Neural network ensembles, such as Bayesian neural networks (BNNs), have shown success in the areas of uncertainty estimation and robustness. However, a crucial challenge prohibits their use in practice. BNNs require a large number of predictions to produce reliable results, leading to a significant increase in computational cost. To alleviate this issue, we propose spatial smoothing, a method that ensembles neighboring feature map points of convolutional neural networks. By simply adding a few blur layers to the models, we empirically show that spatial smoothing improves accuracy, uncertainty estimation, and robustness of BNNs across a whole range of ensemble sizes. In particular, BNNs incorporating spatial smoothing achieve high predictive performance merely with a handful of ensembles. Moreover, this method also can be applied to canonical deterministic neural networks to improve the performances. A number of evidences suggest that the improvements can be attributed to the stabilized feature maps and the smoothing of the loss landscape. In addition, we provide a fundamental explanation for prior works — namely, global average pooling, pre-activation, and ReLU6 — by addressing them as special cases of spatial smoothing. These not only enhance accuracy, but also improve uncertainty estimation and robustness by making the loss landscape smoother …

It is an important problem in trustworthy machine learning to recognize out-of-distribution (OOD) inputs which are inputs unrelated to the in-distribution task. Many out-of-distribution detection methods have been suggested in recent years. The goal of this paper is to recognize common objectives as well as to identify the implicit scoring functions of different OOD detection methods. We focus on the sub-class of methods that use surrogate OOD data during training in order to learn an OOD detection score that generalizes to new unseen out-distributions at test time.We show that binary discrimination between in- and (different) out-distributions is equivalent to several distinct formulations of the OOD detection problem. When trained in a shared fashion with a standard classifier, this binary discriminator reaches an OOD detection performance similar to that of Outlier Exposure. Moreover, we show that the confidence loss which is used by Outlier Exposure has an implicit scoring function which differs in a non-trivial fashion from the theoretically optimal scoring function in the case where training and test out-distribution are the same, which again is similar to the one used when training an Energy-Based OOD detector or when adding a background class. In practice, when trained in exactly the same …

Negative sampling~(NS) loss plays an important role in learning knowledge graph embedding~(KGE) to handle a huge number of entities. However, the performance of KGE degrades without hyperparameters such as the margin term and number of negative samples in NS loss being appropriately selected. Currently, empirical hyperparameter tuning addresses this problem at the cost of computational time. To solve this problem, we theoretically analyzed NS loss to assist hyperparameter tuning and understand the better use of the NS loss in KGE learning. Our theoretical analysis showed that scoring methods with restricted value ranges, such as TransE and RotatE, require appropriate adjustment of the margin term or the number of negative samples different from those without restricted value ranges, such as RESCAL, ComplEx, and DistMult. We also propose subsampling methods specialized for the NS loss in KGE studied from a theoretical aspect. Our empirical analysis on the FB15k-237, WN18RR, and YAGO3-10 datasets showed that the results of actually trained models agree with our theoretical findings.

Certifiable robustness is a highly desirable property for adopting deep neural networks (DNNs) in safety-critical scenarios, but often demands tedious computations to establish. The main hurdle lies in the massive amount of non-linearity in large DNNs. To trade off the DNN expressiveness (which calls for more non-linearity) and robustness certification scalability (which prefers more linearity), we propose a novel solution to strategically manipulate neurons, by "grafting" appropriate levels of linearity. The core of our proposal is to first linearize insignificant ReLU neurons, to eliminate the non-linear components that are both redundant for DNN performance and harmful to its certification. We then optimize the associated slopes and intercepts of the replaced linear activations for restoring model performance while maintaining certifiability. Hence, typical neuron pruning could be viewed as a special case of grafting a linear function of the fixed zero slopes and intercept, that might overly restrict the network flexibility and sacrifice its performance. Extensive experiments on multiple datasets and network backbones show that our linearity grafting can (1) effectively tighten certified bounds; (2) achieve competitive certifiable robustness without certified robust training (i.e., over 30% improvements on CIFAR-10 models); and (3) scale up complete verification to large adversarially trained models with …

In this paper, we develop a new graph kernel, namely the Hierarchical Transitive-Aligned Kernel, by transitively aligning the vertices between graphs through a family of hierarchical prototype graphs. Comparing to most existing state-of-the-art graph kernels, the proposed kernel has three theoretical advantages. First, it incorporates the locational correspondence information between graphs into the kernel computation, and thus overcomes the shortcoming of ignoring structural correspondences arising in most R-convolution kernels. Second, it guarantees the transitivity between the correspondence information that is not available for most existing matching kernels. Third, it incorporates the information of all graphs under comparisons into the kernel computation process, and thus encapsulates richer characteristics. Experimental evaluations demonstrate the effectiveness of the new transitive-aligned kernel.

We propose efficient random features for approximating a new and rich class of kernel functions that we refer to as Generalized Zonal Kernels (GZK). Our proposed GZK family, generalizes the zonal kernels (i.e., dot-product kernels on the unit sphere) by introducing radial factors in the Gegenbauer series expansion of these kernel functions. The GZK class of kernels includes a wide range of ubiquitous kernel functions such as the entirety of dot-product kernels as well as the Gaussian and the recently introduced Neural Tangent kernels. Interestingly, by exploiting the reproducing property of the Gegenbauer (Zonal) Harmonics, we can construct efficient random features for the GZK family based on randomly oriented Gegenbauer harmonics. We prove subspace embedding guarantees for our Gegenbauer features which ensures that our features can be used for approximately solving learning problems such as kernel k-means clustering, kernel ridge regression, etc. Empirical results show that our proposed features outperform recent kernel approximation methods.

Recent years have seen a surge of interest in meta-learning techniques for tackling the few-shot learning (FSL) problem. However, the meta-learner is prone to overfitting since there are only a few available samples, which can be identified as sampling noise on a clean dataset. Besides, when handling the data with noisy labels, the meta-learner could be extremely sensitive to label noise on a corrupted dataset. To address these two challenges, we present Eigen-Reptile (ER) that updates the meta-parameters with the main direction of historical task-specific parameters. Specifically, the main direction is computed in a fast way, where the scale of the calculated matrix is related to the number of gradient steps for the specific task instead of the number of parameters. Furthermore, to obtain a more accurate main direction for Eigen-Reptile in the presence of many noisy labels, we further propose Introspective Self-paced Learning (ISPL). We have theoretically and experimentally demonstrated the soundness and effectiveness of the proposed Eigen-Reptile and ISPL. Particularly, our experiments on different tasks show that the proposed method is able to outperform or achieve highly competitive performance compared with other gradient-based methods with or without noisy labels. The code and data for the proposed method are …

Measures of similarity (or dissimilarity) are a key ingredient to many machine learning algorithms. We introduce DID, a pairwise dissimilarity measure applicable to a wide range of data spaces, which leverages the data's internal structure to be invariant to diffeomorphisms. We prove that DID enjoys properties which make it relevant for theoretical study and practical use. By representing each datum as a function, DID is defined as the solution to an optimization problem in a Reproducing Kernel Hilbert Space and can be expressed in closed-form. In practice, it can be efficiently approximated via Nyström sampling. Empirical experiments support the merits of DID.

We study a nonparametric approach to Bayesian computation via feature means, where the expectation of prior features is updated to yield expected posterior features, based on regression from kernel or neural net features of the observations. All quantities involved in the Bayesian update are learned from observed data, making the method entirely model-free. The resulting algorithm is a novel instance of a kernel Bayes' rule (KBR). Our approach is based on importance weighting, which results in superior numerical stability to the existing approach to KBR, which requires operator inversion. We show the convergence of the estimator using a novel consistency analysis on the importance weighting estimator in the infinity norm. We evaluate our KBR on challenging synthetic benchmarks, including a filtering problem with a state-space model involving high dimensional image observations. The proposed method yields uniformly better empirical performance than the existing KBR, and competitive performance with other competing methods.We evaluate our KBR on challenging synthetic benchmarks, including a filtering problem with a state-space model involving high dimensional image observations. The proposed method yields uniformly better empirical performance than the existing KBR, and competitive performance with other competing methods.

We propose a new conditional dependence measure and a statistical test for conditional independence. The measure is based on the difference between analytic kernel embeddings of two well-suited distributions evaluated at a finite set of locations. We obtain its asymptotic distribution under the null hypothesis of conditional independence and design a consistent statistical test from it. We conduct a series of experiments showing that our new test outperforms state-of-the-art methods both in terms of type-I and type-II errors even in the high dimensional setting.

Kernel mean embeddings are a powerful tool to represent probability distributions over arbitrary spaces as single points in a Hilbert space. Yet, the cost of computing and storing such embeddings prohibits their direct use in large-scale settings. We propose an efficient approximation procedure based on the Nyström method, which exploits a small random subset of the dataset. Our main result is an upper bound on the approximation error of this procedure. It yields sufficient conditions on the subsample size to obtain the standard (1/sqrt(n)) rate while reducing computational costs. We discuss applications of this result for the approximation of the maximum mean discrepancy and quadrature rules, and we illustrate our theoretical findings with numerical experiments.

The problem of learning functions over spaces of probabilities - or distribution regression - is gaining significant interest in the machine learning community. The main challenge in these settings is to identify a suitable representation capturing all relevant properties of a distribution. The well-established approach in this sense is to use kernel mean embeddings, which lift kernel-induced similarity on the input domain at the probability level. This strategy effectively tackles the two-stage sampling nature of the problem, enabling one to derive estimators with strong statistical guarantees, such as universal consistency and excess risk bounds. However, kernel mean embeddings implicitly hinge on the maximum mean discrepancy (MMD), a metric on probabilities, which is not the most suited to capture geometrical relations between distributions. In contrast, optimal transport (OT) metrics, are potentially more appealing. In this work, we propose an OT-based estimator for distribution regression. We build on the Sliced Wasserstein distance to obtain an OT-based representation. We study the theoretical properties of a kernel ridge regression estimator based on such representation, for which we prove universal consistency and excess risk bounds. Preliminary experiments complement our theoretical findings by showing the effectiveness of the proposed approach and compare it with MMD-based estimators.

Since reinforcement learning algorithms are notoriously data-intensive, the task of sampling observations from the environment is usually split across multiple agents. However, transferring these observations from the agents to a central location can be prohibitively expensive in terms of the communication cost, and it can also compromise the privacy of each agent's local behavior policy. In this paper, we consider a federated reinforcement learning framework where multiple agents collaboratively learn a global model, without sharing their individual data and policies. Each agent maintains a local copy of the model and updates it using locally sampled data. Although having N agents enables the sampling of N times more data, it is not clear if it leads to proportional convergence speedup. We propose federated versions of on-policy TD, off-policy TD and Q-learning, and analyze their convergence. For all these algorithms, to the best of our knowledge, we are the first to consider Markovian noise and multiple local updates, and prove a linear convergence speedup with respect to the number of agents. To obtain these results, we show that federated TD and Q-learning are special cases of a general framework for federated stochastic approximation with Markovian noise, and we leverage this framework to …

We study the entropic Gromov-Wasserstein and its unbalanced version between (unbalanced) Gaussian distributions with different dimensions. When the metric is the inner product, which we refer to as inner product Gromov-Wasserstein (IGW), we demonstrate that the optimal transportation plans of entropic IGW and its unbalanced variant are (unbalanced) Gaussian distributions. Via an application of von Neumann's trace inequality, we obtain closed-form expressions for the entropic IGW between these Gaussian distributions. Finally, we consider an entropic inner product Gromov-Wasserstein barycenter of multiple Gaussian distributions. We prove that the barycenter is a Gaussian distribution when the entropic regularization parameter is small. We further derive a closed-form expression for the covariance matrix of the barycenter.

This paper proposes an extension of a popular decentralized discrete-time learning procedure when repeating a static game called fictitious play (FP) (Brown, 1951; Robinson, 1951) to a dynamic model called discounted stochastic game (Shapley, 1953). Our family of discrete-time FP procedures is proven to converge to the set of stationary Nash equilibria in identical interest discounted stochastic games. This extends similar convergence results for static games (Monderer & Shapley, 1996a). We then analyze the continuous-time counterpart of our FP procedures, which include as a particular case the best-response dynamic introduced and studied by Leslie et al. (2020) in the context of zero-sum stochastic games. We prove the converge of this dynamics to stationary Nash equilibria in identical-interest and zero-sum discounted stochastic games. Thanks to stochastic approximations, we can infer from the continuous-time convergence some discrete time results such as the convergence to stationary equilibria in zero-sum and team stochastic games (Holler, 2020).

Interior point methods (IPMs) are a common approach for solving linear programs (LPs) with strong theoretical guarantees and solid empirical performance. The time complexity of these methods is dominated by the cost of solving a linear system of equations at each iteration. In common applications of linear programming, particularly in machine learning and scientific computing, the size of this linear system can become prohibitively large, requiring the use of iterative solvers, which provide an approximate solution to the linear system. However, approximately solving the linear system at each iteration of an IPM invalidates the theoretical guarantees of common IPM analyses. To remedy this, we theoretically and empirically analyze (slightly modified) predictor-corrector IPMs when using approximate linear solvers: our approach guarantees that, when certain conditions are satisfied, the number of IPM iterations does not increase and that the final solution remains feasible. We also provide practical instantiations of approximate linear solvers that satisfy these conditions for special classes of constraint matrices using randomized linear algebra.

In many online decision processes, the optimizing agent is called to choose between large numbers of alternatives with many inherent similarities; in turn, these similarities imply closely correlated losses that may confound standard discrete choice models and bandit algorithms. We study this question in the context of nested bandits, a class of adversarial multi-armed bandit problems where the learner seeks to minimize their regret in the presence of a large number of distinct alternatives with a hierarchy of embedded (non-combinatorial) similarities. In this setting, optimal algorithms based on the exponential weights blueprint (like Hedge, EXP3, and their variants) may incur significant regret because they tend to spend excessive amounts of time exploring irrelevant alternatives with similar, suboptimal costs. To account for this, we propose a nested exponential weights (NEW) algorithm that performs a layered exploration of the learner's set of alternatives based on a nested, step-by-step selection method. In so doing, we obtain a series of tight bounds for the learner's regret showing that online learning problems with a high degree of similarity between alternatives can be resolved efficiently, without a red bus / blue bus paradox occurring.

