Recurrent neural networks (RNNs) are a popular choice for modeling sequential data. Modern RNN architectures assume constant time-intervals between observations. However, in many datasets (e.g. medical records) observation times are irregular and can carry important information. To address this challenge, we propose continuous recurrent units (CRUs) – a neural architecture that can naturally handle irregular intervals between observations. The CRU assumes a hidden state, which evolves according to a linear stochastic differential equation and is integrated into an encoder-decoder framework. The recursive computations of the CRU can be derived using the continuous-discrete Kalman filter and are in closed form. The resulting recurrent architecture has temporal continuity between hidden states and a gating mechanism that can optimally integrate noisy observations. We derive an efficient parameterization scheme for the CRU that leads to a fast implementation f-CRU. We empirically study the CRU on a number of challenging datasets and find that it can interpolate irregular time series better than methods based on neural ordinary differential equations.

The estimation of time-varying quantities is a fundamental component of decision making in fields such as healthcare and finance. However, the practical utility of such estimates is limited by how accurately they quantify predictive uncertainty. In this work, we address the problem of estimating the joint predictive distribution of high-dimensional multivariate time series. We propose a versatile method, based on the transformer architecture, that estimates joint distributions using an attention-based decoder that provably learns to mimic the properties of non-parametric copulas. The resulting model has several desirable properties: it can scale to hundreds of time series, supports both forecasting and interpolation, can handle unaligned and non-uniformly sampled data, and can seamlessly adapt to missing data during training. We demonstrate these properties empirically and show that our model produces state-of-the-art predictions on multiple real-world datasets.

Recently, certifiable robust training methods via bound propagation have been proposed for training neural networks with certifiable robustness guarantees. However, no neural architectures with regular convolution and linear layers perform better in the certifiable training than the plain CNNs, since the output bounds for the deep explicit models increase quickly as their depth increases. And such a phenomenon significantly hinders certifiable training. Meanwhile, the Deep Equilibrium Model~(DEQ) is more representative and robust due to their equivalent infinite depth and controllable global Lipschitz. But no work has been proposed to explore whether DEQ can show advantages in certified training. In this work, we aim to tackle the problem of DEQ's certified training. To obtain the output bound based on the bound propagation scheme in the implicit model, we first involve the adjoint DEQ for bound approximation. Furthermore, we also use the weight orthogonalization method and other tricks specified for DEQ to stabilize the certifiable training. With our approach, we can obtain the certifiable DEQ called CerDEQ. Our CerDEQ can achieve state-of-the-art performance compared with models using regular convolution and linear layers on $\ell_\infty$ tasks with $\epsilon=8/255$: $64.72\%$ certified error for CIFAR-$10$ and $94.45\%$ certified error for Tiny ImageNet.

Incorporating symmetry as an inductive bias into neural network architecture has led to improvements in generalization, data efficiency, and physical consistency in dynamics modeling. Methods such as CNNs or equivariant neural networks use weight tying to enforce symmetries such as shift invariance or rotational equivariance. However, despite the fact that physical laws obey many symmetries, real-world dynamical data rarely conforms to strict mathematical symmetry either due to noisy or incomplete data or to symmetry breaking features in the underlying dynamical system. We explore approximately equivariant networks which are biased towards preserving symmetry but are not strictly constrained to do so. By relaxing equivariance constraints, we find that our models can outperform both baselines with no symmetry bias and baselines with overly strict symmetry in both simulated turbulence domains and real-world multi-stream jet flow.

Causal discovery in the form of a directed acyclic graph (DAG) for time series data has been widely studied in various domains. The resulting DAG typically represents a dynamic Bayesian network (DBN), capturing both the instantaneous and time-delayed relationships among variables of interest. We propose a new algorithm, IDYNO, to learn the DAG structure from potentially nonlinear times series data by using a continuous optimization framework that includes a recent formulation for continuous acyclicity constraint. The proposed algorithm is designed to handle both observational and interventional time series data. We demonstrate the promising performance of our method on synthetic benchmark datasets against state-of-the-art baselines. In addition, we show that the proposed method can more accurately learn the underlying structure of a sequential decision model, such as a Markov decision process, with a fixed policy in typical continuous control tasks.

