponding ODE model to the higher-order non-Euclidean setting. Last but not least, our unified framework is used to construct the unified AGM-G ODE, a novel ODE model for minimizing the gradient norm of strongly convex functions.

This paper considers the problem of learning single ReLU neuron with squared loss (a.k.a., ReLU regression) in the overparameterized regime, where the input dimension can exceed the number of samples. We analyze a Perceptron-type algorithm called GLM-tron [Kakade et al. 2011], and provide its dimension-free risk upper bounds for high-dimensional ReLU regression in both well-specified and misspecified settings. Our risk bounds recover several existing results as special cases. Moreover, in the well-specified setting, we also provide an instance-wise matching risk lower bound for GLM-tron. Our upper and lower risk bounds provide a sharp characterization of the high-dimensional ReLU regression problems that can be learned via GLM-tron. On the other hand, we provide some negative results for stochastic gradient descent (SGD) for ReLU regression with symmetric Bernoulli data: if the model is well-specified, the excess risk of SGD is provably no better than that of GLM-tron ignoring constant factors, for each problem instance; and in the noiseless case, GLM-tron can achieve a small risk while SGD unavoidably suffers from a constant risk in expectation. These results together suggest that GLM-tron might be more preferable than SGD for high-dimensional ReLU regression.

We investigate online classification with paid stochastic experts. Here, before making their prediction, each expert must be paid. The amount that we pay each expert directly influences the accuracy of their prediction through some unknown Lipschitz ``productivity'' function. In each round, the learner must decide how much to pay each expert and then make a prediction. They incur a cost equal to a weighted sum of the prediction error and upfront payments for all experts. We introduce an online learning algorithm whose total cost after $T$ rounds exceeds that of a predictor which knows the productivity of all experts in advance by at most $\mathcal{O}\big(K^2(\ln T)\sqrt{T}\big)$ where $K$ is the number of experts. In order to achieve this result, we combine Lipschitz bandits and online classification with surrogate losses. These tools allow us to improve upon the bound of order $T^{2/3}$ one would obtain in the standard Lipschitz bandit setting. Our algorithm is empirically evaluated on synthetic data.

We give an improved theoretical analysis of score-based generative modeling. Under a score estimate with small $L^2$ error (averaged across timesteps), we provide efficient convergence guarantees for any data distribution with second-order moment, by either employing early stopping or assuming smoothness condition on the score function of the data distribution. Our result does not rely on any log-concavity or functional inequality assumption and has a logarithmic dependence on the smoothness. In particular, we show that under only a finite second moment condition, approximating the following in reverse KL divergence in $\epsilon$-accuracy can be done in $\tilde O\left(\frac{d \log (1/\delta)}{\epsilon}\right)$ steps: 1) the variance-$\delta$ Gaussian perturbation of any data distribution; 2) data distributions with $1/\delta$-smooth score functions. Our analysis also provides a quantitative comparison between different discrete approximations and may guide the choice of discretization points in practice.

Black box optimisation of an unknown function from expensive and noisy evaluations is a ubiquitous problem in machine learning, academic research and industrial production. An abstraction of the problem can be formulated as a kernel based bandit problem (also known as Bayesian optimisation), where a learner aims at optimising a kernelized function through sequential noisy observations. The existing work predominantly assumes feedback is immediately available; an assumption which fails in many real world situations, including recommendation systems, clinical trials and hyperparameter tuning. We consider a kernel bandit problem under stochastically delayed feedback, and propose an algorithm with $\tilde{\mathcal{O}}\left(\sqrt{\Gamma_k(T) T}+\mathbb{E}[\tau]\right)$ regret, where $T$ is the number of time steps, $\Gamma_k(T)$ is the maximum information gain of the kernel with $T$ observations, and $\tau$ is the delay random variable. This represents a significant improvement over the state of the art regret bound of $\tilde{\mathcal{O}}\left(\Gamma_k(T)\sqrt{ T}+\mathbb{E}[\tau]\Gamma_k(T)\right)$ reported in (Verma et al., 2022). In particular, for very non-smooth kernels, the information gain grows almost linearly in time, trivializing the existing results. We also validate our theoretical results with simulations.

We consider the problem of solving large-scale instances of the Max-Cut semidefinite program (SDP), i.e., optimizing a linear function over $n\times n$ positive semidefinite (PSD) matrices with unit diagonal. When the cost matrix is PSD, we show how to exactly reformulate the problem as maximizing a smooth concave function over PSD matrices with unit trace. By applying the Frank-Wolfe method, we obtain a simple algorithm that is compatible with recent sampling-based techniques to solve SDPs using low memory. We demonstrate the practical performance of our method on $10^6\times 10^6$ instances of the max-cut SDP with costs having up to $5 \times 10^6$ non-zero entries. Theoretically, we show that our method solves problems with diagonally dominant costs to relative error $\epsilon$ in $O(n\epsilon^{-1})$ calls to a randomized approximate largest eigenvalue subroutine, each of which succeeds with high probability after $O(\log(n)\epsilon^{-1/2})$ matrix-vector multiplications with the cost matrix.

Large language models show impressive results at predicting structured text such as code, but also commonly introduce errors and hallucinations in their output. When used to assist software developers, these models may make mistakes that users must go back and fix, or worse, introduce subtle bugs that users may miss entirely. We propose Randomized Utility-driven Synthesis of Uncertain REgions (R-U-SURE), an approach for building uncertainty-aware suggestions based on a decision-theoretic model of goal-conditioned utility, using random samples from a generative model as a proxy for the unobserved possible intents of the end user. Our technique combines minimum-Bayes-risk decoding, dual decomposition, and decision diagrams in order to efficiently produce structured uncertainty summaries, given only sample access to an arbitrary generative model of code and an optional AST parser. We demonstrate R-U-SURE on three developer-assistance tasks, and show that it can be applied different user interaction patterns without retraining the model and leads to more accurate uncertainty estimates than token-probability baselines. We also release our implementation as an open-source library at https://github.com/google-research/rusure.

In this work, we investigate the implicit regularization induced by teacher-student learning dynamics in self-distillation. To isolate its effect, we describe a simple experiment where we consider teachers at random initialization instead of trained teachers. Surprisingly, when distilling a student into such a random teacher, we observe that the resulting model and its representations already possess very interesting characteristics; (1) we observe a strong improvement of the distilled student over its teacher in terms of probing accuracy. (2) The learned representations are data-dependent and transferable between different tasks but deteriorate strongly if trained on random inputs. (3) The student checkpoint contains sparse subnetworks, so-called lottery tickets, and lies on the border of linear basins in the supervised loss landscape. These observations have interesting consequences for several important areas in machine learning: (1) Self-distillation can work solely based on the implicit regularization present in the gradient dynamics without relying on any dark knowledge, (2) self-supervised learning can learn features even in the absence of data augmentation and (3) training dynamics during the early phase of supervised training do not necessarily require label information. Finally, we shed light on an intriguing local property of the loss landscape: the process of feature learning is strongly amplified if the student is initialized closely to the teacher. These results raise interesting questions about the nature of the landscape that have remained unexplored so far. Code is available at https://github.com/safelix/dinopl.

Evaluating fairness can be challenging in practice because the sensitive attributes of data are often inaccessible due to privacy constraints. The go-to approach that the industry frequently adopts is using off-the-shelf proxy models to predict the missing sensitive attributes, e.g. Meta (Alao et al., 2021) and Twitter (Belli et al., 2022). Despite its popularity, there are three important questions unanswered: (1) Is directly using proxies efficacious in measuring fairness? (2) If not, is it possible to accurately evaluate fairness using proxies only? (3) Given the ethical controversy over infer-ring user private information, is it possible to only use weak (i.e. inaccurate) proxies in order to protect privacy? Our theoretical analyses show that directly using proxy models can give a false sense of (un)fairness. Second, we develop an algorithm that is able to measure fairness (provably) accurately with only three properly identified proxies. Third, we show that our algorithm allows the use of only weak proxies (e.g. with only 68.85% accuracy on COMPAS), adding an extra layer of protection on user privacy. Experiments validate our theoretical analyses and show our algorithm can effectively measure and mitigate bias. Our results imply a set of practical guidelines for prac-titioners on how to use proxies properly. Code is available at https://github.com/UCSC-REAL/fair-eval.