We initiate the study of the effects of non-transparency in decision rules on individuals' ability to improve in strategic learning settings. Inspired by real-life settings, such as loan approvals and college admissions, we remove the assumption typically made in the strategic learning literature, that the decision rule is fully known to individuals, and focus instead on settings where it is inaccessible. In their lack of knowledge, individuals try to infer this rule by learning from their peers (e.g., friends and acquaintances who previously applied for a loan), naturally forming groups in the population, each with possibly different type and level of information regarding the decision rule. We show that, in equilibrium, the principal's decision rule optimizing welfare across sub-populations may cause a strong negative externality: the true quality of some of the groups can actually deteriorate. On the positive side, we show that, in many natural cases, optimal improvement can be guaranteed simultaneously for all sub-populations. We further introduce a measure we term information overlap proxy, and demonstrate its usefulness in characterizing the disparity in improvements across sub-populations. Finally, we identify a natural condition under which improvement can be guaranteed for all sub-populations while maintaining high predictive accuracy. We complement …

The goal of explainable Artificial Intelligence (XAI) is to generate human-interpretable explanations, but there are no computationally precise theories of how humans interpret AI generated explanations. The lack of theory means that validation of XAI must be done empirically, on a case-by-case basis, which prevents systematic theory-building in XAI. We propose a psychological theory of how humans draw conclusions from saliency maps, the most common form of XAI explanation, which for the first time allows for precise prediction of explainee inference conditioned on explanation. Our theory posits that absent explanation humans expect the AI to make similar decisions to themselves, and that they interpret an explanation by comparison to the explanations they themselves would give. Comparison is formalized via Shepard's universal law of generalization in a similarity space, a classic theory from cognitive science. A pre-registered user study on AI image classifications with saliency map explanations demonstrate that our theory quantitatively matches participants' predictions of the AI.

Local differential privacy (LDP) can be adopted to anonymize richer user data attributes that will be input to sophisticated machine learning (ML) tasks. However, today's LDP approaches are largely task-agnostic and often lead to severe performance loss -- they simply inject noise to all data attributes according to a given privacy budget, regardless of what features are most relevant for the ultimate task. In this paper, we address how to significantly improve the ultimate task performance with multi-dimensional user data by considering a task-aware privacy preservation problem. The key idea is to use an encoder-decoder framework to learn (and anonymize) a task-relevant latent representation of user data. We obtain an analytical near-optimal solution for the linear setting with mean-squared error (MSE) task loss. We also provide an approximate solution through a gradient-based learning algorithm for general nonlinear cases. Extensive experiments demonstrate that our task-aware approach significantly improves ultimate task accuracy compared to standard benchmark LDP approaches with the same level of privacy guarantee.

Humans have come to rely on machines for reducing excessive information to manageable representations. But this reliance can be abused -- strategic machines might craft representations that manipulate their users. How can a user make good choices based on strategic representations? We formalize this as a learning problem, and pursue algorithms for decision-making that are robust to manipulation.In our main setting of interest, the system represents attributes of an item to the user, who then decides whether or not to consume. We model this interaction through the lens of strategic classification (Hardt et al. 2016), reversed: the user, who learns, plays first; and the system, which responds, plays second. The system must respond with representations that reveal `nothing but the truth' but need not reveal the entire truth. Thus, the user faces the problem of learning set functionsunder strategic subset selection, which presents distinct algorithmic and statistical challenges. Our main result is a learning algorithm that minimizes error despite strategic representations, and our theoretical analysis sheds light on the trade-off between learning effort and susceptibility to manipulation.

In this paper, we explore applications of deep learning in statistical physics. We choose the Boltzmann equation as a typical example, where neural networks serve as a closure to its moment system. We present two types of neural networks to embed the convexity of entropy and to preserve the minimum entropy principle and intrinsic mathematical structures of the moment system of the Boltzmann equation. We derive an error bound for the generalization gap of convex neural networks which are trained in Sobolev norm and use the results to construct data sampling methods for neural network training. Numerical experiments demonstrate that the neural entropy closure is significantly faster than classical optimizers while maintaining sufficient accuracy.

We introduce a compositional physics-aware FInite volume Neural Network (FINN) for learning spatiotemporal advection-diffusion processes. FINN implements a new way of combining the learning abilities of artificial neural networks with physical and structural knowledge from numerical simulation by modeling the constituents of partial differential equations (PDEs) in a compositional manner. Results on both one- and two-dimensional PDEs (Burgers’, diffusion-sorption, diffusion-reaction, Allen–Cahn) demonstrate FINN’s superior modeling accuracy and excellent out-of-distribution generalization ability beyond initial and boundary conditions. With only one tenth of the number of parameters on average, FINN outperforms pure machine learning and other state-of-the-art physics-aware models in all cases—often even by multiple orders of magnitude. Moreover, FINN outperforms a calibrated physical model when approximating sparse real-world data in a diffusion-sorption scenario, confirming its generalization abilities and showing explanatory potential by revealing the unknown retardation factor of the observed process.

Large pre-trained language models (LMs) have demonstrated impressive capabilities in generating long, fluent text; however, there is little to no analysis on their ability to maintain entity coherence and consistency. In this work, we focus on the end task of narrative generation and systematically analyse the long-range entity coherence and consistency in generated stories. First, we propose a set of automatic metrics for measuring model performance in terms of entity usage. Given these metrics, we quantify the limitations of current LMs. Next, we propose augmenting a pre-trained LM with a dynamic entity memory in an end-to-end manner by using an auxiliary entity-related loss for guiding the reads and writes to the memory. We demonstrate that the dynamic entity memory increases entity coherence according to both automatic and human judgment and helps preserving entity-related information especially in settings with a limited context window. Finally, we also validate that our automatic metrics are correlated with human ratings and serve as a good indicator of the quality of generated stories.

Despite remarkable progress on visual recognition tasks, deep neural-nets still struggle to generalize well when training data is scarce or highly imbalanced, rendering them extremely vulnerable to real-world examples. In this paper, we present a surprisingly simple yet highly effective method to mitigate this limitation: using pure noise images as additional training data. Unlike the common use of additive noise or adversarial noise for data augmentation, we propose an entirely different perspective by directly training on pure random noise images. We present a new Distribution-Aware Routing Batch Normalization layer (DAR-BN), which enables training on pure noise images in addition to natural images within the same network. This encourages generalization and suppresses overfitting. Our proposed method significantly improves imbalanced classification performance, obtaining state-of-the-art results on a large variety of long-tailed image classification datasets (CIFAR-10-LT, CIFAR-100-LT, ImageNet-LT, Places-LT, and CelebA-5). Furthermore, our method is extremely simple and easy to use as a general new augmentation tool (on top of existing augmentations), and can be incorporated in any training scheme. It does not require any specialized data generation or training procedures, thus keeping training fast and efficient.

Recent studies in lossy compression show that distortion and perceptual quality are at odds with each other, which put forward the tradeoff between distortion and perception (D-P). Intuitively, to attain different perceptual quality, different decoders have to be trained. In this paper, we present a nontrivial finding that only two decoders are sufficient for optimally achieving arbitrary (an infinite number of different) D-P tradeoff. We prove that arbitrary points of the D-P tradeoff bound can be achieved by a simple linear interpolation between the outputs of a minimum MSE decoder and a specifically constructed perfect perceptual decoder. Meanwhile, the perceptual quality (in terms of the squared Wasserstein-2 distancemetric) can be quantitatively controlled by the interpolation factor. Furthermore, to construct a perfect perceptual decoder, we propose two theoretically optimal training frameworks. The new frameworks are different from the distortion-plus-adversarial loss based heuristic framework widely used in existing methods, which are not only theoretically optimal but also can yield state-of-the-art performance in practical perceptual decoding. Finally, we validate our theoretical finding and demonstrate the superiority of our frameworks via experiments. Code is available at: https://github.com/ZeyuYan/ControllablePerceptual-Compression

Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering, however, we are not only interested in a forward simulation but also in solving inverse problems with constraints defined by a partial differential equation (PDE). Here we explore GNNs to solve such PDE-constrained inverse problems. Given a sparse set of measurements, we are interested in recovering the initial condition or parameters of the PDE. We demonstrate that GNNs combined with autodecoder-style priors are well-suited for these tasks, achieving more accurate estimates of initial conditions or physical parameters than other learned approaches when applied to the wave equation or Navier Stokes equations. We also demonstrate computational speedups of up to 90x using GNNs compared to principled solvers.

Deep learning models are able to approximate one specific dynamical system but struggle at learning generalisable dynamics, where dynamical systems obey the same laws of physics but contain different numbers of elements (e.g., double- and triple-pendulum systems). To relieve this issue, we proposed the Modular Lagrangian Network (ModLaNet), a structural neural network framework with modularity and physical inductive bias. This framework models the energy of each element using modularity and then construct the target dynamical system via Lagrangian mechanics. Modularity is beneficial for reusing trained networks and reducing the scale of networks and datasets. As a result, our framework can learn from the dynamics of simpler systems and extend to more complex ones, which is not feasible using other relevant physics-informed neural networks. We examine our framework for modelling double-pendulum or three-body systems with small training datasets, where our models achieve the best data efficiency and accuracy performance compared with counterparts. We also reorganise our models as extensions to model multi-pendulum and multi-body systems, demonstrating the intriguing reusable feature of our framework.

Extracting information on fluid motion directly from images is challenging. Fluid flow represents a complex dynamic system governed by the Navier-Stokes equations. General optical flow methods are typically designed for rigid body motion, and thus struggle if applied to fluid motion estimation directly. Further, optical flow methods only focus on two consecutive frames without utilising historical temporal information, while the fluid motion (velocity field) can be considered a continuous trajectory constrained by time-dependent partial differential equations (PDEs). This discrepancy has the potential to induce physically inconsistent estimations. Here we propose an unsupervised learning based prediction-correction scheme for fluid flow estimation. An estimate is first given by a PDE-constrained optical flow predictor, which is then refined by a physical based corrector. The proposed approach outperforms optical flow methods and shows competitive results compared to existing supervised learning based methods on a benchmark dataset. Furthermore, the proposed approach can generalize to complex real-world fluid scenarios where ground truth information is effectively unknowable. Finally, experiments demonstrate that the physical corrector can refine flow estimates by mimicking the operator splitting method commonly utilised in fluid dynamical simulation.

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward this goal often suffered from a lack of interpretability and tractability. In particular, the high-dimensional latent spaces often required for a faithful embedding, even when the underlying dynamics lives on a lower-dimensional manifold, can hamper theoretical analysis. Motivated by the emerging principles of dendritic computation, we augment a dynamically interpretable and mathematically tractable piecewise-linear (PL) recurrent neural network (RNN) by a linear spline basis expansion. We show that this approach retains all the theoretically appealing properties of the simple PLRNN, yet boosts its capacity for approximating arbitrary nonlinear dynamical systems in comparatively low dimensions. We employ two frameworks for training the system, one combining BPTT with teacher forcing, and another based on fast and scalable variational inference. We show that the dendritically expanded PLRNN achieves better reconstructions with fewer parameters and dimensions on various dynamical systems benchmarks and compares favorably to other methods, while retaining a tractable and interpretable structure.

Inversion techniques are widely used to reconstruct subsurface physical properties (e.g., velocity, conductivity) from surface-based geophysical measurements (e.g., seismic, electric/magnetic (EM) data). The problems are governed by partial differential equations (PDEs) like the wave or Maxwell's equations. Solving geophysical inversion problems is challenging due to the ill-posedness and high computational cost. To alleviate those issues, recent studies leverage deep neural networks to learn the inversion mappings from measurements to the property directly.In this paper, we show that such a mapping can be well modeled by a very shallow (but not wide) network with only five layers. This is achieved based on our new finding of an intriguing property: a near-linear relationship between the input and output, after applying integral transform in high dimensional space. In particular, when dealing with the inversion from seismic data to subsurface velocity governed by a wave equation, the integral results of velocity with Gaussian kernels are linearly correlated to the integral of seismic data with sine kernels. Furthermore, this property can be easily turned into a light-weight encoder-decoder network for inversion. The encoder contains the integration of seismic data and the linear transformation without need for fine-tuning. The decoder only consists of a single transformer …

Jet tagging is a critical yet challenging classification task in particle physics. While deep learning has transformed jet tagging and significantly improved performance, the lack of a large-scale public dataset impedes further enhancement. In this work, we present JetClass, a new comprehensive dataset for jet tagging. The JetClass dataset consists of 100 M jets, about two orders of magnitude larger than existing public datasets. A total of 10 types of jets are simulated, including several types unexplored for tagging so far. Based on the large dataset, we propose a new Transformer-based architecture for jet tagging, called Particle Transformer (ParT). By incorporating pairwise particle interactions in the attention mechanism, ParT achieves higher tagging performance than a plain Transformer and surpasses the previous state-of-the-art, ParticleNet, by a large margin. The pre-trained ParT models, once fine-tuned, also substantially enhance the performance on two widely adopted jet tagging benchmarks. The dataset, code and models are publicly available at https://github.com/jet-universe/particle_transformer.

GPUs have become the dominant computing platforms for many applications, while programming GPUs with the widely-used CUDA parallel programming model is difficult. As sequential C code is relatively easy to obtain either from legacy repositories or by manual implementation, automatically translating C to its parallel CUDA counterpart is promising to relieve the burden of GPU programming. However, because of huge differences between the sequential C and the parallel CUDA programming model, existing approaches fail to conduct the challenging auto-parallelized program translation. In this paper, we propose a learning-based framework, i.e., BabelTower, to address this problem. We first create a large-scale dataset consisting of compute-intensive function-level monolingual corpora. We further propose using back-translation with a discriminative reranker to cope with unpaired corpora and parallel semantic conversion. Experimental results show that BabelTower outperforms state-of-the-art by 1.79, 6.09, and 9.39 in terms of BLEU, CodeBLEU, and specifically designed ParaBLEU, respectively. The CUDA code generated by BabelTower attains a speedup of up to 347x over the sequential C code, and the developer productivity is improved by at most 3.8x.

Self-supervised learning in speech involves training a speech representation network on a large-scale unannotated speech corpus, and then applying the learned representations to downstream tasks. Since the majority of the downstream tasks of SSL learning in speech largely focus on the content information in speech, the most desirable speech representations should be able to disentangle unwanted variations, such as speaker variations, from the content. However, disentangling speakers is very challenging, because removing the speaker information could easily result in a loss of content as well, and the damage of the latter usually far outweighs the benefit of the former. In this paper, we propose a new SSL method that can achieve speaker disentanglement without severe loss of content. Our approach is adapted from the HuBERT framework, and incorporates disentangling mechanisms to regularize both the teacher labels and the learned representations. We evaluate the benefit of speaker disentanglement on a set of content-related downstream tasks, and observe a consistent and notable performance advantage of our speaker-disentangled representations.