Certified defenses such as randomized smoothing have shown promise towards building reliable machine learning systems against $\ell_p$ norm bounded attacks. However, existing methods are insufficient or unable to provably defend against semantic transformations, especially those without closed-form expressions (such as defocus blur and pixelate), which are more common in practice and often unrestricted. To fill up this gap, we propose generalized randomized smoothing (GSmooth), a unified theoretical framework for certifying robustness against general semantic transformations via a novel dimension augmentation strategy. Under the GSmooth framework, we present a scalable algorithm that uses a surrogate image-to-image network to approximate the complex transformation. The surrogate model provides a powerful tool for studying the properties of semantic transformations and certifying robustness. Experimental results on several datasets demonstrate the effectiveness of our approach for robustness certification against multiple kinds of semantic transformations and corruptions, which is not achievable by the alternative baselines.

Neural Ordinary Differential Equations model dynamical systems with ODEs learned by neural networks.However, ODEs are fundamentally inadequate to model systems with long-range dependencies or discontinuities, which are common in engineering and biological systems. Broader classes of differential equations (DE) have been proposed as remedies, including delay differential equations and integro-differential equations.Furthermore, Neural ODE suffers from numerical instability when modelling stiff ODEs and ODEs with piecewise forcing functions.In this work, we propose Neural Laplace, a unifying framework for learning diverse classes of DEs including all the aforementioned ones.Instead of modelling the dynamics in the time domain, we model it in the Laplace domain, where the history-dependencies and discontinuities in time can be represented as summations of complex exponentials. To make learning more efficient, we use the geometrical stereographic map of a Riemann sphere to induce more smoothness in the Laplace domain.In the experiments, Neural Laplace shows superior performance in modelling and extrapolating the trajectories of diverse classes of DEs, including the ones with complex history dependency and abrupt changes.

We enhance auto-regressive language models by conditioning on document chunks retrieved from a large corpus, based on local similarity with preceding tokens. With a 2 trillion token database, our Retrieval-Enhanced Transformer (RETRO) obtains comparable performance to GPT-3 and Jurassic-1 on the Pile, despite using 25× fewer parameters. After fine-tuning, RETRO performance translates to downstream knowledge-intensive tasks such as question answering. RETRO combines a frozen Bert retriever, a differentiable encoder and a chunked cross-attention mechanism to predict tokens based on an order of magnitude more data than what is typically consumed during training. We typically train RETRO from scratch, yet can also rapidly RETROfit pre-trained transformers with retrieval and still achieve good performance. Our work opens up new avenues for improving language models through explicit memory at unprecedented scale.

Time series alignment methods call for highly expressive, differentiable and invertible warping functions which preserve temporal topology, i.e diffeomorphisms. Diffeomorphic warping functions can be generated from the integration of velocity fields governed by an ordinary differential equation (ODE). Gradient-based optimization frameworks containing diffeomorphic transformations require to calculate derivatives to the differential equation's solution with respect to the model parameters, i.e. sensitivity analysis. Unfortunately, deep learning frameworks typically lack automatic-differentiation-compatible sensitivity analysis methods; and implicit functions, such as the solution of ODE, require particular care. Current solutions appeal to adjoint sensitivity methods, ad-hoc numerical solvers or ResNet's Eulerian discretization. In this work, we present a closed-form expression for the ODE solution and its gradient under continuous piecewise-affine (CPA) velocity functions. We present a highly optimized implementation of the results on CPU and GPU. Furthermore, we conduct extensive experiments on several datasets to validate the generalization ability of our model to unseen data for time-series joint alignment. Results show significant improvements both in terms of efficiency and accuracy.

Adversarial training (AT) defends deep neural networks against adversarial attacks. One challenge that limits its practical application is the performance degradation on clean samples. A major bottleneck identified by previous works is the widely used batch normalization (BN), which struggles to model the different statistics of clean and adversarial training samples in AT. Although the dominant approach is to extend BN to capture this mixture of distribution, we propose to completely eliminate this bottleneck by removing all BN layers in AT. Our normalizer-free robust training (NoFrost) method extends recent advances in normalizer-free networks to AT for its unexplored advantage on handling the mixture distribution challenge. We show that NoFrost achieves adversarial robustness with only a minor sacrifice on clean sample accuracy. On ImageNet with ResNet50, NoFrost achieves $74.06\%$ clean accuracy, which drops merely $2.00\%$ from standard training. In contrast, BN-based AT obtains $59.28\%$ clean accuracy, suffering a significant $16.78\%$ drop from standard training. In addition, NoFrost achieves a $23.56\%$ adversarial robustness against PGD attack, which improves the $13.57\%$ robustness in BN-based AT. We observe better model smoothness and larger decision margins from NoFrost, which make the models less sensitive to input perturbations and thus more robust. Moreover, when incorporating more data augmentations into NoFrost, it achieves comprehensive robustness against multiple distribution shifts. Code and pre-trained models are public at https://github.com/amazon-research/normalizer-free-robust-training.