3D point clouds serve as a crucial data representation in numerous real-world applications such as autonomous driving, robotics, and medical imaging. While the advancements in deep learning have spurred the utilization of 3D point clouds, deep models are notoriously vulnerable to adversarial attacks. Various defense solutions have been proposed to build robust models against adversarial attacks. In this work, we pinpoint a major limitation of the leading empirical defense, adversarial training, when applied to 3D point cloud models: gradient obfuscation, which significantly hampers robustness against potent attacks. To bridge the gap, we propose PointDP, a purification strategy that leverages diffusion models to defend against 3D adversarial attacks. Since PointDP does not rely on predefined adversarial examples for training, it can defend against a variety of threats. We conduct a comprehensive evaluation of PointDP across six representative 3D point cloud architectures, employing sixteen strong and adaptive attacks to manifest its foundational robustness. Our evaluation shows that PointDP achieves significantly better (i.e., 12.6%-40.3%) adversarial robustness than state-of-the-art methods under strong attacks bounded by different $\ell_p$ norms.

Image inpainting refers to the task of generating a complete, natural image based on a partially revealed reference image. Recently, many research interests have been focused on addressing this problem using fixed diffusion models. These approaches typically directly replace the revealed region of the intermediate or final generated images with that of the reference image or its variants. However, since the unrevealed regions are not directly modified to match the context, it results in incoherence between revealed and unrevealed regions. To address the incoherence problem, a small number of methods introduce a rigorous Bayesian framework, but they tend to introduce mismatches between the generated and the reference images due to the approximation errors in computing the posterior distributions. In this paper, we propose CoPaint, which can coherently inpaint the whole image without introducing mismatches. CoPaint also uses the Bayesian framework to jointly modify both revealed and unrevealed regions but approximates the posterior distribution in a way that allows the errors to gradually drop to zero throughout the denoising steps, thus strongly penalizing any mismatches with the reference image. Our experiments verify that CoPaint can outperform the existing diffusion-based methods under both objective and subjective metrics.

Existing reinforcement learning (RL) mainly utilize online or offline settings. The online methods explore the environment with expensive time cost, and the offline methods efficiently obtain reward signals by sacrificing the exploration capability. We propose semi-offline RL, a novel paradigm that can smoothly transit from the offline setting to the online setting, balances the exploration capability and training cost, and provides a theoretical foundation for comparing different RL settings. Based on the semi-offline MDP formulation, we present the RL setting that is optimal in terms of optimization cost, asymptotic error, and overfitting error bound. Extensive experiments show that our semi-offline RL approach is effective in various text generation tasks and datasets, and yields comparable or usually better performance compared with the state-of-the-art methods.

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save communication cost, we then extend DProxSGT to a compressed method by compressing the communicated information. Both methods need only $\mathcal{O}(1)$ samples per worker for each proximal update, which is important to achieve good generalization performance on training deep neural networks. With a smoothness condition on the expected loss function (but not on each sample function), the proposed methods can achieve an optimal sample complexity result to produce a near-stationary point. Numerical experiments on training neural networks demonstrate the significantly better generalization performance of our methods over large-batch training methods and momentum variance-reduction methods and also, the ability of handling heterogeneous data by the gradient tracking scheme.

In this paper, we prove the representation defects of a cascaded convolutional decoder network, considering the capacity of representing different frequency components of an input sample. We conduct the discrete Fourier transform on each channel of the feature map in an intermediate layer of the decoder network. Then, we extend the 2D circular convolution theorem to represent the forward and backward propagations through convolutional layers in the frequency domain. Based on this, we prove three defects in representing feature spectrums. First, we prove that the convolution operation, the zero-padding operation, and a set of other settings all make a convolutional decoder network more likely to weaken high-frequency components. Second, we prove that the upsampling operation generates a feature spectrum, in which strong signals repetitively appear at certain frequencies. Third, we prove that if the frequency components in the input sample and frequency components in the target output for regression have a small shift, then the decoder usually cannot be effectively learned.

Human brains respond to semantic features of presented stimuli with different neurons. This raises the question of whether deep neural networks admit a similar behavior pattern. To investigate this phenomenon, this paper identifies a small cluster of neurons associated with a specific subject in a diffusion model. We call those neurons the concept neurons. They can be identified by statistics of network gradients to a stimulation connected with the given subject. The concept neurons demonstrate magnetic properties in interpreting and manipulating generation results. Shutting them can directly yield the related subject contextualized in different scenes. Concatenating multiple clusters of concept neurons can vividly generate all related concepts in a single image. Our method attains impressive performance for multi-subject customization, even four or more subjects. For large-scale applications, the concept neurons are environmentally friendly as we only need to store a sparse cluster of int index instead of dense float32 parameter values, reducing storage consumption by 90% compared with previous customized generation methods. Extensive qualitative and quantitative studies on diverse scenarios show the superiority of our method in interpreting and manipulating diffusion models.

Prompt-tuning is an emerging strategy to adapt large language models (LLM) to downstream tasks by learning a (soft-)prompt parameter from data. Despite its success in LLMs, there is limited theoretical understanding of the power of prompt-tuning and the role of the attention mechanism in prompting. In this work, we explore prompt-tuning for one-layer attention architectures and study contextual mixture-models where each input token belongs to a context-relevant or -irrelevant set. We isolate the role of prompt-tuning through a self-contained prompt-attention model. Our contributions are as follows: (1) We show that softmax-prompt-attention is provably more expressive than softmax-self-attention and linear-prompt-attention under our contextual data model. (2) We analyze the initial trajectory of gradient descent and show that it learns the prompt and prediction head with near-optimal sample complexity and demonstrate how the prompt can provably attend to sparse context-relevant tokens. (3) Assuming a known prompt but an unknown prediction head, we characterize the exact finite sample performance of prompt-attention which reveals the fundamental performance limits and the precise benefit of the context information. We also provide experiments that verify our theoretical insights on real datasets and demonstrate how prompt-tuning enables the model to attend to context-relevant information.

Diffusion-based methods, represented as stochastic differential equations on a continuous-time domain, have recently proven successful as non-adversarial generative models. Training such models relies on denoising score matching, which can be seen as multi-scale denoising autoencoders. Here, we augment the denoising score matching framework to enable representation learning without any supervised signal. GANs and VAEs learn representations by directly transforming latent codes to data samples. In contrast, the introduced diffusion-based representation learning relies on a new formulation of the denoising score matching objective and thus encodes the information needed for denoising. We illustrate how this difference allows for manual control of the level of details encoded in the representation. Using the same approach, we propose to learn an infinite-dimensional latent code that achieves improvements on state-of-the-art models on semi-supervised image classification. We also compare the quality of learned representations of diffusion score matching with other methods like autoencoder and contrastively trained systems through their performances on downstream tasks. Finally, we also ablate with a different SDE formulation for diffusion models and show that the benefits on downstream tasks are still present on changing the underlying differential equation.

The geometric structure of data is an important inductive bias in machine learning. In this work, we characterize the data manifolds entailed by structural causal models. The strengths of the proposed framework are twofold: firstly, the geometric structure of the data manifolds is causally informed, and secondly, it enables causal reasoning about the data manifolds in an interventional and a counterfactual sense. We showcase the versatility of the proposed framework by applying it to the generation of causally-grounded counterfactual explanations for machine learning classifiers, measuring distances along the data manifold in a differential geometric-principled manner.

The concentration of measure inequalities serves an essential role in statistics and machine learning. This paper gives unbounded analogues of the McDiarmid-type exponential inequalities for three popular classes of distributions, namely sub-Gaussian, sub-exponential and heavy-tailed distributions. The inequalities in the sub-Gaussian and sub-exponential cases are distribution-dependent compared with the recent results, and the inequalities in the heavy-tailed case are not available in the previous works. The usefulness of the inequalities is illustrated through applications to the sample mean, U-statistics and V-statistics.