Deep learning has recently achieved initial success in program analysis tasks such as bug detection. Lacking real bugs, most existing works construct training and test data by injecting synthetic bugs into correct programs. Despite achieving high test accuracy (e.g., >90%), the resulting bug detectors are found to be surprisingly unusable in practice, i.e., <10% precision when used to scan real software repositories. In this work, we argue that this massive performance difference is caused by a distribution shift, i.e., a fundamental mismatch between the real bug distribution and the synthetic bug distribution used to train and evaluate the detectors. To address this key challenge, we propose to train a bug detector in two phases, first on a synthetic bug distribution to adapt the model to the bug detection domain, and then on a real bug distribution to drive the model towards the real distribution. During these two phases, we leverage a multi-task hierarchy, focal loss, and contrastive learning to further boost performance. We evaluate our approach extensively on three widely studied bug types, for which we construct new datasets carefully designed to capture the real bug distribution. The results demonstrate that our approach is practically effective and successfully mitigates the …

We show that the input correlation matrix of typical classification datasets has an eigenspectrum where, after a sharp initial drop, a large number of small eigenvalues are distributed uniformly over an exponentially large range. This structure is mirrored in a network trained on this data: we show that the Hessian and the Fisher Information Matrix (FIM) have eigenvalues that are spread uniformly over exponentially large ranges. We call such eigenspectra ``sloppy'' because sets of weights corresponding to small eigenvalues can be changed by large magnitudes without affecting the loss. Networks trained on atypical datasets with non-sloppy inputs do not share these traits and deep networks trained on such datasets generalize poorly. Inspired by this, we study the hypothesis that sloppiness of inputs aids generalization in deep networks. We show that if the Hessian is sloppy, we can compute non-vacuous PAC-Bayes generalization bounds analytically. By exploiting our empirical observation that training predominantly takes place in the non-sloppy subspace of the FIM, we develop data-distribution dependent PAC-Bayes priors that lead to accurate generalization bounds using numerical optimization.

Across applications spanning supervised classification and sequential control, deep learning has been reported to find shortcut'' solutions that fail catastrophically under minor changes in the data distribution. In this paper, we show empirically that DNNs can be coaxed to avoid poor shortcuts by providing an additionalpriming'' feature computed from key input features, usually a coarse output estimate. Priming relies on approximate domain knowledge of these task-relevant key input features, which is often easy to obtain in practical settings. For example, one might prioritize recent frames over past frames in a video input for visual imitation learning, or salient foreground over background pixels for image classification. On NICO image classification, MuJoCo continuous control, and CARLA autonomous driving, our priming strategy works significantly better than several popular state-of-the-art approaches for feature selection and data augmentation. We connect these empirical findings to recent theoretical results on DNN optimization, and argue theoretically that priming distracts the optimizer away from poor shortcuts by creating better, simpler shortcuts.

Even the largest neural networks make errors, and once-correct predictions can become invalid as the world changes. Model editors make local updates to the behavior of base (pre-trained) models to inject updated knowledge or correct undesirable behaviors. Existing model editors have shown promise, but also suffer from insufficient expressiveness: they struggle to accurately model an edit's intended scope (examples affected by the edit), leading to inaccurate predictions for test inputs loosely related to the edit, and they often fail altogether after many edits. As a higher-capacity alternative, we propose Semi-Parametric Editing with a Retrieval-Augmented Counterfactual Model (SERAC), which stores edits in an explicit memory and learns to reason over them to modulate the base model's predictions as needed. To enable more rigorous evaluation of model editors, we introduce three challenging language model editing problems based on question answering, fact-checking, and dialogue generation. We find that only SERAC achieves high performance on all three problems, consistently outperforming existing approaches to model editing by a significant margin. Code, data, and additional project information will be made available at https://sites.google.com/view/serac-editing.

Pruning, the task of sparsifying deep neural networks, received increasing attention recently. Although state-of-the-art pruning methods extract highly sparse models, they neglect two main challenges: (1) the process of finding these sparse models is often very expensive; (2) unstructured pruning does not provide benefits in terms of GPU memory, training time, or carbon emissions. We propose Early Compression via Gradient Flow Preservation (EarlyCroP), which efficiently extracts state-of-the-art sparse models before or early in training addressing challenge (1), and can be applied in a structured manner addressing challenge (2). This enables us to train sparse networks on commodity GPUs whose dense versions would be too large, thereby saving costs and reducing hardware requirements. We empirically show that EarlyCroP outperforms a rich set of baselines for many tasks (incl. classification, regression) and domains (incl. computer vision, natural language processing, and reinforcment learning). EarlyCroP leads to accuracy comparable to dense training while outperforming pruning baselines.

Investigating active learning, we focus on the relation between the number of labeled examples (budget size), and suitable querying strategies. Our theoretical analysis shows a behavior reminiscent of phase transition: typical examples are best queried when the budget is low, while unrepresentative examples are best queried when the budget is large. Combined evidence shows that a similar phenomenon occurs in common classification models. Accordingly, we propose TypiClust -- a deep active learning strategy suited for low budgets. In a comparative empirical investigation of supervised learning, using a variety of architectures and image datasets, TypiClust outperforms all other active learning strategies in the low-budget regime. Using TypiClust in the semi-supervised framework, performance gets an even more significant boost. In particular, state-of-the-art semi-supervised methods trained on CIFAR-10 with 10 labeled examples selected by TypiClust, reach 93.2% accuracy -- an improvement of 39.4% over random selection. Code is available at https://github.com/avihu111/TypiClust.

Spiking neural networks (SNNs) that mimic information transmission in the brain can energy-efficiently process spatio-temporal information through discrete and sparse spikes, thereby receiving considerable attention. To improve accuracy and energy efficiency of SNNs, most previous studies have focused solely on training methods, and the effect of architecture has rarely been studied. We investigate the design choices used in the previous studies in terms of the accuracy and number of spikes and figure out that they are not best-suited for SNNs. To further improve the accuracy and reduce the spikes generated by SNNs, we propose a spike-aware neural architecture search framework called AutoSNN. We define a search space consisting of architectures without undesirable design choices. To enable the spike-aware architecture search, we introduce a fitness that considers both the accuracy and number of spikes. AutoSNN successfully searches for SNN architectures that outperform hand-crafted SNNs in accuracy and energy efficiency. We thoroughly demonstrate the effectiveness of AutoSNN on various datasets including neuromorphic datasets.

The great success of machine learning with massive amounts of data comes at a price of huge computation costs and storage for training and tuning. Recent studies on dataset condensation attempt to reduce the dependence on such massive data by synthesizing a compact training dataset. However, the existing approaches have fundamental limitations in optimization due to the limited representability of synthetic datasets without considering any data regularity characteristics. To this end, we propose a novel condensation framework that generates multiple synthetic data with a limited storage budget via efficient parameterization considering data regularity. We further analyze the shortcomings of the existing gradient matching-based condensation methods and develop an effective optimization technique for improving the condensation of training data information. We propose a unified algorithm that drastically improves the quality of condensed data against the current state-of-the-art on CIFAR-10, ImageNet, and Speech Commands.

With the success of Transformers in the computer vision field, the automated design of vision Transformers has attracted significant attention. Recently, MetaFormer found that simple average pooling can achieve impressive performance, which naturally raises the question of how to design a search space to search diverse and high-performance Transformer-like architectures. By revisiting typical search spaces, we design micro-meso-macro space to search for Transformer-like architectures, namely BurgerFormer. Micro, meso, and macro correspond to the granularity levels of operation, block and stage, respectively. At the microscopic level, we enrich the atomic operations to include various normalizations, activation functions, and basic operations (e.g., multi-head self attention, average pooling). At the mesoscopic level, a hamburger structure is searched out as the basic BurgerFormer block. At the macroscopic level, we search for the depth, width, and expansion ratio of the network based on the multi-stage architecture. Meanwhile, we propose a hybrid sampling method for effectively training the supernet. Experimental results demonstrate that the searched BurgerFormer architectures achieve comparable even superior performance compared with current state-of-the-art Transformers on the ImageNet and COCO datasets. The codes can be available at https://github.com/xingxing-123/BurgerFormer.

An intriguing phenomenon that arises from the high-dimensional learning dynamics of neural networks is the phenomenon of ``double descent''. The more commonly studied aspect of this phenomenon corresponds to \textit{model-wise} double descent where the test error exhibits a second descent with increasing model complexity, beyond the classical U-shaped error curve. In this work, we investigate the origins of the less studied \textit{epoch-wise} double descent in which the test error undergoes two non-monotonous transitions, or descents as the training time increases. We study a linear teacher-student setup exhibiting epoch-wise double descent similar to that in deep neural networks. In this setting, we derive closed-form analytical expressions describing the generalization error in terms of low-dimensional scalar macroscopic variables. We find that double descent can be attributed to distinct features being learned at different scales: as fast-learning features overfit, slower-learning features start to fit, resulting in a second descent in test error. We validate our findings through numerical simulations where our theory accurately predicts empirical findings and remains consistent with observations in deep neural networks.

Recent studies have demonstrated that gradient matching-based dataset synthesis, or dataset condensation (DC), methods can achieve state-of-theart performance when applied to data-efficient learning tasks. However, in this study, we prove that the existing DC methods can perform worse than the random selection method when taskirrelevant information forms a significant part of the training dataset. We attribute this to the lack of participation of the contrastive signals between the classes resulting from the class-wise gradient matching strategy. To address this problem, we propose Dataset Condensation with Contrastive signals (DCC) by modifying the loss function to enable the DC methods to effectively capture the differences between classes. In addition, we analyze the new loss function in terms of training dynamics by tracking the kernel velocity. Furthermore, we introduce a bi-level warm-up strategy to stabilize the optimization. Our experimental results indicate that while the existing methods are ineffective for fine-grained image classification tasks, the proposed method can successfully generate informative synthetic datasets for the same tasks. Moreover, we demonstrate that the proposed method outperforms the baselines even on benchmark datasets such as SVHN, CIFAR-10, and CIFAR-100. Finally, we demonstrate the high applicability of the proposed method by applying it to continual learning tasks.

In compressed sensing, the goal is to reconstruct the signal from an underdetermined system of linear measurements. Thus, prior knowledge about the signal of interest and its structure is required. Additionally, in many scenarios, the signal has an unknown orientation prior to measurements. To address such recovery problems, we propose using equivariant generative models as a prior, which encapsulate orientation information in their latent space. Thereby, we show that signals with unknown orientations can be recovered with iterative gradient descent on the latent space of these models and provide additional theoretical recovery guarantees. We construct an equivariant variational autoencoder and use the decoder as generative prior for compressed sensing. We discuss additional potential gains of the proposed approach in terms of convergence and latency.

Injecting discrete logical constraints into neural network learning is one of the main challenges in neuro-symbolic AI. We find that a straight-through-estimator, a method introduced to train binary neural networks, could effectively be applied to incorporate logical constraints into neural network learning. More specifically, we design a systematic way to represent discrete logical constraints as a loss function; minimizing this loss using gradient descent via a straight-through-estimator updates the neural network's weights in the direction that the binarized outputs satisfy the logical constraints. The experimental results show that by leveraging GPUs and batch training, this method scales significantly better than existing neuro-symbolic methods that require heavy symbolic computation for computing gradients. Also, we demonstrate that our method applies to different types of neural networks, such as MLP, CNN, and GNN, making them learn with no or fewer labeled data by learning directly from known constraints.

Training on web-scale data can take months. But much computation and time is wasted on redundant and noisy points that are already learnt or not learnable. To accelerate training, we introduce Reducible Holdout Loss Selection (RHO-LOSS), a simple but principled technique which selects approximately those points for training that most reduce the model's generalization loss. As a result, RHO-LOSS mitigates the weaknesses of existing data selection methods: techniques from the optimization literature typically select "hard" (e.g. high loss) points, but such points are often noisy (not learnable) or less task-relevant. Conversely, curriculum learning prioritizes "easy" points, but such points need not be trained on once learned. In contrast, RHO-LOSS selects points that are learnable, worth learning, and not yet learnt. RHO-LOSS trains in far fewer steps than prior art, improves accuracy, and speeds up training on a wide range of datasets, hyperparameters, and architectures (MLPs, CNNs, and BERT). On the large web-scraped image dataset Clothing-1M, RHO-LOSS trains in 18x fewer steps and reaches 2% higher final accuracy than uniform data shuffling.

Offline or batch reinforcement learning seeks to learn a near-optimal policy using history data without active exploration of the environment. To counter the insufficient coverage and sample scarcity of many offline datasets, the principle of pessimism has been recently introduced to mitigate high bias of the estimated values. While pessimistic variants of model-based algorithms (e.g., value iteration with lower confidence bounds) have been theoretically investigated, their model-free counterparts --- which do not require explicit model estimation --- have not been adequately studied, especially in terms of sample efficiency. To address this inadequacy, we study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes, and characterize its sample complexity under the single-policy concentrability assumption which does not require the full coverage of the state-action space. In addition, a variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity. Altogether, this work highlights the efficiency of model-free algorithms in offline RL when used in conjunction with pessimism and variance reduction.

Label Ranking (LR) corresponds to the problem of learning a hypothesis that maps features to rankings over a finite set of labels. We adopt a nonparametric regression approach to LR and obtain theoretical performance guarantees for this fundamental practical problem. We introduce a generative model for Label Ranking, in noiseless and noisy nonparametric regression settings, and provide sample complexity bounds for learning algorithms in both cases. In the noiseless setting, we study the LR problem with full rankings and provide computationally efficient algorithms using decision trees and random forests in the high-dimensional regime. In the noisy setting, we consider the more general cases of LR with incomplete and partial rankings from a statistical viewpoint and obtain sample complexity bounds using the One-Versus-One approach of multiclass classification. Finally, we complement our theoretical contributions with experiments, aiming to understand how the input regression noise affects the observed output.

Stochastic high dimensional bandit problems with low dimensional structures are useful in different applications such as online advertising and drug discovery. In this work, we propose a simple unified algorithm for such problems and present a general analysis framework for the regret upper bound of our algorithm. We show that under some mild unified assumptions, our algorithm can be applied to different high-dimensional bandit problems. Our framework utilizes the low dimensional structure to guide the parameter estimation in the problem, therefore our algorithm achieves the comparable regret bounds in the LASSO bandit as a sanity check, as well as novel bounds that depend logarithmically on dimensions in the low-rank matrix bandit, the group sparse matrix bandit, and in a new problem: the multi-agent LASSO bandit.

Linear contextual bandits and their variants are usually solved using algorithms guided by parameter estimation. Cauchy-Schwartz inequality established that estimation errors dominate algorithm regrets, and thus, accurate estimators suffice to guarantee algorithms with low regrets. In this paper, we complete the reverse direction by establishing the necessity. In particular, we provide a generic transformation from algorithms for linear contextual bandits to estimators for linear models, and show that algorithm regrets dominate estimation errors of their induced estimators, i.e., low-regret algorithms must imply accurate estimators. Moreover, our analysis reduces the regret lower bound to an estimation error, bridging the lower bound analysis in linear contextual bandit problems and linear regression.