Inspired by Lottery Ticket Hypothesis that competitive subnetworks exist within a dense network, we propose a continual learning method referred to as Winning SubNetworks (WSN), which sequentially learns and selects an optimal subnetwork for each task. Specifically, WSN jointly learns the model weights and task-adaptive binary masks pertaining to subnetworks associated with each task whilst attempting to select a small set of weights to be activated (winning ticket) by reusing weights of the prior subnetworks. The proposed method is inherently immune to catastrophic forgetting as each selected subnetwork model does not infringe upon other subnetworks. Binary masks spawned per winning ticket are encoded into one N-bit binary digit mask, then compressed using Huffman coding for a sub-linear increase in network capacity with respect to the number of tasks.

Long-term time series forecasting is challenging since prediction accuracy tends to decrease dramatically with the increasing horizon. Although Transformer-based methods have significantly improved state-of-the-art results for long-term forecasting, they are not only computationally expensive but more importantly, are unable to capture the global view of time series (e.g. overall trend). To address these problems, we propose to combine Transformer with the seasonal-trend decomposition method, in which the decomposition method captures the global profile of time series while Transformers capture more detailed structures. To further enhance the performance of Transformer for long-term prediction, we exploit the fact that most time series tend to have a sparse representation in a well-known basis such as Fourier transform, and develop a frequency enhanced Transformer. Besides being more effective, the proposed method, termed as Frequency Enhanced Decomposed Transformer (FEDformer), is more efficient than standard Transformer with a linear complexity to the sequence length. Our empirical studies with six benchmark datasets show that compared with state-of-the-art methods, Fedformer can reduce prediction error by 14.8% and 22.6% for multivariate and univariate time series, respectively. Code is publicly available at https://github.com/MAZiqing/FEDformer.

A major drawback of adversarially robust models, in particular for large scale datasets like ImageNet, is the extremely long training time compared to standard models. Moreover, models should be robust not only to one $l_p$-threat model but ideally to all of them. In this paper we propose Extreme norm Adversarial Training (E-AT) for multiple-norm robustness which is based on geometric properties of $l_p$-balls. E-AT costs up to three times less than other adversarial training methods for multiple-norm robustness. Using E-AT we show that for ImageNet a single epoch and for CIFAR-10 three epochs are sufficient to turn any $l_p$-robust model into a multiple-norm robust model. In this way we get the first multiple-norm robust model for ImageNet and boost the state-of-the-art for multiple-norm robustness to more than $51\%$ on CIFAR-10. Finally, we study the general transfer via fine-tuning of adversarial robustness between different individual $l_p$-threat models and improve the previous SOTA $l_1$-robustness on both CIFAR-10 and ImageNet. Extensive experiments show that our scheme works across datasets and architectures including vision transformers.

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these deterministic uncertainty methods (DUMs) achieve strong performance on detecting out-of-distribution (OOD) data while adding negligible computational costs at inference time. However, it remains unclear whether DUMs are well calibrated and can seamlessly scale to real-world applications - both prerequisites for their practical deployment. To this end, we first provide a taxonomy of DUMs, and evaluate their calibration under continuous distributional shifts. Then, we extend them to semantic segmentation. We find that, while DUMs scale to realistic vision tasks and perform well on OOD detection, the practicality of current methods is undermined by poor calibration under distributional shifts.

To improve model generalization, model designers often restrict the features that their models use, either implicitly or explicitly. In this work, we explore the design space of leveraging such feature priors by viewing them as distinct perspectives on the data. Specifically, we find that models trained with diverse sets of explicit feature priors have less overlapping failure modes, and can thus be combined more effectively. Moreover, we demonstrate that jointly training such models on additional (unlabeled) data allows them to correct each other's mistakes, which, in turn, leads to better generalization and resilience to spurious correlations.