Some extremely low-dimensional yet crucial geometric eigen-lengths often determine the success of some geometric tasks. For example, the height of an object is important to measure to check if it can fit between the shelves of a cabinet, while the width of a couch is crucial when trying to move it through a doorway. Humans have materialized such crucial geometric eigen-lengths in common sense since they are very useful in serving as succinct yet effective, highly interpretable, and universal object representations. However, it remains obscure and underexplored if learning systems can be equipped with similar capabilities of automatically discovering such key geometric quantities from doing tasks. In this work, we therefore for the first time formulate and propose a novel learning problem on this question and set up a benchmark suite including tasks, data, and evaluation metrics for studying the problem. We focus on a family of common fitting tasks as the testbed for the proposed learning problem. We explore potential solutions and demonstrate the feasibility of learning eigen-lengths from simply observing successful and failed fitting trials. We also attempt geometric grounding for more accurate eigen-length measurement and study the reusability of the learned geometric eigen-lengths across multiple tasks. Our work marks the first exploratory step toward learning crucial geometric eigen-lengths and we hope it can inspire future research in tackling this important yet underexplored problem.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

Causal effect identification is a fundamental task in artificial intelligence. A most ideal scenario for causal effect identification is that there is a directed acyclic graph as a prior causal graph encoding the causal relations of all relevant variables. In real tasks, however, the prior causal graph is usually not available, and some relevant variables may be latent as well. With observational data, we can only learn a partial ancestral graph (PAG), which contains some indeterminate causal relations. Since many causal graphs can correspond to one PAG, they are possibly associated with different causal effects. The aim of this paper is to estimate these possible causal effects via covariate adjustment given a PAG. This task is challenging because the number of causal graphs corresponding to a PAG grows super-exponentially with the number of variables. We propose a new graphical characterization for possible adjustment sets, and based on this, we develop the first method to determine the set of possible causal effects that are consistent with the given PAG without enumerating any causal graphs. Our method can output the same set as the enumeration method with super-exponentially less complexity. Experiments validate the effectiveness and tremendous efficiency improvement of the proposed method.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

We design learning rate schedules that minimize regret for SGD-based online learning in the presence of a changing data distribution. We fully characterize the optimal learning rate schedule for online linear regression via a novel analysis with stochastic differential equations. For general convex loss functions, we propose new learning rate schedules that are robust to distribution shift, and give upper and lower bounds for the regret that only differ by constants. For non-convex loss functions, we define a notion of regret based on the gradient norm of the estimated models and propose a learning schedule that minimizes an upper bound on the total expected regret. Intuitively, one expects changing loss landscapes to require more exploration, and we confirm that optimal learning rate schedules typically have higher learning rates in the presence of distribution shift. Finally, we provide experiments that illustrate these learning rate schedules and their regret.

Two central paradigms have emerged in the reinforcement learning (RL) community: online RL and offline RL. In the online RL setting, the agent has no prior knowledge of the environment, and must interact with it in order to find an $\epsilon$-optimal policy. In the offline RL setting, the learner instead has access to a fixed dataset to learn from, but is unable to otherwise interact with the environment, and must obtain the best policy it can from this offline data. Practical scenarios often motivate an intermediate setting: if we have some set of offline data and may also interact with the environment, how can we best use the offline data to minimize the number of online interactions necessary to learn an $\epsilon$-optimal policy. In this work, we consider this setting, which we call the FineTuneRL setting, for MDPs with linear structure. We characterize the necessary number of online samples needed in this setting given access to some offline dataset, and develop an algorithm, FTPedel, which is provably optimal, up to $H$ factors. We show through an explicit example that combining offline data with online interactions can lead to a provable improvement over either purely offline or purely online RL. Finally, our results illustrate the distinction between verifiable learning, the typical setting considered in online RL, and unverifiable learning, the setting often considered in offline RL, and show that there is a formal separation between these regimes.

This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling, density evaluation, and unbiased ELBO estimation. We then show that MixFlows have MCMC-like convergence guarantees when the flow map is ergodic and measure-preserving, and provide bounds on the accumulation of error for practical implementations where the flow map is approximated. Finally, we develop an implementation of MixFlows based on uncorrected discretized Hamiltonian dynamics combined with deterministic momentum refreshment. Simulated and real data experiments show that MixFlows can provide more reliable posterior approximations than several black-box normalizing flows, as well as samples of comparable quality to those obtained from state-of-the-art MCMC methods.

Gaussian process upper confidence bound (GP-UCB) is a theoretically promising approach for black-box optimization; however, the confidence parameter $\beta$ is considerably large in the theorem and chosen heuristically in practice. Then, randomized GP-UCB (RGP-UCB) uses a randomized confidence parameter, which follows the Gamma distribution, to mitigate the impact of manually specifying $\beta$. This study first generalizes the regret analysis of RGP-UCB to a wider class of distributions, including the Gamma distribution. Furthermore, we propose improved RGP-UCB (IRGP-UCB) based on a two-parameter exponential distribution, which achieves tighter Bayesian regret bounds. IRGP-UCB does not require an increase in the confidence parameter in terms of the number of iterations, which avoids over-exploration in the later iterations. Finally, we demonstrate the effectiveness of IRGP-UCB through extensive experiments.

Overparametrization often helps improve the generalization performance. This paper presents a dual view of overparametrization suggesting that downsampling may also help generalize. Focusing on the proportional regime $m\asymp n \asymp p$, where $m$ represents the sketching size, $n$ is the sample size, and $p$ is the feature dimensionality, we investigate two out-of-sample prediction risks of the sketched ridgeless least square estimator. Our findings challenge conventional beliefs by showing that downsampling does not always harm generalization but can actually improve it in certain cases. We identify the optimal sketching size that minimizes out-of-sample prediction risks and demonstrate that the optimally sketched estimator exhibits stabler risk curves, eliminating the peaks of those for the full-sample estimator. To facilitate practical implementation, we propose an empirical procedure to determine the optimal sketching size. Finally, we extend our analysis to cover central limit theorems and misspecified models. Numerical studies strongly support our theory.

Gradient Descent (GD) is a powerful workhorse of modern machine learning thanks to its scalability and efficiency in high-dimensional spaces. Its ability to find local minimisers is only guaranteed for losses with Lipschitz gradients, where it can be seen as a 'bona-fide' discretisation of an underlying gradient flow. Yet, many ML setups involving overparametrised models do not fall into this problem class, which has motivated research beyond the so-called ''Edge of Stability'' (EoS), where the step-size crosses the admissibility threshold inversely proportional to the Lipschitz constant above. Perhaps surprisingly, GD has been empirically observed to still converge regardless of local instability and oscillatory behavior. The incipient theoretical analysis of this phenomena has mainly focused in the overparametrised regime, where the effect of choosing a large learning rate may be associated to a `Sharpness-Minimisation' implicit regularisation within the manifold of minimisers, under appropriate asymptotic limits. In contrast, in this work we directly examine the conditions for such unstable convergence, focusing on simple, yet representative, learning problems, via analysis of two-step gradient updates. Specifically, we characterize a local condition involving third-order derivatives that guarantees existence and convergence to fixed points of the two-step updates, and leverage such property in a teacher-student setting, under population loss. Finally, starting from Matrix Factorization, we provide observations of period-2 orbit of GD in high-dimensional settings with intuition of its dynamics, along with exploration into more general settings.

This paper presents $\mathrm{E}(n)$ Equivariant Message Passing Simplicial Networks (EMPSNs), a novel approach to learning on geometric graphs and point clouds that is equivariant to rotations, translations, and reflections. EMPSNs can learn high-dimensional simplex features in graphs (e.g. triangles), and use the increase of geometric information of higher-dimensional simplices in an $\mathrm{E}(n)$ equivariant fashion. EMPSNs simultaneously generalize $\mathrm{E}(n)$ Equivariant Graph Neural Networks to a topologically more elaborate counterpart and provide an approach for including geometric information in Message Passing Simplicial Networks, thereby serving as a proof of concept for combining geometric and topological information in graph learning. The results indicate that EMPSNs can leverage the benefits of both approaches, leading to a general increase in performance when compared to either method individually, being on par with state-of-the-art approaches for learning on geometric graphs. Moreover, the results suggest that incorporating geometric information serves as an effective measure against over-smoothing in message passing networks, especially when operating on high-dimensional simplicial structures.

This work studies the estimation of many statistical quantiles under differential privacy. More precisely, given a distribution and access to i.i.d. samples from it, we study the estimation of the inverse of its cumulative distribution function (the quantile function) at specific points. For instance, this task is of key importance in private data generation. We present two different approaches. The first one consists in privately estimating the empirical quantiles of the samples and using this result as an estimator of the quantiles of the distribution. In particular, we study the statistical properties of the recently published algorithm introduced by (Kaplan et al., 2022) that privately estimates the quantiles recursively. The second approach is to use techniques of density estimation in order to uniformly estimate the quantile function on an interval. In particular, we show that there is a tradeoff between the two methods. When we want to estimate many quantiles, it is better to estimate the density rather than estimating the quantile function at specific points.