We propose a novel theoretical framework of analysis for Generative Adversarial Networks (GANs). We reveal a fundamental flaw of previous analyses which, by incorrectly modeling GANs' training scheme, are subject to ill-defined discriminator gradients. We overcome this issue which impedes a principled study of GAN training, solving it within our framework by taking into account the discriminator's architecture. To this end, we leverage the theory of infinite-width neural networks for the discriminator via its Neural Tangent Kernel. We characterize the trained discriminator for a wide range of losses and establish general differentiability properties of the network. From this, we derive new insights about the convergence of the generated distribution, advancing our understanding of GANs' training dynamics. We empirically corroborate these results via an analysis toolkit based on our framework, unveiling intuitions that are consistent with GAN practice.

Controllable generative sequence models with the capability to extract and replicate the style of specific examples enable many applications, including narrating audiobooks in different voices, auto-completing and auto-correcting written handwriting, and generating missing training samples for downstream recognition tasks. However, under an unsupervised-style setting, typical training algorithms for controllable sequence generative models suffer from the training-inference mismatch, where the same sample is used as content and style input during training but unpaired samples are given during inference. In this paper, we tackle the training-inference mismatch encountered during unsupervised learning of controllable generative sequence models. The proposed method is simple yet effective, where we use a style transformation module to transfer target style information into an unrelated style input. This method enables training using unpaired content and style samples and thereby mitigate the training-inference mismatch. We apply style equalization to text-to-speech and text-to-handwriting synthesis on three datasets. We conduct thorough evaluation, including both quantitative and qualitative user studies. Our results show that by mitigating the training-inference mismatch with the proposed style equalization, we achieve style replication scores comparable to real data in our user studies.

Computational antibody design seeks to automatically create an antibody that binds to an antigen. The binding affinity is governed by the 3D binding interface where antibody residues (paratope) closely interact with antigen residues (epitope). Thus, the key question of antibody design is how to predict the 3D paratope-epitope complex (i.e., docking) for paratope generation. In this paper, we propose a new model called Hierarchical Structure Refinement Network (HSRN) for paratope docking and design. During docking, HSRN employs a hierarchical message passing network to predict atomic forces and use them to refine a binding complex in an iterative, equivariant manner. During generation, its autoregressive decoder progressively docks generated paratopes and builds a geometric representation of the binding interface to guide the next residue choice. Our results show that HSRN significantly outperforms prior state-of-the-art on paratope docking and design benchmarks.

Adversarial purification refers to a class of defense methods that remove adversarial perturbations using a generative model. These methods do not make assumptions on the form of attack and the classification model, and thus can defend pre-existing classifiers against unseen threats. However, their performance currently falls behind adversarial training methods. In this work, we propose DiffPure that uses diffusion models for adversarial purification: Given an adversarial example, we first diffuse it with a small amount of noise following a forward diffusion process, and then recover the clean image through a reverse generative process. To evaluate our method against strong adaptive attacks in an efficient and scalable way, we propose to use the adjoint method to compute full gradients of the reverse generative process. Extensive experiments on three image datasets including CIFAR-10, ImageNet and CelebA-HQ with three classifier architectures including ResNet, WideResNet and ViT demonstrate that our method achieves the state-of-the-art results, outperforming current adversarial training and adversarial purification methods, often by a large margin.

Multi-label classification (MLC) is a prediction task where each sample can have more than one label. We propose a novel contrastive learning boosted multi-label prediction model based on a Gaussian mixture variational autoencoder (C-GMVAE), which learns a multimodal prior space and employs a contrastive loss. Many existing methods introduce extra complex neural modules like graph neural networks to capture the label correlations, in addition to the prediction modules. We find that by using contrastive learning in the supervised setting, we can exploit label information effectively in a data-driven manner, and learn meaningful feature and label embeddings which capture the label correlations and enhance the predictive power. Our method also adopts the idea of learning and aligning latent spaces for both features and labels. In contrast to previous works based on a unimodal prior, C-GMVAE imposes a Gaussian mixture structure on the latent space, to alleviate the posterior collapse and over-regularization issues. C-GMVAE outperforms existing methods on multiple public datasets and can often match other models' full performance with only 50\% of the training data. Furthermore, we show that the learnt embeddings provide insights into the interpretation of label-label interactions.

Scene graphs are powerful abstractions that capture relationships between objects in images by modeling objects as nodes and relationships as edges.Generation of realistic synthetic scene graphs has applications like scene synthesis and data augmentation for supervised learning. Existing graph generative models are predominantly targeted toward molecular graphs, leveraging the limited vocabulary of atoms and bonds and also the well-defined semantics of chemical compounds. In contrast, scene graphs have much larger object and relation vocabularies, and their semantics are latent. To address this challenge, we propose a variational autoencoder for scene graphs, which is optimized for the maximum mean discrepancy (MMD) between the ground truth scene graph distribution and distribution of the generated scene graphs. Our method views a scene graph as a collection of star graphs and encodes it into a latent representation of the underlying stars. The decoder generates scene graphs by learning to sample the component stars and edges between them. Our experiments show that our method is able to mimic the underlying scene graph generative process more accurately than several state-of-the-art baselines.

Developing architectures suitable for modeling raw audio is a challenging problem due to the high sampling rates of audio waveforms. Standard sequence modeling approaches like RNNs and CNNs have previously been tailored to fit the demands of audio, but the resultant architectures make undesirable computational tradeoffs and struggle to model waveforms effectively. We propose SaShiMi, a new multi-scale architecture for waveform modeling built around the recently introduced S4 model for long sequence modeling. We identify that S4 can be unstable during autoregressive generation, and provide a simple improvement to its parameterization by drawing connections to Hurwitz matrices. SaShiMi yields state-of-the-art performance for unconditional waveform generation in the autoregressive setting. Additionally, SaShiMi improves non-autoregressive generation performance when used as the backbone architecture for a diffusion model. Compared to prior architectures in the autoregressive generation setting, SaShiMi generates piano and speech waveforms which humans find more musical and coherent respectively, e.g. 2× better mean opinion scores than WaveNet on an unconditional speech generation task. On a music generation task, SaShiMi outperforms WaveNet on density estimation and speed at both training and inference even when using 3× fewer parameters

We propose a new representation of visual data that disentangles object position from appearance. Our method, termed Deep Latent Particles (DLP), decomposes the visual input into low-dimensional latent ``particles'', where each particle is described by its spatial location and features of its surrounding region. To drive learning of such representations, we follow a VAE-based based approach and introduce a prior for particle positions based on a spatial-Softmax architecture, and a modification of the evidence lower bound loss inspired by the Chamfer distance between particles. We demonstrate that our DLP representations are useful for downstream tasks such as unsupervised keypoint (KP) detection, image manipulation, and video prediction for scenes composed of multiple dynamic objects. In addition, we show that our probabilistic interpretation of the problem naturally provides uncertainty estimates for particle locations, which can be used for model selection, among other tasks.

Advances in differentiable numerical integrators have enabled the use of gradient descent techniques to learn ordinary differential equations (ODEs), where a flexible function approximator (often a neural network) is used to estimate the system dynamics, given as a time derivative. However, these integrators can be unsatisfactorily slow and unstable when learning systems of ODEs from long sequences. We propose to learn an ODE of interest from data by viewing its dynamics as a vector field related to another base vector field via a diffeomorphism (i.e., a differentiable bijection), represented by an invertible neural network (INN). By learning both the INN and the dynamics of the base ODE, we provide an avenue to offload some of the complexity in modelling the dynamics directly on to the INN. Consequently, by restricting the base ODE to be amenable to integration, we can speed up and improve the robustness of integrating trajectories from the learned system. We demonstrate the efficacy of our method in training and evaluating benchmark ODE systems, as well as within continuous-depth neural networks models. We show that our approach attains speed-ups of up to two orders of magnitude when integrating learned ODEs.

We propose Neuro-Symbolic Hierarchical Rule Induction, an efficient interpretable neuro-symbolic model, to solve Inductive Logic Programming (ILP) problems. In this model, which is built from a pre-defined set of meta-rules organized in a hierarchical structure, first-order rules are invented by learning embeddings to match facts and body predicates of a meta-rule. To instantiate, we specifically design an expressive set of generic meta-rules, and demonstrate they generate a consequent fragment of Horn clauses. As a differentiable model, HRI can be trained both via supervised learning and reinforcement learning. To converge to interpretable rules, we inject a controlled noise to avoid local optima and employ an interpretability-regularization term. We empirically validate our model on various tasks (ILP, visual genome, reinforcement learning) against relevant state-of-the-art methods, including traditional ILP methods and neuro-symbolic models.

Real-world data is high-dimensional: a book, image, or musical performance can easily contain hundreds of thousands of elements even after compression. However, the most commonly used autoregressive models, Transformers, are prohibitively expensive to scale to the number of inputs and layers needed to capture this long-range structure. We develop Perceiver AR, an autoregressive, modality-agnostic architecture which uses cross-attention to map long-range inputs to a small number of latents while also maintaining end-to-end causal masking. Perceiver AR can directly attend to over a hundred thousand tokens, enabling practical long-context density estimation without the need for hand-crafted sparsity patterns or memory mechanisms. When trained on images or music, Perceiver AR generates outputs with clear long-term coherence and structure. Our architecture also obtains state-of-the-art likelihood on long-sequence benchmarks, including 64x64 ImageNet images and PG-19 books.

Learning the tail behavior of a distribution is a notoriously difficult problem. By definition, the number of samples from the tail is small, and deep generative models, such as normalizing flows, tend to concentrate on learning the body of the distribution. In this paper, we focus on improving the ability of normalizing flows to correctly capture the tail behavior and, thus, form more accurate models. We prove that the marginal tailedness of an autoregressive flow can be controlled viathe tailedness of the marginals of its base distribution. This theoretical insight leads us to a novel type of flows based on flexible base distributions and data-driven linear layers. An empirical analysis shows that the proposed method improveson the accuracy—especially on the tails of the distribution—and is able to generate heavy-tailed data. We demonstrate its application on a weather and climate example, in which capturing the tail behavior is essential.

We present SkexGen, a novel autoregressive generative model for computer-aided design (CAD) construction sequences containing sketch-and-extrude modeling operations. Our model utilizes distinct Transformer architectures to encode topological, geometric, and extrusion variations of construction sequences into disentangled codebooks. Autoregressive Transformer decoders generate CAD construction sequences sharing certain properties specified by the codebook vectors. Extensive experiments demonstrate that our disentangled codebook representation generates diverse and high-quality CAD models, enhances user control, and enables efficient exploration of the design space. The code is available at https://samxuxiang.github.io/skexgen.

Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. Existing approaches, however, require the supervision of consecutive particle properties, including positions and velocities. In this paper, we consider a partially observable scenario known as fluid dynamics grounding, that is, inferring the state transitions and interactions within the fluid particle systems from sequential visual observations of the fluid surface. We propose a differentiable two-stage network named NeuroFluid. Our approach consists of (i) a particle-driven neural renderer, which involves fluid physical properties into the volume rendering function, and (ii) a particle transition model optimized to reduce the differences between the rendered and the observed images. NeuroFluid provides the first solution to unsupervised learning of particle-based fluid dynamics by training these two models jointly. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities.

In the maximum state entropy exploration framework, an agent interacts with a reward-free environment to learn a policy that maximizes the entropy of the expected state visitations it is inducing. Hazan et al. (2019) noted that the class of Markovian stochastic policies is sufficient for the maximum state entropy objective, and exploiting non-Markovianity is generally considered pointless in this setting. In this paper, we argue that non-Markovianity is instead paramount for maximum state entropy exploration in a finite-sample regime. Especially, we recast the objective to target the expected entropy of the induced state visitations in a single trial. Then, we show that the class of non-Markovian deterministic policies is sufficient for the introduced objective, while Markovian policies suffer non-zero regret in general. However, we prove that the problem of finding an optimal non-Markovian policy is NP-hard. Despite this negative result, we discuss avenues to address the problem in a tractable way and how non-Markovian exploration could benefit the sample efficiency of online reinforcement learning in future works.

In this paper, we propose a novel Reinforcement Learning (RL) framework for problems with continuous action spaces: Action Quantization from Demonstrations (AQuaDem). The proposed approach consists in learning a discretization of continuous action spaces from human demonstrations. This discretization returns a set of plausible actions (in light of the demonstrations) for each input state, thus capturing the priors of the demonstrator and their multimodal behavior. By discretizing the action space, any discrete action deep RL technique can be readily applied to the continuous control problem. Experiments show that the proposed approach outperforms state-of-the-art methods such as SAC in the RL setup, and GAIL in the Imitation Learning setup. We provide a website with interactive videos: https://google-research.github.io/aquadem/ and make the code available: https://github.com/google-research/google-research/tree/master/aquadem.

Recent progress in state-only imitation learning extends the scope of applicability of imitation learning to real-world settings by relieving the need for observing expert actions.However, existing solutions only learn to extract a state-to-action mapping policy from the data, without considering how the expert plans to the target. This hinders the ability to leverage demonstrations and limits the flexibility of the policy.In this paper, we introduce Decoupled Policy Optimization (DePO), which explicitly decouples the policy as a high-level state planner and an inverse dynamics model. With embedded decoupled policy gradient and generative adversarial training, DePO enables knowledge transfer to different action spaces or state transition dynamics, and can generalize the planner to out-of-demonstration state regions.Our in-depth experimental analysis shows the effectiveness of DePO on learning a generalized target state planner while achieving the best imitation performance. We demonstrate the appealing usage of DePO for transferring across different tasks by pre-training, and the potential for co-training agents with various skills.

Understanding a decision-maker's priorities by observing their behavior is critical for transparency and accountability in decision processes—such as in healthcare. Though conventional approaches to policy learning almost invariably assume stationarity in behavior, this is hardly true in practice: Medical practice is constantly evolving as clinical professionals fine-tune their knowledge over time. For instance, as the medical community's understanding of organ transplantations has progressed over the years, a pertinent question is: How have actual organ allocation policies been evolving? To give an answer, we desire a policy learning method that provides interpretable representations of decision-making, in particular capturing an agent's non-stationary knowledge of the world, as well as operating in an offline manner. First, we model the evolving behavior of decision-makers in terms of contextual bandits, and formalize the problem of Inverse Contextual Bandits ("ICB"). Second, we propose two concrete algorithms as solutions, learning parametric and non-parametric representations of an agent's behavior. Finally, using both real and simulated data for liver transplantations, we illustrate the applicability and explainability of our method, as well as benchmarking and validating the accuracy of our algorithms.

We propose a novel formulation for the Inverse Reinforcement Learning (IRL) problem, which jointly accounts for the compatibility with the expert behavior of the identified reward and its effectiveness for the subsequent forward learning phase. Albeit quite natural, especially when the final goal is apprenticeship learning (learning policies from an expert), this aspect has been completely overlooked by IRL approaches so far.We propose a new model-free IRL method that is remarkably able to autonomously find a trade-off between the error induced on the learned policy when potentially choosing a sub-optimal reward, and the estimation error caused by using finite samples in the forward learning phase, which can be controlled by explicitly optimizing also the discount factor of the related learning problem. The approach is based on a min-max formulation for the robust selection of the reward parameters and the discount factor so that the distance between the expert's policy and the learned policy is minimized in the successive forward learning task when a finite and possibly small number of samples is available.Differently from the majority of other IRL techniques, our approach does not involve any planning or forward Reinforcement Learning problems to be solved. After presenting the formulation, we provide …

Prevalent imitation learning methods seek to produce behavior that matches or exceeds average human performance. This often prevents achieving expert-level or superhuman performance when identifying the better demonstrations to imitate is difficult. We instead assume demonstrations are of varying quality and seek to induce behavior that is unambiguously better (i.e., Pareto dominant or minimally subdominant) than all human demonstrations. Our minimum subdominance inverse optimal control training objective is primarily defined by high quality demonstrations; lower quality demonstrations, which are more easily dominated, are effectively ignored instead of degrading imitation. With increasing probability, our approach produces superhuman behavior incurring lower cost than demonstrations on the demonstrator’s unknown cost function—even if that cost function differs for each demonstration. We apply our approach on a computer cursor pointing task, producing behavior that is 78% superhuman, while minimizing demonstration suboptimality provides 50% superhuman behavior—and only 72% even after selective data cleaning.

We develop algorithms for imitation learning from policy data that was corrupted by temporally correlated noise in expert actions. When noise affects multiple timesteps of recorded data, it can manifest as spurious correlations between states and actions that a learner might latch on to, leading to poor policy performance. To break up these spurious correlations, we apply modern variants of the instrumental variable regression (IVR) technique of econometrics, enabling us to recover the underlying policy without requiring access to an interactive expert. In particular, we present two techniques, one of a generative-modeling flavor (DoubIL) that can utilize access to a simulator, and one of a game-theoretic flavor (ResiduIL) that can be run entirely offline. We find both of our algorithms compare favorably to behavioral cloning on simulated control tasks.

We study the problem of designing autonomous agents that can learn to cooperate effectively with a potentially suboptimal partner while having no access to the joint reward function. This problem is modeled as a cooperative episodic two-agent Markov decision process. We assume control over only the first of the two agents in a Stackelberg formulation of the game, where the second agent is acting so as to maximise expected utility given the first agent's policy. How should the first agent act in order to learn the joint reward function as quickly as possible and so that the joint policy is as close to optimal as possible? We analyse how knowledge about the reward function can be gained in this interactive two-agent scenario. We show that when the learning agent's policies have a significant effect on the transition function, the reward function can be learned efficiently.

A misspecified reward can degrade sample efficiency and induce undesired behaviors in reinforcement learning (RL) problems. We propose symbolic reward machines for incorporating high-level task knowledge when specifying the reward signals. Symbolic reward machines augment existing reward machine formalism by allowing transitions to carry predicates and symbolic reward outputs. This formalism lends itself well to inverse reinforcement learning, whereby the key challenge is determining appropriate assignments to the symbolic values from a few expert demonstrations. We propose a hierarchical Bayesian approach for inferring the most likely assignments such that the concretized reward machine can discriminate expert demonstrated trajectories from other trajectories with high accuracy. Experimental results show that learned reward machines can significantly improve training efficiency for complex RL tasks and generalize well across different task environment configurations.

In this paper, we propose a robust imitation learning (IL) framework that improves the robustness of IL when environment dynamics are perturbed. The existing IL framework trained in a single environment can catastrophically fail with perturbations in environment dynamics because it does not capture the situation that underlying environment dynamics can be changed. Our framework effectively deals with environments with varying dynamics by imitating multiple experts in sampled environment dynamics to enhance the robustness in general variations in environment dynamics. In order to robustly imitate the multiple sample experts, we minimize the risk with respect to the Jensen-Shannon divergence between the agent's policy and each of the sample experts. Numerical results show that our algorithm significantly improves robustness against dynamics perturbations compared to conventional IL baselines.

We study the problem of offline Imitation Learning (IL) where an agent aims to learn an optimal expert behavior policy without additional online environment interactions. Instead, the agent is provided with a supplementary offline dataset from suboptimal behaviors. Prior works that address this problem either require that expert data occupies the majority proportion of the offline dataset, or need to learn a reward function and perform offline reinforcement learning (RL) afterwards. In this paper, we aim to address the problem without additional steps of reward learning and offline RL training for the case when demonstrations contain a large proportion of suboptimal data. Built upon behavioral cloning (BC), we introduce an additional discriminator to distinguish expert and non-expert data. We propose a cooperation framework to boost the learning of both tasks, Based on this framework, we design a new IL algorithm, where the outputs of the discriminator serve as the weights of the BC loss. Experimental results show that our proposed algorithm achieves higher returns and faster training speed compared to baseline algorithms.

In label-noise learning, estimating the transition matrix is a hot topic as the matrix plays an important role in building statistically consistent classifiers. Traditionally, the transition from clean labels to noisy labels (i.e., clean-label transition matrix (CLTM)) has been widely exploited to learn a clean label classifier by employing the noisy data. Motivated by that classifiers mostly output Bayes optimal labels for prediction, in this paper, we study to directly model the transition from Bayes optimal labels to noisy labels (i.e., Bayes-label transition matrix (BLTM)) and learn a classifier to predict Bayes optimal labels. Note that given only noisy data, it is ill-posed to estimate either the CLTM or the BLTM. But favorably, Bayes optimal labels have less uncertainty compared with the clean labels, i.e., the class posteriors of Bayes optimal labels are one-hot vectors while those of clean labels are not. This enables two advantages to estimate the BLTM, i.e., (a) a set of examples with theoretically guaranteed Bayes optimal labels can be collected out of noisy data; (b) the feasible solution space is much smaller. By exploiting the advantages, we estimate the BLTM parametrically by employing a deep neural network, leading to better generalization and superior classification performance.

Recently, methods have been proposed that exploit the invariance of prediction models with respect to changing environments to infer subsets of the causal parents of a response variable. If the environments influence only few of the underlying mechanisms, the subset identified by invariant causal prediction (ICP), for example, may be small, or even empty. We introduce the concept of minimal invariance and propose invariant ancestry search (IAS). In its population version, IAS outputs a set which contains only ancestors of the response and is a superset of the output of ICP. When applied to data, corresponding guarantees hold asymptotically if the underlying test for invariance has asymptotic level and power. We develop scalable algorithms and perform experiments on simulated and real data.

Many machine learning models for online applications, such as recommender systems, are often trained on data with cyclical properties. These data sequentially arrive from a time-varying distribution that is periodic in time. Existing algorithms either use streaming learning to track a time-varying set of optimal model parameters, yielding a dynamic regret that scales linearly in time; or partition the data of each cycle into multiple segments and train a separate model for each---a pluralistic approach that is computationally and storage-wise expensive.In this paper, we have designed a novel approach to overcome the aforementioned shortcomings. Our method, named "Fourier learning", encodes the periodicity into the model representation using a partial Fourier sequence, and trains the coefficient functions modeled by neural networks. Particularly, we design a Fourier multi-layer perceptron (F-MLP) that can be trained on streaming data with stochastic gradient descent (streaming-SGD), and we derive its convergence guarantees. We demonstrate Fourier learning's better performance with extensive experiments on synthetic and public datasets, as well as on a large-scale recommender system that is updated in real-time, and trained with tens of millions of samples per day.

Modern neural models trained on textual data rely on pre-trained representations that emerge without direct supervision. As these representations are increasingly being used in real-world applications, the inability to \emph{control} their content becomes an increasingly important problem. In this work, we formulate the problem of identifying a linear subspace that corresponds to a given concept, and removing it from the representation. We formulate this problem as a constrained, linear minimax game, and show that existing solutions are generally not optimal for this task. We derive a closed-form solution for certain objectives, and propose a convex relaxation that works well for others. When evaluated in the context of binary gender removal, the method recovers a low-dimensional subspace whose removal mitigates bias by intrinsic and extrinsic evaluation. Surprisingly, we show that the method---despite being linear---is highly expressive, effectively mitigating bias in the output layers of deep, nonlinear classifiers while maintaining tractability and interpretability.

This paper demonstrates how to recover causal graphs from the score of the data distribution in non-linear additive (Gaussian) noise models. Using score matching algorithms as a building block, we show how to design a new generation of scalable causal discovery methods. To showcase our approach, we also propose a new efficient method for approximating the score's Jacobian, enabling to recover the causal graph. Empirically, we find that the new algorithm, called SCORE, is competitive with state-of-the-art causal discovery methods while being significantly faster.

Meta-learning aims to extract meta-knowledge from historical tasks to accelerate learning on new tasks. Typical meta-learning algorithms like MAML learn a globally-shared meta-model for all tasks. However, when the task environments are complex, task model parameters are diverse and a common meta-model is insufficient to capture all the meta-knowledge. To address this challenge, in this paper, task model parameters are structured into multiple subspaces, and each subspace represents one type of meta-knowledge. We propose an algorithm to learn the meta-parameters (\ie, subspace bases). We theoretically study the generalization properties of the learned subspaces. Experiments on regression and classification meta-learning datasets verify the effectiveness of the proposed algorithm.

Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing techniques, we propose an optimization objective derived by formulating continual learning as sequential function-space variational inference. In contrast to existing methods that regularize neural network parameters directly, this objective allows parameters to vary widely during training, enabling better adaptation to new tasks. Compared to objectives that directly regularize neural network predictions, the proposed objective allows for more flexible variational distributions and more effective regularization. We demonstrate that, across a range of task sequences, neural networks trained via sequential function-space variational inference achieve better predictive accuracy than networks trained with related methods while depending less on maintaining a set of representative points from previous tasks.

Test-time adaptation provides an effective means of tackling the potential distribution shift between model training and inference, by dynamically updating the model at test time. This area has seen fast progress recently, at the effectiveness of handling test shifts. Nonetheless, prior methods still suffer two key limitations: 1) these methods rely on performing backward computation for each test sample, which takes a considerable amount of time; and 2) these methods focus on improving the performance on out-of-distribution test samples and ignore that the adaptation on test data may result in a catastrophic forgetting issue, \ie, the performance on in-distribution test samples may degrade. To address these issues, we propose an efficient anti-forgetting test-time adaptation (EATA) method. Specifically, we devise a sample-efficient entropy minimization loss to exclude uninformative samples out of backward computation, which improves the overall efficiency and meanwhile boosts the out-of-distribution accuracy. Afterward, we introduce a regularization loss to ensure that critical model weights tend to be preserved during adaptation, thereby alleviating the forgetting issue. Extensive experiments on CIFAR-10-C, ImageNet-C, and ImageNet-R verify the effectiveness and superiority of our EATA.

Gaussian processes have become a promising tool for various safety-critical settings, since the posterior variance can be used to directly estimate the model error and quantify risk. However, state-of-the-art techniques for safety-critical settings hinge on the assumption that the kernel hyperparameters are known, which does not apply in general. To mitigate this, we introduce robust Gaussian process uniform error bounds in settings with unknown hyperparameters. Our approach computes a confidence region in the space of hyperparameters, which enables us to obtain a probabilistic upper bound for the model error of a Gaussian process with arbitrary hyperparameters. We do not require to know any bounds for the hyperparameters a priori, which is an assumption commonly found in related work. Instead, we are able to derive bounds from data in an intuitive fashion. We additionally employ the proposed technique to derive performance guarantees for a class of learning-based control problems. Experiments show that the bound performs significantly better than vanilla and fully Bayesian Gaussian processes.

Physical modeling is critical for many modern science and engineering applications. From a data science or machine learning perspective, where more domain-agnostic, data-driven models are pervasive, physical knowledge — often expressed as differential equations — is valuable in that it is complementary to data, and it can potentially help overcome issues such as data sparsity, noise, and inaccuracy. In this work, we propose a simple, yet powerful and general framework — AutoIP, for Automatically Incorporating Physics — that can integrate all kinds of differential equations into Gaussian Processes (GPs) to enhance prediction accuracy and uncertainty quantification. These equations can be linear or nonlinear, spatial, temporal, or spatio-temporal, complete or incomplete with unknown source terms, and so on. Based on kernel differentiation, we construct a GP prior to sample the values of the target function, equation related derivatives, and latent source functions, which are all jointly from a multivariate Gaussian distribution. The sampled values are fed to two likelihoods: one to fit the observations, and the other to conform to the equation. We use the whitening method to evade the strong dependency between the sampled function values and kernel parameters, and we develop a stochastic variational learning algorithm. AutoIP shows improvement …

This paper shows how to adapt several simple and classical sampling-based algorithms for the k-means problem to the setting with outliers. Recently, Bhaskara et al. (NeurIPS 2019) showed how to adapt the classical k-means++ algorithm to the setting with outliers. However, their algorithm needs to output O(log(k)·z) outliers, where z is the number of true outliers, to match the O(log k)-approximation guarantee of k-means++. In this paper, we build on their ideas and show how to adapt several sequential and distributed k-means algorithms to the setting with outliers, but with substantially stronger theoretical guarantees: our algorithms output (1 + ε)z outliers while achieving an O(1/ε)-approximation to the objective function. In the sequential world, we achieve this by adapting a recent algorithm of Lattanzi and Sohler (ICML 2019). In the distributed setting, we adapt a simple algorithm of Guha et al. (IEEE Trans. Know. and Data Engineering 2003) and the popular k-means‖ of Bahmani et al. (PVLDB2012). A theoretical application of our techniques is an algorithm with running time O(nk^2/z) that achieves an O(1)-approximation to the objective function while outputting O(z) outliers, assuming k << z << n. This is complemented with a matching lower bound of Ω(nk^2/z) for this problem …

The Approximate-Proximal Point (APROX) family of model-based stochastic optimization algorithms improve over standard stochastic gradient methods, as they are robust to step size choices, adaptive to problem difficulty, converge on a broader range of problems than stochastic gradientmethods, and converge very fast on interpolation problems, all while retaining nice minibatching properties~\cite{AsiDu19siopt,AsiChChDu20}. In this paper, we propose an acceleration scheme for the APROX family and provide non-asymptotic convergence guarantees, which are order-optimal in all problem-dependent constants and provide even larger minibatching speedups. For interpolation problems where the objective satisfies additional growth conditions, we show that our algorithm achieves linear convergence rates for a wide range of stepsizes. In this setting, we also prove matching lower bounds, identifying new fundamental constants and showing the optimality of the APROX family. We corroborate our theoretical results with empirical testing to demonstrate the gains accurate modeling, acceleration, and minibatching provide.