We address the problem of learning the dynamics of an unknown non-parametric system linking a target and a feature time series. The feature time series is measured on a sparse and irregular grid, while we have access to only a few points of the target time series. Once learned, we can use these dynamics to predict values of the target from the previous values of the feature time series. We frame this task as learning the solution map of a controlled differential equation (CDE). By leveraging the rich theory of signatures, we are able to cast this non-linear problem as a high-dimensional linear regression. We provide an oracle bound on the prediction error which exhibits explicit dependencies on the individual-specific sampling schemes. Our theoretical results are illustrated by simulations which show that our method outperforms existing algorithms for recovering the full time series while being computationally cheap. We conclude by demonstrating its potential on real-world epidemiological data.

A common pipeline in learning-based control is to iteratively estimate a model of system dynamics, and apply a trajectory optimization algorithm - e.g. $\mathtt{iLQR}$ - on the learned model to minimize a target cost. This paper conducts a rigorous analysis of a simplified variant of this strategy for general nonlinear systems. We analyze an algorithm which iterates between estimating local linear models of nonlinear system dynamics and performing $\mathtt{iLQR}$-like policy updates. We demonstrate that this algorithm attains sample complexity polynomial in relevant problem parameters, and, by synthesizing locally stabilizing gains, overcomes exponential dependence in problem horizon. Experimental results validate the performance of our algorithm, and compare to natural deep-learning baselines.

There is an emerging interest in generating robust counterfactual explanations that would remain valid if the model is updated or changed even slightly. Towards finding robust counterfactuals, existing literature often assumes that the original model $m$ and the new model $M$ are bounded in the parameter space, i.e., $\|\text{Params}(M){-}\text{Params}(m)\|{<}\Delta$. However, models can often change significantly in the parameter space with little to no change in their predictions or accuracy on the given dataset. In this work, we introduce a mathematical abstraction termed *naturally-occurring* model change, which allows for arbitrary changes in the parameter space such that the change in predictions on points that lie on the data manifold is limited. Next, we propose a measure -- that we call *Stability* -- to quantify the robustness of counterfactuals to potential model changes for differentiable models, e.g., neural networks. Our main contribution is to show that counterfactuals with sufficiently high value of *Stability* as defined by our measure will remain valid after potential ``naturally-occurring'' model changes with high probability (leveraging concentration bounds for Lipschitz function of independent Gaussians). Since our quantification depends on the local Lipschitz constant around a data point which is not always available, we also examine practical relaxations of our proposed measure and demonstrate experimentally how they can be incorporated to find robust counterfactuals for neural networks that are close, realistic, and remain valid after potential model changes.

In a federated learning (FL) system, distributed clients upload their local models to a central server to aggregate into a global model. Malicious clients may plant backdoors into the global model through uploading poisoned local models, causing images with specific patterns to be misclassified into some target labels. Backdoors planted by current attacks are not durable, and vanish quickly once the attackers stop model poisoning. In this paper, we investigate the connection between the durability of FL backdoors and the relationships between benign images and poisoned images (i.e., the images whose labels are flipped to the target label during local training). Specifically, benign images with the original and the target labels of the poisoned images are found to have key effects on backdoor durability. Consequently, we propose a novel attack, Chameleon, which utilizes contrastive learning to further amplify such effects towards a more durable backdoor. Extensive experiments demonstrate that Chameleon significantly extends the backdoor lifespan over baselines by $1.2\times \sim 4\times$, for a wide range of image datasets, backdoor types, and model architectures.

In symbolic regression, the objective is to find an analytical expression that accurately fits experimental data with the minimal use of mathematical symbols such as operators, variables, and constants. However, the combinatorial space of possible expressions can make it challenging for traditional evolutionary algorithms to find the correct expression in a reasonable amount of time. To address this issue, Neural Symbolic Regression (NSR) algorithms have been developed that can quickly identify patterns in the data and generate analytical expressions. However, these methods, in their current form, lack the capability to incorporate user-defined prior knowledge, which is often required in natural sciences and engineering fields. To overcome this limitation, we propose a novel neural symbolic regression method, named Neural Symbolic Regression with Hypothesis (NSRwH) that enables the explicit incorporation of assumptions about the expected structure of the ground-truth expression into the prediction process. Our experiments demonstrate that the proposed conditioned deep learning model outperforms its unconditioned counterparts in terms of accuracy while also providing control over the predicted expression structure.

In this paper, we study the stochastic linear bandit problem under the additional requirements of differential privacy, robustness and batched observations. In particular, we assume an adversary randomly chooses a constant fraction of the observed rewards in each batch, replacing them with arbitrary numbers. We present differentially private and robust variants of the arm elimination algorithm using logarithmic batch queries under two privacy models and provide regret bounds in both settings. In the first model, every reward in each round is reported by a potentially different client, which reduces to standard local differential privacy (LDP). In the second model, every action is "owned" by a different client, who may aggregate the rewards over multiple queries and privatize the aggregate response instead. To the best of our knowledge, our algorithms are the first simultaneously providing differential privacy and adversarial robustness in the stochastic linear bandits problem.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be $SO(3)$ equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the $SO(3)$ convolutions or tensor products to mathematically equivalent convolutions in $SO(2)$ . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from $O(L^6)$ to $O(L^3)$, where $L$ is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

Variational inference (VI) seeks to approximate a target distribution $\pi$ by an element of a tractable family of distributions. Of key interest in statistics and machine learning is Gaussian VI, which approximates $\pi$ by minimizing the Kullback-Leibler (KL) divergence to $\pi$ over the space of Gaussians. In this work, we develop the (Stochastic) Forward-Backward Gaussian Variational Inference (FB-GVI) algorithm to solve Gaussian VI. Our approach exploits the composite structure of the KL divergence, which can be written as the sum of a smooth term (the potential) and a non-smooth term (the entropy) over the Bures-Wasserstein (BW) space of Gaussians endowed with the Wasserstein distance. For our proposed algorithm, we obtain state-of-the-art convergence guarantees when $\pi$ is log-smooth and log-concave, as well as the first convergence guarantees to first-order stationary solutions when $\pi$ is only log-smooth.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a $2$-competitive deterministic algorithm and a $e/(e-1)$-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an $8$-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

Pretraining a neural network on a large dataset is becoming a cornerstone in machine learning that is within the reach of only a few communities with large-resources. We aim at an ambitious goal of democratizing pretraining. Towards that goal, we train and release a single neural network that can predict high quality ImageNet parameters of other neural networks. By using predicted parameters for initialization we are able to boost training of diverse ImageNet models available in PyTorch. When transferred to other datasets, models initialized with predicted parameters also converge faster and reach competitive final performance.

Multimodal learning is defined as learning over multiple heterogeneous input modalities such as video, audio, and text. In this work, we are concerned with understanding how models behave as the type of modalities differ between training and deployment, a situation that naturally arises in many applications of multimodal learning to hardware platforms. We present a multimodal robustness framework to provide a systematic analysis of common multimodal representation learning methods. Further, we identify robustness short-comings of these approaches and propose two intervention techniques leading to $1.5\times$-$4\times$ robustness improvements on three datasets, AudioSet, Kinetics-400 and ImageNet-Captions. Finally, we demonstrate that these interventions better utilize additional modalities, if present, to achieve competitive results of $44.2$ mAP on AudioSet 20K.

Sampling approaches like Markov chain Monte Carlo were once popular for combinatorial optimization, but the inefficiency of classical methods and the need for problem-specific designs curtailed ongoing development. Recent work has favored data-driven approaches that mitigate the need for hand-craft heuristics, but these are often not usable as out-of-the-box solvers due to dependence on in-distribution training and limited scalability to large instances. In this paper, we revisit the idea of using sampling for combinatorial optimization, motivated by the significant recent advances of gradient-based discrete MCMC and new techniques for parallel neighborhood exploration on accelerators. Remarkably, we find that modern sampling strategies can leverage landscape information to provide general-purpose solvers that require no training and yet are competitive with state of the art combinatorial solvers. In particular, experiments on cover vertex selection, graph partition and routing demonstrate better speed-quality trade-offs over current learning based approaches, and sometimes even superior performance to commercial solvers and specialized algorithms.