This paper studies online algorithms augmented with {\em multiple} machine-learned predictions. We give a generic algorithmic framework for online covering problems with multiple predictions that obtains an online solution that is competitive against the performance of the {\em best} solution obtained from the predictions. Our algorithm incorporates the use of predictions in the classic potential-based analysis of online algorithms. We apply our algorithmic framework to solve classical problems such as online set cover, (weighted) caching, and online facility location in the multiple predictions setting.

Learning-augmented algorithms---in which, traditional algorithms are augmented with machine-learned predictions---have emerged as a framework to go beyond worst-case analysis. The overarching goal is to design algorithms that perform near-optimally when the predictions are accurate yet retain certain worst-case guarantees irrespective of the accuracy of the predictions. This framework has been successfully applied to online problems such as caching where the predictions can be used to alleviate uncertainties. In this paper we introduce and study the setting in which the learning-augmented algorithm can utilize the predictions parsimoniously. We consider the caching problem---which has been extensively studied in the learning-augmented setting---and show that one can achieve quantitatively similar results but only using a \emph{sublinear} number of predictions.

Decision trees are one of the most useful and popular methods in the machine learning toolbox. In this paper, we consider the problem of learning optimal decision trees, a combinatorial optimization problem that is challenging to solve at scale. A common approach in the literature is to use greedy heuristics, which may not be optimal. Recently there has been significant interest in learning optimal decision trees using various approaches (e.g., based on integer programming, dynamic programming)---to achieve computational scalability, most of these approaches focus on classification tasks with binary features. In this paper, we present a new discrete optimization method based on branch-and-bound (BnB) to obtain optimal decision trees. Different from existing customized approaches, we consider both regression and classification tasks with continuous features. The basic idea underlying our approach is to split the search space based on the quantiles of the feature distribution---leading to upper and lower bounds for the underlying optimization problem along the BnB iterations. Our proposed algorithm Quant-BnB shows significant speedups compared to existing approaches for shallow optimal trees on various real datasets.

The optimization of multi-objective submodular systems appears in a wide variety of applications. However, there are currently very few techniques which are able to provide a robust allocation to such systems. In this work, we propose to design and analyse novel algorithms for the robust allocation of submodular systems through lens of quantile maximization. We start by observing that identifying an exact solution for this problem is computationally intractable. To tackle this issue, we propose a proxy for the quantile function using a softmax formulation, and show that this proxy is well suited to submodular optimization. Based on this relaxation, we propose a novel and simple algorithm called SOFTSAT. Theoretical properties are provided for this algorithm as well as novel approximation guarantees. Finally, we provide numerical experiments showing the efficiency of our algorithm with regards to state-of-the-art methods in a test bed of real-world applications, and show that SOFTSAT is particularly robust and well-suited to online scenarios.

Recent years have seen the emergence of pre-trained representations as a powerful abstraction for AI applications in computer vision, natural language, and speech. However, policy learning for control is still dominated by a tabula-rasa learning paradigm, with visuo-motor policies often trained from scratch using data from deployment environments. In this context, we revisit and study the role of pre-trained visual representations for control, and in particular representations trained on large-scale computer vision datasets. Through extensive empirical evaluation in diverse control domains (Habitat, DeepMind Control, Adroit, Franka Kitchen), we isolate and study the importance of different representation training methods, data augmentations, and feature hierarchies. Overall, we find that pre-trained visual representations can be competitive or even better than ground-truth state representations to train control policies. This is in spite of using only out-of-domain data from standard vision datasets, without any in-domain data from the deployment environments.

Learning in general-sum games is unstable and frequently leads to socially undesirable (Pareto-dominated) outcomes. To mitigate this, Learning with Opponent-Learning Awareness (LOLA) introduced opponent shaping to this setting, by accounting for each agent's influence on their opponents' anticipated learning steps. However, the original LOLA formulation (and follow-up work) is inconsistent because LOLA models other agents as naive learners rather than LOLA agents.In previous work, this inconsistency was suggested as a cause of LOLA's failure to preserve stable fixed points (SFPs). First, we formalize consistency and show that higher-order LOLA (HOLA) solves LOLA's inconsistency problem if it converges. Second, we correct a claim made in the literature by Schäfer and Anandkumar (2019), proving that Competitive Gradient Descent (CGD) does not recover HOLA as a series expansion (and fails to solve the consistency problem).Third, we propose a new method called Consistent LOLA (COLA), which learns update functions that are consistent under mutual opponent shaping. It requires no more than second-order derivatives and learns consistent update functions even when HOLA fails to converge. However, we also prove that even consistent update functions do not preserve SFPs, contradicting the hypothesis that this shortcoming is caused by LOLA's inconsistency.Finally, in an empirical evaluation on a …

When deployed, AI agents will encounter problems that are beyond their autonomous problem-solving capabilities. Leveraging human assistance can help agents overcome their inherent limitations and robustly cope with unfamiliar situations. We present a general interactive framework that enables an agent to request and interpret rich, contextually useful information from an assistant that has knowledge about the task and the environment. We demonstrate the practicality of our framework on a simulated human-assisted navigation problem. Aided with an assistance-requesting policy learned by our method, a navigation agent achieves up to a 7× improvement in success rate on tasks that take place in previously unseen environments, compared to fully autonomous behavior. We show that the agent can take advantage of different types of information depending on the context, and analyze the benefits and challenges of learning the assistance-requesting policy when the assistant can recursively decompose tasks into subtasks.

Multi-agent policy gradient methods in centralized training with decentralized execution recently witnessed many progresses. During centralized training, multi-agent credit assignment is crucial, which can substantially promote learning performance. However, explicit multi-agent credit assignment in multi-agent policy gradient methods still receives less attention. In this paper, we investigate multi-agent credit assignment induced by reward shaping and provide a theoretical understanding in terms of its credit assignment and policy bias. Based on this, we propose an exponentially weighted advantage estimator, which is analogous to GAE, to enable multi-agent credit assignment while allowing the tradeoff with policy bias. Empirical results show that our approach can successfully perform effective multi-agent credit assignment, and thus substantially outperforms other advantage estimators.

Conservatism has led to significant progress in offline reinforcement learning (RL) where an agent learns from pre-collected datasets. However, as many real-world scenarios involve interaction among multiple agents, it is important to resolve offline RL in the multi-agent setting. Given the recent success of transferring online RL algorithms to the multi-agent setting, one may expect that offline RL algorithms will also transfer to multi-agent settings directly. Surprisingly, we empirically observe that conservative offline RL algorithms do not work well in the multi-agent setting---the performance degrades significantly with an increasing number of agents. Towards mitigating the degradation, we identify a key issue that non-concavity of the value function makes the policy gradient improvements prone to local optima. Multiple agents exacerbate the problem severely, since the suboptimal policy by any agent can lead to uncoordinated global failure. Following this intuition, we propose a simple yet effective method, Offline Multi-Agent RL with Actor Rectification (OMAR), which combines the first-order policy gradients and zeroth-order optimization methods to better optimize the conservative value functions over the actor parameters. Despite the simplicity, OMAR achieves state-of-the-art results in a variety of multi-agent control tasks.

We study episodic two-player zero-sum Markov games (MGs) in the offline setting, where the goal is to find an approximate Nash equilibrium (NE) policy pair based on a dataset collected a priori. When the dataset does not have uniform coverage over all policy pairs, finding an approximate NE involves challenges in three aspects: (i) distributional shift between the behavior policy and the optimal policy, (ii) function approximation to handle large state space, and (iii) minimax optimization for equilibrium solving. We propose a pessimism-based algorithm, dubbed as pessimistic minimax value iteration (PMVI), which overcomes the distributional shift by constructing pessimistic estimates of the value functions for both players and outputs a policy pair by solving a correlated coarse equilibrium based on the two value functions. Furthermore, we establish a data-dependent upper bound on the suboptimality which recovers a sublinear rate without the assumption on uniform coverage of the dataset. We also prove an information-theoretical lower bound, which shows our upper bound is nearly minimax optimal, which suggests that the data-dependent term is intrinsic. Our theoretical results also highlight a notion of ``relative uncertainty'', which characterizes the necessary and sufficient condition for achieving sample efficiency in offline MGs. To the best of …

We analyze the role of rotational equivariance in convolutional neural networks (CNNs) applied to spherical images. We compare the performance of the group equivariant networks known as S2CNNs and standard non-equivariant CNNs trained with an increasing amount of data augmentation. The chosen architectures can be considered baseline references for the respective design paradigms. Our models are trained and evaluated on single or multiple items from the MNIST- or FashionMNIST dataset projected onto the sphere. For the task of image classification, which is inherently rotationally invariant, we find that by considerably increasing the amount of data augmentation and the size of the networks, it is possible for the standard CNNs to reach at least the same performance as the equivariant network. In contrast, for the inherently equivariant task of semantic segmentation, the non-equivariant networks are consistently outperformed by the equivariant networks with significantly fewer parameters. We also analyze and compare the inference latency and training times of the different networks, enabling detailed tradeoff considerations between equivariant architectures and data augmentation for practical problems.

Data clipping is crucial in reducing noise in quantization operations and improving the achievable accuracy of quantization-aware training (QAT). Current practices rely on heuristics to set clipping threshold scalars and cannot be shown to be optimal. We propose Optimally Clipped Tensors And Vectors (OCTAV), a recursive algorithm to determine MSE-optimal clipping scalars. Derived from the fast Newton-Raphson method, OCTAV finds optimal clipping scalars on the fly, for every tensor, at every iteration of the QAT routine. Thus, the QAT algorithm is formulated with provably minimum quantization noise at each step. In addition, we reveal limitations in common gradient estimation techniques in QAT and propose magnitude-aware differentiation as a remedy to further improve accuracy. Experimentally, OCTAV-enabled QAT achieves state-of-the-art accuracy on multiple tasks. These include training-from-scratch and retraining ResNets and MobileNets on ImageNet, and Squad fine-tuning using BERT models, where OCTAV-enabled QAT consistently preserves accuracy at low precision (4-to-6-bits). Our results require no modifications to the baseline training recipe, except for the insertion of quantization operations where appropriate.

One of the most important and challenging application areas for complex machine learning methods is to predict, characterize and model rich, multi-dimensional, neural data. Recent advances in neural recording techniques have made it possible to monitor the activity of a large number of neurons across different brain regions as animals perform behavioural tasks. This poses the critical challenge of establishing links between neural activity at a microscopic scale, which might for instance represent sensory input, and at a macroscopic scale, which then generates behaviour. Predominant modeling methods apply rather disjoint techniques to these scales; by contrast, we suggest an end-to-end model which exploits recent developments of flexible, but tractable, neural network point-process models to characterize dependencies between stimuli, actions, and neural data. We apply this model to a public dataset collected using Neuropixel probes in mice performing a visually-guided behavioural task as well as a synthetic dataset produced from a hierarchical network model with reciprocally connected sensory and integration circuits intended to characterize animal behaviour in a fixed-duration motion discrimination task. We show that our model outperforms previous approaches and contributes novel insights into the relationships between neural activity and behaviour.

Strong adversarial attacks are important for evaluating the true robustness of deep neural networks. Most existing attacks search in the input space, e.g., using gradient descent, and may miss adversarial examples due to non-convexity. In this work, we systematically search adversarial examples in the activation space of ReLU networks to tackle hard instances where none of the existing adversarial attacks succeed. Unfortunately, searching the activation space typically relies on generic mixed integer programming (MIP) solvers and is limited to small networks and easy problem instances. To improve scalability and practicability, we use branch and bound (BaB) with specialized GPU-based bound propagation methods, and propose a top-down beam-search approach to quickly identify the subspace that may contain adversarial examples. Moreover, we build an adversarial candidates pool using cheap attacks to further assist the search in activation space via diving techniques and a bottom-up large neighborhood search. Our adversarial attack framework, BaB-Attack, opens up a new opportunity for designing novel adversarial attacks not limited to searching the input space, and enables us to borrow techniques from integer programming theory and neural network verification. In experiments, we can successfully generate adversarial examples when existing attacks on input space fail. Compared to off-the-shelf MIP …

Training large neural network (NN) models requires extensive memory resources, and Activation Compression Training (ACT) is a promising approach to reduce training memory footprint. This paper presents GACT, an ACT framework to support a broad range of machine learning tasks for generic NN architectures with limited domain knowledge. By analyzing a linearized version of ACT’s approximate gradient, we prove the convergence of GACT without prior knowledge on operator type or model architecture. To make training stable, we propose an algorithm that decides the compression ratio for each tensor by estimating its impact on the gradient at run time. We implement GACT as a PyTorch library that readily applies to any NN architecture. GACT reduces the activation memory for convolutional NNs, transformers, and graph NNs by up to 8.1x, enabling training with a 4.2x to 24.7x larger batch size, with negligible accuracy loss.

The Neural Tangent Kernel (NTK), defined as the outer product of the neural network (NN) Jacobians, has emerged as a central object of study in deep learning. In the infinite width limit, the NTK can sometimes be computed analytically and is useful for understanding training and generalization of NN architectures. At finite widths, the NTK is also used to better initialize NNs, compare the conditioning across models, perform architecture search, and do meta-learning. Unfortunately, the finite width NTK is notoriously expensive to compute, which severely limits its practical utility. We perform the first in-depth analysis of the compute and memory requirements for NTK computation in finite width networks. Leveraging the structure of neural networks, we further propose two novel algorithms that change the exponent of the compute and memory requirements of the finite width NTK, dramatically improving efficiency.Our algorithms can be applied in a black box fashion to any differentiable function, including those implementing neural networks.We open-source our implementations within the Neural Tangents package at https://github.com/google/neural-tangents.

This work develops mixup for graph data. Mixup has shown superiority in improving the generalization and robustness of neural networks by interpolating features and labels between two random samples. Traditionally, Mixup can work on regular, grid-like, and Euclidean data such as image or tabular data. However, it is challenging to directly adopt Mixup to augment graph data because different graphs typically: 1) have different numbers of nodes; 2) are not readily aligned; and 3) have unique typologies in non-Euclidean space. To this end, we propose G-Mixup to augment graphs for graph classification by interpolating the generator (i.e., graphon) of different classes of graphs. Specifically, we first use graphs within the same class to estimate a graphon. Then, instead of directly manipulating graphs, we interpolate graphons of different classes in the Euclidean space to get mixed graphons, where the synthetic graphs are generated through sampling based on the mixed graphons. Extensive experiments show that G-Mixup substantially improves the generalization and robustness of GNNs.