We study nonparametric density estimation in non-stationary drift settings. Given a sequence of independent samples taken from a distribution that gradually changes in time, the goal is to compute the best estimate for the current distribution. We prove tight minimax risk bounds for both discrete and continuous smooth densities, where the minimum is over all possible estimates and the maximum is over all possible distributions that satisfy the drift constraints. Our technique handles a broad class of drift models and generalizes previous results on agnostic learning under drift.

This paper studies the multi-agent performative prediction (Multi-PP) games over multiplex networks. We consider a distributed learning setting where agents partially cooperate on an agent network, while during learning, the data samples drawn depend on the prediction models of the agent itself and neighboring agents on a population network. The dynamics of Multi-PP games is hence affected by the interplay between both networks. This paper concentrates on this Multi-PP game with the following contributions. Firstly, we analyze sufficient conditions for the existence of the performative stable equilibrium (PSE) and Nash equilibrium (NE) of the Multi-PP games. Secondly, we analyze the changes to the equilibrium induced by perturbed data distributions, and derive the closed-form solutions where the network topologies are explicit. Our results connect the existence of PSE/NE with strengths of agents' cooperation, and the changes of equilibrium solutions across agents with their node centrality, etc. Lastly, we show that a stochastic gradient descent (SGD) based distributed learning procedure finds the PSE under the said sufficient condition. Numerical illustrations on the network effects in Multi-PP games corroborate our findings.

In order for agents in multi-agent systems (MAS) to be safe, they need to take into account the risks posed by the actions of other agents. However, the dominant paradigm in game theory (GT) assumes that agents are not affected by risk from other agents and only strive to maximise their expected utility. For example, in hybrid human-AI driving systems, it is necessary to limit large deviations in reward resulting from car crashes. Although there are equilibrium concepts in game theory that take into account risk aversion, they either assume that agents are risk-neutral with respect to the uncertainty caused by the actions of other agents, or they are not guaranteed to exist. We introduce a new GT-based Risk-Averse Equilibrium (RAE) that always produces a solution that minimises the potential variance in reward accounting for the strategy of other agents. Theoretically and empirically, we show RAE shares many properties with a Nash Equilibrium (NE), establishing convergence properties and generalising to risk-dominant NE in certain cases. To tackle large-scale problems, we extend RAE to the PSRO multi-agent reinforcement learning (MARL) framework. We empirically demonstrate the minimum reward variance benefits of RAE in matrix games with high-risk outcomes. Results on MARL experiments show RAE generalises to risk-dominant NE in a trust dilemma game and that it reduces instances of crashing by 7x in an autonomous driving setting versus the best performing baseline.

Sign Stochastic Gradient Descent (signSGD) is a communication-efficient stochastic algorithm that only uses the sign information of the stochastic gradient to update the model's weights. However, the existing convergence theory of signSGD either requires increasing batch sizes during training or assumes the gradient noise is symmetric and unimodal. Error feedback has been used to guarantee the convergence of signSGD under weaker assumptions at the cost of communication overhead. This paper revisits the convergence of signSGD and proves that momentum can remedy signSGD under weaker assumptions than previous techniques; in particular, our convergence theory does not require the assumption of bounded stochastic gradient or increased batch size. Our results resonate with echoes of previous empirical results where, unlike signSGD, signSGD with momentum maintains good performance even with small batch sizes. Another new result is that signSGD with momentum can achieve an improved convergence rate when the objective function is second-order smooth. We further extend our theory to signSGD with major vote and federated learning.

This work introduces DADAO: the first decentralized, accelerated, asynchronous, primal, first-order algorithm to minimize a sum of $L$-smooth and $\mu$-strongly convex functions distributed over a given network of size $n$. Our key insight is based on modeling the local gradient updates and gossip communication procedures with separate independent Poisson Point Processes. This allows us to decouple the computation and communication steps, which can be run in parallel, while making the whole approach completely asynchronous. This leads to communication acceleration compared to synchronous approaches. Our new method employs primal gradients and does not use a multi-consensus inner loop nor other ad-hoc mechanisms such as Error Feedback, Gradient Tracking, or a Proximal operator. By relating the inverse of the smallest positive eigenvalue of the Laplacian matrix $\chi_1$ and the maximal resistance $\chi_2\leq \chi_1$ of the graph to a sufficient minimal communication rate between the nodes of the network, we show that our algorithm requires $\mathcal{O}(n\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ local gradients and only $\mathcal{O}(n\sqrt{\chi_1\chi_2}\sqrt{\frac{L}{\mu}}\log(\frac{1}{\epsilon}))$ communications to reach a precision $\epsilon$, up to logarithmic terms. Thus, we simultaneously obtain an accelerated rate for both computations and communications, leading to an improvement over state-of-the-art works, our simulations further validating the strength of our relatively unconstrained method.

We study the autonomous exploration (AX) problem proposed by Lim & Auer (2012). In this setting, the objective is to discover a set of $\epsilon$-optimal policies reaching a set $\mathcal{S}\_L^{\rightarrow}$ of incrementally $L$-controllable states. We introduce a novel layered decomposition of the set of incrementally $L$-controllable states that is based on the iterative application of a state-expansion operator. We leverage these results to design Layered Autonomous Exploration (LAE), a novel algorithm for AX that attains a sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}\_{L(1+\epsilon)}\Gamma\_{L(1+\epsilon)} A \ln^{12}(S^{\rightarrow}\_{L(1+\epsilon)})/\epsilon^2)$, where $S^{\rightarrow}\_{L(1+\epsilon)}$ is the number of states that are incrementally $L(1+\epsilon)$-controllable, $A$ is the number of actions, and $\Gamma\_{L(1+\epsilon)}$ is the branching factor of the transitions over such states. LAE improves over the algorithm of Tarbouriech et al. (2020a) by a factor of $L^2$ and it is the first algorithm for AX that works in a countably-infinite state space. Moreover, we show that, under a certain identifiability assumption, LAE achieves minimax-optimal sample complexity of $\tilde{\mathcal{O}}(LS^{\rightarrow}\_{L}A\ln^{12}(S^{\rightarrow}\_{L})/\epsilon^2)$, outperforming existing algorithms and matching for the first time the lower bound proved by Cai et al. (2022) up to logarithmic factors.

We provide a full characterisation of all of the possible alternating group ($A_n$) equivariant neural networks whose layers are some tensor power of $\mathbb{R}^{n}$. In particular, we find a basis of matrices for the learnable, linear, $A_n$--equivariant layer functions between such tensor power spaces in the standard basis of $\mathbb{R}^{n}$. We also describe how our approach generalises to the construction of neural networks that are equivariant to local symmetries.

Likelihood-free inference methods typically make use of a distance between simulated and real data. A common example is the maximum mean discrepancy (MMD), which has previously been used for approximate Bayesian computation, minimum distance estimation, generalised Bayesian inference, and within the nonparametric learning framework. The MMD is commonly estimated at a root-$m$ rate, where $m$ is the number of simulated samples. This can lead to significant computational challenges since a large $m$ is required to obtain an accurate estimate, which is crucial for parameter estimation. In this paper, we propose a novel estimator for the MMD with significantly improved sample complexity. The estimator is particularly well suited for computationally expensive smooth simulators with low- to mid-dimensional inputs. This claim is supported through both theoretical results and an extensive simulation study on benchmark simulators.

Semi-supervised learning is a powerful technique for leveraging unlabeled data to improve machine learning models, but it can be affected by the presence of ``informative" labels, which occur when some classes are more likely to be labeled than others. In the missing data literature, such labels are called missing not at random. In this paper, we propose a novel approach to address this issue by estimating the missing-data mechanism and using inverse propensity weighting to debias any SSL algorithm, including those using data augmentation. We also propose a likelihood ratio test to assess whether or not labels are indeed informative. Finally, we demonstrate the performance of the proposed methods on different datasets, in particular on two medical datasets for which we design pseudo-realistic missing data scenarios.

Multivariate time series data for real-world applications typically contain a significant amount of missing values. The dominant approach for classification with such missing values is to impute them heuristically with specific values (zero, mean, values of adjacent time-steps) or learnable parameters. However, these simple strategies do not take the data generative process into account, and more importantly, do not effectively capture the uncertainty in prediction due to the multiple possibilities for the missing values. In this paper, we propose a novel probabilistic framework for classification with multivariate time series data with missing values. Our model consists of two parts; a deep generative model for missing value imputation and a classifier. Extending the existing deep generative models to better capture structures of time-series data, our deep generative model part is trained to impute the missing values in multiple plausible ways, effectively modeling the uncertainty of the imputation. The classifier part takes the time series data along with the imputed missing values and classifies signals, and is trained to capture the predictive uncertainty due to the multiple possibilities of imputations. Importantly, we show that naïvely combining the generative model and the classifier could result in trivial solutions where the generative model does not produce meaningful imputations. To resolve this, we present a novel regularization technique that can promote the model to produce useful imputation values that help classification. Through extensive experiments on real-world time series data with missing values, we demonstrate the effectiveness of our method.

ML model design either starts with an interpretable model or a Blackbox and explains it post hoc. Blackbox models are flexible but difficult to explain, while interpretable models are inherently explainable. Yet, interpretable models require extensive ML knowledge and tend to be less flexible, potentially underperforming than their Blackbox equivalents. This paper aims to blur the distinction between a post hoc explanation of a Blackbox and constructing interpretable models. Beginning with a Blackbox, we iteratively carve out a mixture of interpretable models and a residual network. The interpretable models identify a subset of samples and explain them using First Order Logic (FOL), providing basic reasoning on concepts from the Blackbox. We route the remaining samples through a flexible residual. We repeat the method on the residual network until all the interpretable models explain the desired proportion of data. Our extensive experiments show that our route, interpret, and repeat approach (1) identifies a richer diverse set of instance-specific concepts with high concept completeness via interpretable models by specializing in various subsets of data without compromising in performance, (2) identifies the relatively ``harder'' samples to explain via residuals, (3) outperforms the interpretable by-design models by significant margins during test-time interventions, (4) can be used to fix the shortcut learned by the original Blackbox.

A critical element of learning with noisy labels is noisy label detection. Notably, numerous previous works assume that no source of labels can be clean in a noisy label detection context. In this work, we relax this assumption and assume that a small subset of the training data is clean, which enables substantial noisy label detection performance gains. Specifically, we propose a novel framework that leverages clean data by framing the problem of noisy label detection with clean data as a multiple hypothesis testing problem. Moreover, we propose BHN, a simple yet effective approach for noisy label detection that integrates the Benjamini-Hochberg (BH) procedure into deep neural networks. BHN achieves $\textit{state-of-the-art}$ performance and outperforms baselines by $\textbf{28.48}$% in terms of false discovery rate (FDR) and by $\textbf{18.99}$% in terms of F1 on CIFAR-10. Extensive ablation studies further demonstrate the superiority of BHN. Our code is available at https://github.com/ChenglinYu/BHN.

Large language models can perform various reasoning tasks by using chain-of-thought prompting, which guides them to find answers through step-by-step demonstrations. However, the quality of the prompts depends on the demonstrations given to the models, and creating many of them by hand is costly. We introduce Synthetic prompting, a method that leverages a few handcrafted examples to prompt the model to generate more examples by itself, and selects effective demonstrations to elicit better reasoning. Our method alternates between a backward and forward process to generate new examples. The backward process generates a question that match a sampled reasoning chain, so that the question is solvable and clear. The forward process produces a more detailed reasoning chain for the question, improving the quality of the example. We evaluate our method on numerical, symbolic, and algorithmic reasoning tasks, and show that it outperforms existing prompting techniques.

While Convolutional Neural Networks (CNNs) have long been investigated and applied, as well as theorized, we aim to provide a slightly different perspective into their nature --- through the perspective of their Hessian maps. The reason is that the loss Hessian captures the pairwise interaction of parameters and therefore forms a natural ground to probe how the architectural aspects of CNNs get manifested in their structure and properties. We develop a framework relying on Toeplitz representation of CNNs, and then utilize it to reveal the Hessian structure and, in particular, its rank. We prove tight upper bounds (with linear activations), which closely follow the empirical trend of the Hessian rank and in practice also hold for more general settings. Overall, our work generalizes and further establishes the key insight that the Hessian rank grows as the square root of the number of parameters, even in CNNs.

Value decomposition is widely used in cooperative multi-agent reinforcement learning, however, its implicit credit assignment mechanism is not yet fully understood due to black-box networks. In this work, we study an interpretable value decomposition framework via the family of generalized additive models. We present a novel method, named Neural Attention Additive Q-learning (N$\text{A}^\text{2}$Q), providing inherent intelligibility of collaboration behavior. N$\text{A}^\text{2}$Q can explicitly factorize the optimal joint policy induced by enriching shape functions to model all possible coalition of agents into individual policies. Moreover, we construct the identity semantics to promote estimating credits together with the global state and individual value functions, where local semantic masks help us diagnose whether each agent captures the relevant-task information. Extensive experiments show that N$\text{A}^\text{2}$Q consistently achieves superior performance compared to different state-of-the-art methods on all challenging tasks, while yielding human-like interpretability.

Current self-supervised learning algorithms are often modality-specific and require large amounts of computational resources. To address these issues, we increase the training efficiency of data2vec, a learning objective that generalizes across several modalities. We do not encode masked tokens, use a fast convolutional decoder and amortize the effort to build teacher representations. data2vec 2.0 benefits from the rich contextualized target representations introduced in data2vec which enable a fast self-supervised learner. Experiments on ImageNet-1K image classification show that data2vec 2.0 matches the accuracy of Masked Autoencoders in 16.4x lower pre-training time, on Librispeech speech recognition it performs as well as wav2vec 2.0 in 10.6x less time, and on GLUE natural language understanding it matches a retrained RoBERTa model in half the time. Trading some speed for accuracy results in ImageNet-1K top-1 accuracy of 86.8% with a ViT-L model trained for 150 epochs.

The number of parameters in large transformers has been observed to grow exponentially. Despite notable performance improvements, concerns have been raised that such a growing model size will run out of data in the near future. As manifested in the neural scaling law, modern learning backbones are not data-efficient. To maintain the utility of the model capacity, training data should be increased proportionally. In this paper, we study the neural scaling law under the previously overlooked data scarcity regime, focusing on the more challenging situation where we need to train a gigantic model with a disproportionately limited supply of available training data. We find that the existing power laws underestimate the data inefficiency of large transformers. Their performance will drop significantly if the training set is insufficient. Fortunately, we discover another blessing - such a data-inefficient scaling law can be restored through a model reusing approach that warm-starts the training of a large model by initializing it using smaller models. Our empirical study shows that model reusing can effectively reproduce the power law under the data scarcity regime. When progressively applying model reusing to expand the model size, we also observe consistent performance improvement in large transformers. We release our code at: https://github.com/VITA-Group/Data-Efficient-Scaling.

Negative and positive curvatures affect optimization in different ways. However, a lot of existing optimization theories are based on the Lipschitz smoothness assumption, which cannot differentiate between the two. In this paper, we propose to use two separate assumptions for positive and negative curvatures, so that we can study the different implications of the two. We analyze the Lookahead and Local SGD methods as concrete examples. Both of them require multiple copies of model parameters and communication among them for every certain period of time in order to prevent divergence. We show that the minimum communication frequency is inversely proportional to the negative curvature, and when the negative curvature becomes zero, we recover the existing theory results for convex optimization. Finally, both experimentally and theoretically, we demonstrate that modern neural networks have highly unbalanced positive/negative curvatures. Thus, an analysis based on separate positive and negative curvatures is more pertinent.

Sketching is one of the most fundamental tools in large-scale machine learning. It enables runtime and memory saving via randomly compressing the original large problem into lower dimensions. In this paper, we propose a novel sketching scheme for the first order method in large-scale distributed learning setting, such that the communication costs between distributed agents are saved while the convergence of the algorithms is still guaranteed. Given gradient information in a high dimension $d$, the agent passes the compressed information processed by a sketching matrix $R\in \mathbb{R}^{s\times d}$ with $s\ll d$, and the receiver de-compressed via the de-sketching matrix $R^\top$ to ``recover'' the information in original dimension. Using such a framework, we develop algorithms for federated learning with lower communication costs. However, such random sketching does not protect the privacy of local data directly. We show that the gradient leakage problem still exists after applying the sketching technique by presenting a specific gradient attack method. As a remedy, we prove rigorously that the algorithm will be differentially private by adding additional random noises in gradient information, which results in a both communication-efficient and differentially private first order approach for federated learning tasks. Our sketching scheme can be further generalized to other learning settings and might be of independent interest itself.