A large number of neural network models of associative memory have been proposed in the literature. These include the classical Hopfield networks (HNs), sparse distributed memories (SDMs), and more recently the modern continuous Hopfield networks (MCHNs), which possess close links with self-attention in machine learning. In this paper, we propose a general framework for understanding the operation of such memory networks as a sequence of three operations: similarity, separation, and projection. We derive all these memory models as instances of our general framework with differing similarity and separation functions. We extend the mathematical framework of Krotov et al (2020) to express general associative memory models using neural network dynamics with local computation, and derive a general energy function that is a Lyapunov function of the dynamics. Finally, using our framework, we empirically investigate the capacity of using different similarity functions for these associative memory models, beyond the dot product similarity measure, and demonstrate empirically that Euclidean or Manhattan distance similarity metrics perform substantially better in practice on many tasks, enabling a more robust retrieval and higher memory capacity than existing~models.

Most existing methods in vision language pre-training rely on object-centric features extracted through object detection and make fine-grained alignments between the extracted features and texts. It is challenging for these methods to learn relations among multiple objects. To this end, we propose a new method called X-VLM to perform `multi-grained vision language pre-training.' The key to learning multi-grained alignments is to locate visual concepts in the image given the associated texts, and in the meantime align the texts with the visual concepts, where the alignments are in multi-granularity. Experimental results show that X-VLM effectively leverages the learned multi-grained alignments to many downstream vision language tasks and consistently outperforms state-of-the-art methods.

We introduce a new training paradigm that enforces interval constraints on neural network parameter space to control forgetting. Contemporary Continual Learning (CL) methods focus on training neural networks efficiently from a stream of data, while reducing the negative impact of catastrophic forgetting, yet they do not provide any firm guarantees that network performance will not deteriorate uncontrollably over time. In this work, we show how to put bounds on forgetting by reformulating continual learning of a model as a continual contraction of its parameter space. To that end, we propose Hyperrectangle Training, a new training methodology where each task is represented by a hyperrectangle in the parameter space, fully contained in the hyperrectangles of the previous tasks. This formulation reduces the NP-hard CL problem back to polynomial time while providing full resilience against forgetting. We validate our claim by developing InterContiNet (Interval Continual Learning) algorithm which leverages interval arithmetic to effectively model parameter regions as hyperrectangles. Through experimental results, we show that our approach performs well in a continual learning setup without storing data from previous tasks.

We consider the question of speeding up classic graph algorithms with machine-learned predictions. In this model, algorithms are furnished with extra advice learned from past or similar instances. Given the additional information, we aim to improve upon the traditional worst-case run-time guarantees. Our contributions are the following:(i) We give a faster algorithm for minimum-weight bipartite matching via learned duals, improving the recent result by Dinitz, Im, Lavastida, Moseley and Vassilvitskii (NeurIPS, 2021);(ii) We extend the learned dual approach to the single-source shortest path problem (with negative edge lengths), achieving an almost linear runtime given sufficiently accurate predictions which improves upon the classic fastest algorithm due to Goldberg (SIAM J. Comput., 1995);(iii) We provide a general reduction-based framework for learning-based graph algorithms, leading to new algorithms for degree-constrained subgraph and minimum-cost 0-1 flow, based on reductions to bipartite matching and the shortest path problem.Finally, we give a set of general learnability theorems, showing that the predictions required by our algorithms can be efficiently learned in a PAC fashion.

Detecting communities in real-world networks and clustering similarity graphs are major data mining tasks with a wide range of applications in graph mining, collaborative filtering, and bioinformatics. In many such applications, overwhelming empirical evidence suggests that communities and clusters are naturally overlapping, i.e., the boundary of a cluster may contain both edges across clusters and nodes that are shared with other clusters, calling for novel hybrid graph partitioning algorithms (HGP). While almost-linear-time approximation algorithms are known for edge-boundary-based graph partitioning, little progress has been made on fast algorithms for HGP, even in the special case of vertex-boundary-based graph partitioning. In this work, we introduce a frame-work based on two novel clustering objectives, which naturally extend the well-studied notion of conductance to clusters with hybrid vertex-and edge-boundary structure. Our main algorithmic contributions are almost-linear-time algorithms O(log n)-approximation algorithms for both these objectives. To this end, we show that the cut-matching framework of (Khandekar et al., 2014) can be significantly extended to incorporate hybrid partitions. Crucially, we implement our approximation algorithm to produce both hybrid partitions and optimality certificates for large graphs, easily scaling to tens of millions of edges, and test our implementation on real-world datasets against other competitive baselines.

We consider two key issues faced by many clustering methods when used for data summarization, namely (a) an unfair representation of "demographic groups'' and (b) distorted summarizations, where data points in the summary represent subsets of the original data of vastly different sizes. Previous work made important steps towards handling separately each of these two issues in the context of the fundamental k-Center clustering objective through the study of fast algorithms for natural models that address them.We show that it is possible to effectively address both (a) and (b) simultaneously by presenting a clustering procedure that works for a canonical combined model and(i) is fast, both in theory and practice,(ii) exhibits a worst-case constant-factor guarantee, and (iii) gives promising computational results showing that there can be significant benefits in addressing both issues together instead of sequentially.

In the correlation clustering problem the input is a signed graph where the sign indicates whether each pair of points should be placed in the same cluster or not. The goal of the problem is to compute a clustering which minimizes the number of disagreements with such recommendation. Thanks to its many practical applications, correlation clustering is a fundamental unsupervised learning problem and has been extensively studied in many different settings. In this paper we study the problem in the classic online setting with recourse; The vertices of the graphs arrive in an online manner and the goal is to maintain an approximate clustering while minimizing the number of times each vertex changes cluster. Our main contribution is an algorithm that achieves logarithmic recourse per vertex in the worst case. We also complement this result with a tight lower bound. Finally we show experimentally that our algorithm achieves better performances than state-of-the-art algorithms on real world data.

In problems involving matrix computations, the concept of leverage has found a large number of applications. In particular, leverage scores, which relate the columns of a matrix to the subspaces spanned by its leading singular vectors, are helpful in revealing column subsets to approximately factorize a matrix with quality guarantees. As such, they provide a solid foundation for a variety of machine-learning methods. In this paper we extend the definition of leverage scores to relate the columns of a matrix to arbitrary subsets of singular vectors. We establish a precise connection between column and singular-vector subsets, by relating the concepts of leverage scores and principal angles between subspaces. We employ this result to design approximation algorithms with provable guarantees for two well-known problems: generalized column subset selection and sparse canonical correlation analysis. We run numerical experiments to provide further insight on the proposed methods. The novel bounds we derive improve our understanding of fundamental concepts in matrix approximations. In addition, our insights may serve as building blocks for further contributions.

Dynamic topic models explore the time evolution of topics in temporally accumulative corpora. While existing topic models focus on the dynamics of individual documents, we propose two neural topic models aimed at learning unified topic distributions that incorporate both document dynamics and network structure. For the first model, by adding a time dimension, we propose Time-Aware Optimal Transport, which measures the probability of a link between two differently timestamped documents using their semantic distance. Since the gradually evolving topological structure of network may also influence the establishment of a new link, for the second model, we further design a Temporal Point Process to capture the impact of historical neighbors on the current link formation at the network level. Experiments on four dynamic document networks demonstrate the advantage of our models in jointly modeling document dynamics and network adjacency.

Contemporary predictive models are hard to interpret as their deep nets exploit numerous complex relations between input elements. This work suggests a theoretical framework for model interpretability by measuring the contribution of relevant features to the functional entropy of the network with respect to the input. We rely on the log-Sobolev inequality that bounds the functional entropy by the functional Fisher information with respect to the covariance of the data. This provides a principled way to measure the amount of information contribution of a subset of features to the decision function. Through extensive experiments, we show that our method surpasses existing interpretability sampling-based methods on various data signals such as image, text, and audio.

In the pursuit of optimizing memory and compute density to accelerate machine learning applications, reduced precision training and inference has been an active area of research. While some approaches selectively apply low precision computations, this may require costly off-chip data transfers or mixed precision support. In this paper, we propose a novel numerical representation, Adaptive Floating Point (AFP), that dynamically adjusts to the characteristics of deep learning data. AFP requires no changes to the model topology, requires no additional training, and applies to all layers of DNN models. We evaluate AFP on aspectrum of representative models in computer vision and NLP, and show that our technique enables ultra-low precision inference of deep learning models while providing accuracy comparable to full precision inference. By dynamically adjusting to ML data, AFP increases memory density by 1.6x, 1.6x, and 3.2x and compute density by 4x, 1.3x, and 12x when compared to BFP, BFloat16, and FP32.

Neural networks are increasingly being used to solve partial differential equations (PDEs), replacing slower numerical solvers. However, a critical issue is that neural PDE solvers require high-quality ground truth data, which usually must come from the very solvers they are designed to replace. Thus, we are presented with a proverbial chicken-and-egg problem. In this paper, we present a method, which can partially alleviate this problem, by improving neural PDE solver sample complexity---Lie point symmetry data augmentation (LPSDA). In the context of PDEs, it turns out we are able to quantitatively derive an exhaustive list of data transformations, based on the Lie point symmetry group of the PDEs in question, something not possible in other application areas. We present this framework and demonstrate how it can easily be deployed to improve neural PDE solver sample complexity by an order of magnitude.

Learning with adversarial robustness has been a challenge in contemporary machine learning, and recent years have witnessed increasing attention on robust decision trees and ensembles, mostly working with high computational complexity or without guarantees of provable robustness. This work proposes the Fast Provably Robust Decision Tree (FPRDT) with the smallest computational complexity O(n log n), a tradeoff between global and local optimizations over the adversarial 0/1 loss. We further develop the Provably Robust AdaBoost (PRAdaBoost) according to our robust decision trees, and present convergence analysis for training adversarial 0/1 loss. We conduct extensive experiments to support our approaches; in particular, our approaches are superior to those unprovably robust methods, and achieve better or comparable performance to those provably robust methods yet with the smallest running time.

Optimal transport is a framework for comparing measures whereby a cost is incurred for transporting one measure to another. Recent works have aimed to improve optimal transport plans through the introduction of various forms of structure. We introduce novel order constraints into the optimal transport formulation to allow for the incorporation of structure. We define an efficient method for obtaining explainable solutions to the new formulation that scales far better than standard approaches. The theoretical properties of the method are provided. We demonstrate experimentally that order constraints improve explainability using the e-SNLI (Stanford Natural Language Inference) dataset that includes human-annotated rationales as well as on several image color transfer examples.

We derive analytic bounds on the noise invariance of majority vote classifiers operating on compressed inputs. Specifically, starting from recent bounds on the true risk of majority vote classifiers, we extend the applicability of PAC-Bayesian theory to quantify the resilience of majority votes to input noise stemming from compression. The derived bounds are intuitive in binary classification settings, where they can be measured as expressions of voter differentials and voter pair agreement. By combining measures of input distortion with analytic guarantees on noise invariance, we prescribe rate-efficient machines to compress inputs without affecting subsequent classification. Our validation shows how bounding noise invariance can inform the compression stage for any majority vote classifier such that worst-case implications of bad input reconstructions are known, and inputs can be compressed to the minimum amount of information needed prior to inference.

Recent papers have developed alternating least squares (ALS) methods for CP and tensor ring decomposition with a per-iteration cost which is sublinear in the number of input tensor entries for low-rank decomposition. However, the per-iteration cost of these methods still has an exponential dependence on the number of tensor modes when parameters are chosen to achieve certain worst-case guarantees. In this paper, we propose sampling-based ALS methods for the CP and tensor ring decompositions whose cost does not have this exponential dependence, thereby significantly improving on the previous state-of-the-art. We provide a detailed theoretical analysis and also apply the methods in a feature extraction experiment.

Model-agnostic meta learning (MAML) is currently one of the dominating approaches for few-shot meta-learning. Albeit its effectiveness, the training of MAML can be challenging due to the innate bilevel problem structure. Specifically, the loss landscape of MAML is much complex with possibly many more saddle points and local minima than its empirical risk minimization counterpart. To address this challenge, we leverage the recently invented sharpness-aware minimization and develop a sharpness-aware MAML approach that we term Sharp-MAML. We empirically demonstrate that Sharp-MAML and its computation-efficient variant can outperform popular existing MAML baselines (e.g., +12% accuracy on Mini-Imagenet). We complement the empirical study with the convergence analysis and the generalization bound of Sharp-MAML. To the best of our knowledge, this is the first empirical and theoretical study on sharpness-aware minimization in the context of bilevel optimization.

The recent focus on the efficiency of deep neural networks (DNNs) has led to significant work on model compression approaches, of which weight pruning is one of the most popular.At the same time, there is rapidly-growing computational support for efficiently executing the unstructured-sparse models obtained via pruning. Yet, most existing pruning methods minimize just the number of remaining weights, i.e. the size of the model, rather than optimizing for inference time.We address this gap by introducing SPDY, a new compression method which automatically determines layer-wise sparsity targets achieving a desired inference speedup on a given system, while minimizing accuracy loss. SPDY is the composition of two new techniques. The first is an efficient and general dynamic programming algorithm for solving constrained layer-wise compression problems, given a set of layer-wise error scores.The second technique is a local search procedure for automatically determining such scores in an accurate and robust manner.Experiments across popular vision and language models show that SPDY guarantees speedups while recovering higher accuracy relative to existing strategies, both for one-shot and gradual pruning scenarios, and is compatible with most existing pruning approaches. We also extend our approach to the recently-proposed task of pruning with very little data, where we …

As the computational requirements for machine learning systems and the size and complexity of machine learning frameworks increases, essential framework innovation has become challenging. While computational needs have driven recent compiler, networking, and hardware advancements, utilization of those advancements by machine learning tools is occurring at a slower pace. This is in part due to the difficulties involved in prototyping new computational paradigms with existing frameworks. Large frameworks prioritize machine learning researchers and practitioners as end users and pay comparatively little attention to systems researchers who can push frameworks forward --- we argue that both are equally important stakeholders. We introduce Flashlight, an open-source library built to spur innovation in machine learning tools and systems by prioritizing open, modular, customizable internals and state-of-the-art, research-ready models and training setups across a variety of domains. Flashlight allows systems researchers to rapidly prototype and experiment with novel ideas in machine learning computation and has low overhead, competing with and often outperforming other popular machine learning frameworks. We see Flashlight as a tool enabling research that can benefit widely used libraries downstream and bring machine learning and systems researchers closer together.