This paper proposes an online, provably robust, and scalable Bayesian approach for changepoint detection. The resulting algorithm has key advantages over previous work: it provides provable robustness by leveraging the generalised Bayesian perspective, and also addresses the scalability issues of previous attempts. Specifically, the proposed generalised Bayesian formalism leads to conjugate posteriors whose parameters are available in closed form by leveraging diffusion score matching. The resulting algorithm is exact, can be updated through simple algebra, and is more than 10 times faster than its closest competitor.

A fundamental problem in data management is to find the elements in an array that match a query. Recently, learned indexes are being extensively used to solve this problem, where they learn a model to predict the location of the items in the array. They are empirically shown to outperform non-learned methods (e.g., B-trees or binary search that answer queries in $O(\log n)$ time) by orders of magnitude. However, success of learned indexes has not been theoretically justified. Only existing attempt shows the same query time of $O(\log n)$, but with a constant factor improvement in space complexity over non-learned methods, under some assumptions on data distribution. In this paper, we significantly strengthen this result, showing that under mild assumptions on data distribution, and the same space complexity as non-learned methods, learned indexes can answer queries in $O(\log\log n)$ expected query time. We also show that allowing for slightly larger but still near-linear space overhead, a learned index can achieve $O(1)$ expected query time. Our results theoretically prove learned indexes are orders of magnitude faster than non-learned methods, theoretically grounding their empirical success.

In this paper, we establish efficient and uncoupled learning dynamics so that, when employed by all players in multiplayer perfect-recall imperfect-information extensive-form games, the trigger regret of each player grows as $O(\log T)$ after $T$ repetitions of play. This improves exponentially over the prior best known trigger-regret bound of $O(T^{1/4})$, and settles a recent open question by Bai et al. (2022). As an immediate consequence, we guarantee convergence to the set of extensive-form correlated equilibria and coarse correlated equilibria at a near-optimal rate of $\frac{\log T}{T}$. Building on prior work, at the heart of our construction lies a more general result regarding fixed points deriving from rational functions with polynomial degree, a property that we establish for the fixed points of (coarse) trigger deviation functions. Moreover, our construction leverages a refined regret circuit for the convex hull, which---unlike prior guarantees---preserves the RVU property introduced by Syrgkanis et al. (NIPS, 2015); this observation has an independent interest in establishing near-optimal regret under learning dynamics based on a CFR-type decomposition of the regret.

Population Based Training (PBT) is an efficient hyperparameter optimization algorithm. PBT is a single-objective algorithm, but many real-world hyperparameter optimization problems involve two or more conflicting objectives. In this work, we therefore introduce a multi-objective version of PBT, MO-PBT. Our experiments on diverse multi-objective hyperparameter optimization problems (Precision/Recall, Accuracy/Fairness, Accuracy/Adversarial Robustness) show that MO-PBT outperforms random search, single-objective PBT, and the state-of-the-art multi-objective hyperparameter optimization algorithm MO-ASHA.

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high dimensions: the mean model, the Gaussian graphical model, and the linear regression model. In all three cases, we derive non-asymptotic bounds for the accuracy of the DCDP change point estimators. We demonstrate that the DCDP procedures consistently estimate the change points with sharp, and in some cases, optimal rates while incurring significantly smaller computational costs than the best available algorithms. Our findings are supported by extensive numerical experiments on both synthetic and real data.

The first contribution of this paper is the introduction of a new performance measure of a RL algorithm that is more discriminating than the regret, that we call the *regret of exploration* that measures the asymptotic cost of exploration. The second contribution is a new *performance test* (PT) to end episodes in RL optimistic algorithms. This test is based on the performance of the current policy with respect to the best policy over the current confidence set. This is in contrast with all existing RL algorithms whose episode lengths are only based on the number of visits to the states. This modification does not harm the regret and brings an additional property. We show that while all current episodic RL algorithms have a linear regret of exploration, our method has a $O(\log{T})$ regret of exploration for non-degenerate deterministic MDPs.

In this paper, we present efficient quantum algorithms that are exponentially faster than classical algorithms for solving the quantum optimal control problem. This problem involves finding the control variable that maximizes a physical quantity at time $T$, where the system is governed by a time-dependent Schrödinger equation. This type of control problem also has an intricate relation with machine learning. Our algorithms are based on a time-dependent Hamiltonian simulation method and a fast gradient-estimation algorithm. We also provide a comprehensive error analysis to quantify the total error from various steps, such as the finite-dimensional representation of the control function, the discretization of the Schrödinger equation, the numerical quadrature, and optimization. Our quantum algorithms require fault-tolerant quantum computers.

In this paper, we study the role of feedback in online learning with switching costs. It has been shown that the minimax regret is $\widetilde{\Theta}(T^{2/3})$ under bandit feedback and improves to $\widetilde{\Theta}(\sqrt{T})$ under full-information feedback, where $T$ is the length of the time horizon. However, it remains largely unknown how the amount and type of feedback generally impact regret. To this end, we first consider the setting of bandit learning with extra observations; that is, in addition to the typical bandit feedback, the learner can freely make a total of $B_{\mathrm{ex}}$ *extra observations*. We fully characterize the minimax regret in this setting, which exhibits an interesting *phase-transition phenomenon*: when $B_{\mathrm{ex}} = O(T^{2/3})$, the regret remains $\widetilde{\Theta}(T^{2/3})$, but when $B_{\mathrm{ex}} = \Omega(T^{2/3})$, it becomes $\widetilde{\Theta}(T/\sqrt{B_{\mathrm{ex}}})$, which improves as the budget $B_{\mathrm{ex}}$ increases. To design algorithms that can achieve the minimax regret, it is instructive to consider a more general setting where the learner has a budget of $B$ *total* observations. We fully characterize the minimax regret in this setting as well and show that it is $\widetilde{\Theta}(T/\sqrt{B})$, which scales smoothly with the total budget $B$. Furthermore, we propose a generic algorithmic framework, which enables us to design different learning algorithms that can achieve matching upper bounds for both settings based on the amount and type of feedback. One interesting finding is that while bandit feedback can still guarantee optimal regret when the budget is relatively limited, it no longer suffices to achieve optimal regret when the budget is relatively large.

In recent years, decentralized bilevel optimization has gained significant attention thanks to its versatility in modeling a wide range of multi-agent learning problems, such as multi-agent reinforcement learning and multi-agent meta-learning. However, one unexplored and fundamental problem in this area is how to solve decentralized stochastic bilevel optimization problems with **domain constraints** while achieving low sample and communication complexities. This problem often arises from multi-agent learning problems with safety constraints. As shown in this paper, constrained decentralized bilevel optimization is far more challenging than its unconstrained counterpart due to the complex coupling structure, which necessitates new algorithm design and analysis techniques. Toward this end, we investigate a class of constrained decentralized bilevel optimization problems, where multiple agents collectively solve a nonconvex-strongly-convex bilevel problem with constraints in the upper-level variables. We propose an algorithm called Prometheus (proximal tracked stochastic recursive estimator) that achieves the first $\mathcal{O}(\epsilon^{-1})$ results in both sample and communication complexities for constrained decentralized bilevel optimization, where $\epsilon>0$ is a desired stationarity error. Collectively, the results in this work contribute to a theoretical foundation for low sample- and communication-complexity constrained decentralized bilevel learning.

Prediction of a $\textbf{varying number}$ of $\textbf{ordered clusters}$ from sets of $\textbf{any cardinality}$ is a challenging task for neural networks, combining elements of set representation, clustering and learning to order. This task arises in many diverse areas, ranging from medical triage and early discharge, through machine part management and multi-channel signal analysis for petroleum exploration to product catalog structure prediction. This paper focuses on that last area, which exemplifies a number of challenges inherent to adaptive ordered clustering, referred to further as the eponymous $\textit{Catalog Problem}$. These include learning variable cluster constraints, exhibiting relational reasoning and managing combinatorial complexity. Despite progress in both neural clustering and set-to-sequence methods, no joint, fully differentiable model exists to-date. We develop such a modular architecture, referred to further as Neural Ordered Clusters (NOC), enhance it with a specific mechanism for learning cluster-level cardinality constraints, and provide a robust comparison of its performance in relation to alternative models. We test our method on three datasets, including synthetic catalog structures and PROCAT, a dataset of real-world catalogs consisting of over 1.5M products, achieving state-of-the-art results on a new, more challenging formulation of the underlying problem, which has not been addressed before. Additionally, we examine the network's ability to learn higher-order interactions.

The generalization performance of machine learning methods depends heavily on the quality of data representation. However, existing researches rarely consider representation learning from the perspective of generalization error. In this paper, we prove that generalization error of representation learning function can be estimated effectively by solving two convex optimization problems. Based on it, we propose a general representation learning framework. And then, we apply the proposed framework to two most commonly used nonlinear mapping methods, i.e., kernel based method and deep neural network (DNN), and thus design a kernel selection method and a DNN boosting framework, correspondingly. Finally, extensive experiments verify the effectiveness of the proposed methods.

Graph Neural Networks (GNNs) have displayed considerable promise in graph representation learning across various applications. The core learning process requires the initialization of model weight matrices within each GNN layer, which is typically accomplished via classic initialization methods such as Xavier initialization. However, these methods were originally motivated to stabilize the variance of hidden embeddings and gradients across layers of Feedforward Neural Networks (FNNs) and Convolutional Neural Networks (CNNs) to avoid vanishing gradients and maintain steady information flow. In contrast, within the GNN context classical initializations disregard the impact of the input graph structure and message passing on variance. In this paper, we analyze the variance of forward and backward propagation across GNN layers and show that the variance instability of GNN initializations comes from the combined effect of the activation function, hidden dimension, graph structure and message passing. To better account for these influence factors, we propose a new initialization method for Variance Instability Reduction within GNN Optimization (Virgo), which naturally tends to equate forward and backward variances across successive layers. We conduct comprehensive experiments on 15 datasets to show that Virgo can lead to superior model performance and more stable variance at initialization on node classification, link prediction and graph classification tasks.

We introduce EM-Network, a novel self-distillation approach that effectively leverages target information for supervised sequence-to-sequence (seq2seq) learning. In contrast to conventional methods, it is trained with oracle guidance, which is derived from the target sequence. Since the oracle guidance compactly represents the target-side context that can assist the sequence model in solving the task, the EM-Network achieves a better prediction compared to using only the source input. To allow the sequence model to inherit the promising capability of the EM-Network, we propose a new self-distillation strategy, where the original sequence model can benefit from the knowledge of the EM-Network in a one-stage manner. We conduct comprehensive experiments on two types of seq2seq models: connectionist temporal classification (CTC) for speech recognition and attention-based encoder-decoder (AED) for machine translation. Experimental results demonstrate that the EM-Network significantly advances the current state-of-the-art approaches, improving over the best prior work on speech recognition and establishing state-of-the-art performance on WMT'14 and IWSLT'14.

We present a fully Bayesian autoencoder model that treats both local latent variables and global decoder parameters in a Bayesian fashion. This approach allows for flexible priors and posterior approximations while keeping the inference costs low. To achieve this, we introduce an amortized MCMC approach by utilizing an implicit stochastic network to learn sampling from the posterior over local latent variables. Furthermore, we extend the model by incorporating a Sparse Gaussian Process prior over the latent space, allowing for a fully Bayesian treatment of inducing points and kernel hyperparameters and leading to improved scalability. Additionally, we enable Deep Gaussian Process priors on the latent space and the handling of missing data. We evaluate our model on a range of experiments focusing on dynamic representation learning and generative modeling, demonstrating the strong performance of our approach in comparison to existing methods that combine Gaussian Processes and autoencoders.

Multi-task learning has the potential to improve generalization by maximizing positive transfer between tasks while reducing task interference. Fully achieving this potential is hindered by manually designed architectures that remain static throughout training. On the contrary, learning in the brain occurs through structural changes that are in tandem with changes in synaptic strength. Thus, we propose Multi-Task Structural Learning (MTSL) that simultaneously learns the multi-task architecture and its parameters. MTSL begins with an identical single-task network for each task and alternates between a task-learning phase and a structural-learning phase. In the task learning phase, each network specializes in the corresponding task. In each of the structural learning phases, starting from the earliest layer, locally similar task layers first transfer their knowledge to a newly created group layer before being removed. MTSL then uses the group layer in place of the corresponding removed task layers and moves on to the next layers. Our empirical results show that MTSL achieves competitive generalization with various baselines and improves robustness to out-of-distribution data.

Providing generalization guarantees for modern neural networks has been a crucial task in statistical learning. Recently, several studies have attempted to analyze the generalization error in such settings by using tools from fractal geometry. While these works have successfully introduced new mathematical tools to apprehend generalization, they heavily rely on a Lipschitz continuity assumption, which in general does not hold for neural networks and might make the bounds vacuous. In this work, we address this issue and prove fractal geometry-based generalization bounds without requiring any Lipschitz assumption. To achieve this goal, we build up on a classical covering argument in learning theory and introduce a data-dependent fractal dimension. Despite introducing a significant amount of technical complications, this new notion lets us control the generalization error (over either fixed or random hypothesis spaces) along with certain mutual information (MI) terms. To provide a clearer interpretation to the newly introduced MI terms, as a next step, we introduce a notion of `geometric stability' and link our bounds to the prior art. Finally, we make a rigorous connection between the proposed data-dependent dimension and topological data analysis tools, which then enables us to compute the dimension in a numerically efficient way. We support our theory with experiments conducted on various settings.

Graph Neural Networks (GNNs) are limited in their propagation operators. In many cases, these operators often contain non-negative elements only and are shared across channels, limiting the expressiveness of GNNs. Moreover, some GNNs suffer from over-smoothing, limiting their depth. On the other hand, Convolutional Neural Networks (CNNs) can learn diverse propagation filters, and phenomena like over-smoothing are typically not apparent in CNNs. In this paper, we bridge these gaps by incorporating trainable channel-wise weighting factors $\omega$ to learn and mix multiple smoothing and sharpening propagation operators at each layer. Our generic method is called $\omega$GNN, and is easy to implement. We study two variants: $\omega$GCN and $\omega$GAT. For $\omega$GCN, we theoretically analyse its behaviour and the impact of $\omega$ on the obtained node features. Our experiments confirm these findings, demonstrating and explaining how both variants do not over-smooth. Additionally, we experiment with 15 real-world datasets on node- and graph-classification tasks, where our $\omega$GCN and $\omega$GAT perform on par with state-of-the-art methods.

Transformer has achieved remarkable success in language, image, and speech processing. Recently, various efficient attention architectures have been proposed to improve transformer's efficiency while largely preserving its efficacy, especially in modeling long sequences. A widely-used benchmark to test these efficient methods' capability on long-range modeling is Long Range Arena (LRA). However, LRA only focuses on the standard bidirectional (or noncausal) self attention, and completely ignores cross attentions and unidirectional (or causal) attentions, which are equally important to downstream applications. In this paper, we propose Comprehensive Attention Benchmark (CAB) under a fine-grained attention taxonomy with four distinguishable attention patterns, namely, noncausal self, causal self, noncausal cross, and causal cross attentions. CAB collects seven real-world tasks from different research areas to evaluate efficient attentions under the four attention patterns. Among these tasks, CAB validates efficient attentions in eight backbone networks to show their generalization across neural architectures. We conduct exhaustive experiments to benchmark the performances of nine widely-used efficient attention architectures designed with different philosophies on CAB. Extensive experimental results also shed light on the fundamental problems of efficient attentions, such as efficiency length against vanilla attention, performance consistency across attention patterns, the benefit of attention mechanisms, and interpolation/extrapolation on long-context language modeling.

Understanding how convolutional neural networks (CNNs) can efficiently learn high-dimensional functions remains a fundamental challenge. A popular belief is that these models harness the local and hierarchical structure of natural data such as images. Yet, we lack a quantitative understanding of how such structure affects performance, e.g., the rate of decay of the generalisation error with the number of training samples. In this paper, we study infinitely-wide deep CNNs in the kernel regime. First, we show that the spectrum of the corresponding kernel inherits the hierarchical structure of the network, and we characterise its asymptotics. Then, we use this result together with generalisation bounds to prove that deep CNNs adapt to the spatial scale of the target function. In particular, we find that if the target function depends on low-dimensional subsets of adjacent input variables, then the decay of the error is controlled by the effective dimensionality of these subsets. Conversely, if the target function depends on the full set of input variables, then the error decay is controlled by the input dimension. We conclude by computing the generalisation error of a deep CNN trained on the output of another deep CNN with randomly-initialised parameters. Interestingly, we find that, despite their hierarchical structure, the functions generated by infinitely-wide deep CNNs are too rich to be efficiently learnable in high dimension.