This work addresses meta-learning (ML) by considering deep networks with stochastic local winner-takes-all (LWTA) activations. This type of network units results in sparse representations from each model layer, as the units are organized into blocks where only one unit generates a non-zero output. The main operating principle of the introduced units rely on stochastic principles, as the network performs posterior sampling over competing units to select the winner. Therefore, the proposed networks are explicitly designed to extract input data representations of sparse stochastic nature, as opposed to the currently standard deterministic representation paradigm. Our approach produces state-of-the-art predictive accuracy on few-shot image classification and regression experiments, as well as reduced predictive error on an active learning setting; these improvements come with an immensely reduced computational cost. Code is available at: https://github.com/Kkalais/StochLWTA-ML

Tensor decomposition is a fundamental framework to analyze data that can be represented by multi-dimensional arrays. In practice, tensor data are often accompanied with temporal information, namely the time points when the entry values were generated. This information implies abundant, complex temporal variation patterns. However, current methods always assume the factor representations of the entities in each tensor mode are static, and never consider their temporal evolution. To fill this gap, we propose NONparametric FActor Trajectory learning for dynamic tensor decomposition (NONFAT). We place Gaussian process (GP) priors in the frequency domain and conduct inverse Fourier transform via Gauss-Laguerre quadrature to sample the trajectory functions. In this way, we can overcome data sparsity and obtain robust trajectory estimates across long time horizons. Given the trajectory values at specific time points, we use a second-level GP to sample the entry values and to capture the temporal relationship between the entities. For efficient and scalable inference, we leverage the matrix Gaussian structure in the model, introduce a matrix Gaussian posterior, and develop a nested sparse variational learning algorithm. We have shown the advantage of our method in several real-world applications.

High-order interaction events are common in real-world applications. Learning embeddings that encode the complex relationships of the participants from these events is of great importance in knowledge mining and predictive tasks. Despite the success of existing approaches, e.g. Poisson tensor factorization, they ignore the sparse structure underlying the data, namely the occurred interactions are far less than the possible interactions among all the participants. In this paper, we propose Nonparametric Embeddings of Sparse High-order interaction events (NESH). We hybridize a sparse hypergraph (tensor) process and a matrix Gaussian process to capture both the asymptotic structural sparsity within the interactions and nonlinear temporal relationships between the participants. We prove strong asymptotic bounds (including both a lower and an upper bound ) of the sparse ratio, which reveals the asymptotic properties of the sampled structure. We use batch-normalization, stick-breaking construction and sparse variational GP approximations to develop an efficient, scalable model inference algorithm. We demonstrate the advantage of our approach in several real-world applications.

The linearised Laplace method for estimating model uncertainty has received renewed attention in the Bayesian deep learning community. The method provides reliable error bars and admits a closed-form expression for the model evidence, allowing for scalable selection of model hyperparameters. In this work, we examine the assumptions behind this method, particularly in conjunction with model selection.We show that these interact poorly with some now-standard tools of deep learning--stochastic approximation methods and normalisation layers--and make recommendations for how to better adapt this classic method to the modern setting.We provide theoretical support for our recommendations and validate them empirically on MLPs, classic CNNs, residual networks with and without normalisation layers, generative autoencoders and transformers.

We study methods for estimating model uncertainty for neural networks (NNs) in regression. To isolate the effect of model uncertainty, we focus on a noiseless setting with scarce training data. We introduce five important desiderata regarding model uncertainty that any method should satisfy. However, we find that established benchmarks often fail to reliably capture some of these desiderata, even those that are required by Bayesian theory. To address this, we introduce a new approach for capturing model uncertainty for NNs, which we call Neural Optimization-based Model Uncertainty (NOMU). The main idea of NOMU is to design a network architecture consisting of two connected sub-NNs, one for model prediction and one for model uncertainty, and to train it using a carefully-designed loss function. Importantly, our design enforces that NOMU satisfies our five desiderata. Due to its modular architecture, NOMU can provide model uncertainty for any given (previously trained) NN if given access to its training data. We evaluate NOMU in various regressions tasks and noiseless Bayesian optimization (BO) with costly evaluations. In regression, NOMU performs at least as well as state-of-the-art methods. In BO, NOMU even outperforms all considered benchmarks.

How do we compare between hypotheses that are entirely consistent with observations? The marginal likelihood (aka Bayesian evidence), which represents the probability of generating our observations from a prior, provides a distinctive approach to this foundational question, automatically encoding Occam's razor. Although it has been observed that the marginal likelihood can overfit and is sensitive to prior assumptions, its limitations for hyperparameter learning and discrete model comparison have not been thoroughly investigated. We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing. We then highlight the conceptual and practical issues in using the marginal likelihood as a proxy for generalization. Namely, we show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search, and can lead to both underfitting and overfitting in hyperparameter learning. We provide a partial remedy through a conditional marginal likelihood, which we show is more aligned with generalization, and practically valuable for large-scale hyperparameter learning, such as in deep kernel learning.

PAC-Bayesian error bounds provide a theoretical guarantee on the generalization abilities of meta-learning from training tasks to unseen tasks. However, it is still unclear how tight PAC-Bayesian bounds we can achieve for meta-learning. In this work, we propose a general PAC-Bayesian framework to cope with single-task learning and meta-learning uniformly. With this framework, we generalize the two tightest PAC-Bayesian bounds (i.e., kl-bound and Catoni-bound) from single-task learning to standard meta-learning, resulting in fast convergence rates for PAC-Bayesian meta-learners. By minimizing the derived two bounds, we develop two meta-learning algorithms for classification problems with deep neural networks. For regression problems, by setting Gibbs optimal posterior for each training task, we obtain the closed-form formula of the minimizer of our Catoni-bound, leading to an efficient Gibbs meta-learning algorithm. Although minimizing our kl-bound can not yield a closed-form solution, we show that it can be extended for analyzing the more challenging meta-learning setting where samples from different training tasks exhibit interdependencies. Experiments empirically show that our proposed meta-learning algorithms achieve competitive results with respect to latest works.

A primary focus area in continual learning research is alleviating the "catastrophic forgetting" problem in neural networks by designing new algorithms that are more robust to the distribution shifts. While the recent progress in continual learning literature is encouraging, our understanding of what properties of neural networks contribute to catastrophic forgetting is still limited. To address this, instead of focusing on continual learning algorithms, in this work, we focus on the model itself and study the impact of "width" of the neural network architecture on catastrophic forgetting, and show that width has a surprisingly significant effect on forgetting. To explain this effect, we study the learning dynamics of the network from various perspectives such as gradient orthogonality, sparsity, and lazy training regime. We provide potential explanations that are consistent with the empirical results across different architectures and continual learning benchmarks.

Meta learning automatically infers an inductivebias, that includes the hyperparameter of the baselearningalgorithm, by observing data from a finitenumber of related tasks. This paper studiesPAC-Bayes bounds on meta generalizationgap. The meta-generalization gap comprises twosources of generalization gaps: the environmentleveland task-level gaps resulting from observationof a finite number of tasks and data samplesper task, respectively. In this paper, by upperbounding arbitrary convex functions, which linkthe expected and empirical losses at the environmentand also per-task levels, we obtain new PAC-Bayesbounds. Using these bounds, we developnew PAC-Bayes meta-learning algorithms. Numericalexamples demonstrate the merits of theproposed novel bounds and algorithm in comparisonto prior PAC-Bayes bounds for meta-learning

Recent empirical evidence has driven conventional wisdom to believe that gradient-based meta-learning (GBML) methods perform well at few-shot learning because they learn an expressive data representation that is shared across tasks. However, the mechanics of GBML have remained largely mysterious from a theoretical perspective. In this paper, we prove that two well-known GBML methods, MAML and ANIL, as well as their first-order approximations, are capable of learning common representation among a set of given tasks. Specifically, in the well-known multi-task linear representation learning setting, they are able to recover the ground-truth representation at an exponentially fast rate. Moreover, our analysis illuminates that the driving force causing MAML and ANIL to recover the underlying representation is that they adapt the final layer of their model, which harnesses the underlying task diversity to improve the representation in all directions of interest. To the best of our knowledge, these are the first results to show that MAML and/or ANIL learn expressive representations and to rigorously explain why they do so.

Minwise hashing (MinHash) is an important and practical algorithm for generating random hashes to approximate the Jaccard (resemblance) similarity in massive binary (0/1) data. The basic theory of MinHash requires applying hundreds or even thousands of independent random permutations to each data vector in the dataset, in order to obtain reliable results for (e.g.,) building large-scale learning models or approximate near neighbor search. In this paper, we propose Circulant MinHash (C-MinHash) and provide the surprising theoretical results that using only two independent random permutations in a circulant manner leads to uniformly smaller Jaccard estimation variance than that of the classical MinHash with K independent permutations. Experiments are conducted to show the effectiveness of the proposed method. We also propose a more convenient C-MinHash variant which reduces two permutations to just one, with extensive numerical results to validate that it achieves essentially the same estimation accuracy as using two permutations.

Plug-and-Play (PnP) methods solve ill-posed inverse problems through iterative proximal algorithms by replacing a proximal operator by a denoising operation. When applied with deep neural network denoisers, these methods have shown state-of-the-art visual performance for image restoration problems. However, their theoretical convergence analysis is still incomplete. Most of the existing convergence results consider nonexpansive denoisers, which is non-realistic, or limit their analysis to strongly convex data-fidelity terms in the inverse problem to solve. Recently, it was proposed to train the denoiser as a gradient descent step on a functional parameterized by a deep neural network. Using such a denoiser guarantees the convergence of the PnP version of the Half-Quadratic-Splitting (PnP-HQS) iterative algorithm. In this paper, we show that this gradient denoiser can actually correspond to the proximal operator of another scalar function. Given this new result, we exploit the convergence theory of proximal algorithms in the nonconvex setting to obtain convergence results for PnP-PGD (Proximal Gradient Descent) and PnP-ADMM (Alternating Direction Method of Multipliers). When built on top of a smooth gradient denoiser, we show that PnP-PGD and PnP-ADMM are convergent and target stationary points of an explicit functional. These convergence results are confirmed with numerical experiments on deblurring, super-resolution …

Maximizing a monotone k-submodular function subject to cardinality constraints is a general model for several applications ranging from influence maximization with multiple products to sensor placement with multiple sensor types and online ad allocation. Due to the large problem scale in many applications and the online nature of ad allocation, a need arises for algorithms that process elements in a streaming fashion and possibly make online decisions. In this work, we develop a new streaming algorithm for maximizing a monotone k-submodular function subject to a per-coordinate cardinality constraint attaining an approximation guarantee close to the state of the art guarantee in the offline setting. Though not typical for streaming algorithms, our streaming algorithm also readily applies to the online setting with free disposal. Our algorithm is combinatorial and enjoys fast running time and small number of function evaluations. Furthermore, its guarantee improves as the cardinality constraints get larger, which is especially suited for the large scale applications. For the special case of maximizing a submodular function with large budgets, our combinatorial algorithm matches the guarantee of the state-of-the-art continuous algorithm, which requires significantly more time and function evaluations.

Training machine learning models on massive datasets incurs substantialcomputational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the training examples that generalize on par with the full training data. However, existing methods are limited in providing theoretical guarantees for the quality of the models trained on the extracted subsets, and may perform poorly in practice. We propose AdaCore, a method that leverages the geometry of the data to extract subsets of the training examples for efficient machine learning. The key idea behind our method is to dynamically approximate the curvature of the loss function via an exponentially-averaged estimate of the Hessian to select weighted subsets (coresets) that provide a close approximation of the full gradient preconditioned with the Hessian. We prove rigorous guarantees for the convergence of various first and second-order methods applied to the subsets chosen by AdaCore. Our extensive experiments show that AdaCore extracts coresets with higher quality compared to baselines and speeds up training of convex and non-convex machine learning models, such as logistic regression and neural networks, by over 2.9x over the full data and 4.5x over random subsets.

In this paper, we extend a Burer-Monteiro style method to compute low rank Semi-Definite Programming (SDP) bounds for the MAP problem on discrete graphical models with an arbitrary number of states and arbitrary pairwise potentials. We consider both a penalized constraint approach and a dedicated Block Coordinate Descent (BCD) approach which avoids large penalty coefficients in the cost matrix. We show our algorithm is decreasing. Experiments show that the BCD approach compares favorably to the penalized approach and to usual linear bounds relying on convergent message passing approaches.

Neural networks tend to achieve better accuracy with training if they are larger — even if the resulting models are overparameterized. Nevertheless, carefully removing such excess of parameters before, during, or after training may also produce models with similar or even improved accuracy. In many cases, that can be curiously achieved by heuristics as simple as removing a percentage of the weights with the smallest absolute value — even though absolute value is not a perfect proxy for weight relevance. With the premise that obtaining significantly better performance from pruning depends on accounting for the combined effect of removing multiple weights, we revisit one of the classic approaches for impact-based pruning: the Optimal Brain Surgeon (OBS). We propose a tractable heuristic for solving the combinatorial extension of OBS, in which we select weights for simultaneous removal, and we combine it with a single-pass systematic update of unpruned weights. Our selection method outperforms other methods for high sparsity, and the single-pass weight update is also advantageous if applied after those methods.

Reinforcement learning (RL) is inefficient on long-horizon tasks due to sparse rewards and its policy can be fragile to slightly perturbed environments. We address these challenges via a curriculum of tasks with coupled environments, generated by two policies trained jointly with RL: (1) a co-operative planning policy recursively decomposing a hard task into a coarse-to-fine sub-task tree; and (2) an adversarial policy modifying the environment in each sub-task. They are complementary to acquire more informative feedback for RL: (1) provides dense reward of easier sub-tasks while (2) modifies sub-tasks' environments to be more challenging and diverse. Conversely, they are trained by RL's dense feedback on sub-tasks so their generated curriculum keeps adaptive to RL's progress. The sub-task tree enables an easy-to-hard curriculum for every policy: its top-down construction gradually increases sub-tasks the planner needs to generate, while the adversarial training between the environment and RL follows a bottom-up traversal that starts from a dense sequence of easier sub-tasks allowing more frequent environment changes. We compare EAT-C with RL/planning targeting similar problems and methods with environment generators or adversarial agents. Extensive experiments on diverse tasks demonstrate the advantages of our method on improving RL's efficiency and generalization.

Inferring the abstract relational and causal structure of the world is a major challenge for reinforcement-learning (RL) agents. For humans, language—particularly in the form of explanations—plays a considerable role in overcoming this challenge. Here, we show that language can play a similar role for deep RL agents in complex environments. While agents typically struggle to acquire relational and causal knowledge, augmenting their experience by training them to predict language descriptions and explanations can overcome these limitations. We show that language can help agents learn challenging relational tasks, and examine which aspects of language contribute to its benefits. We then show that explanations can help agents to infer not only relational but also causal structure. Language can shape the way that agents to generalize out-of-distribution from ambiguous, causally-confounded training, and explanations even allow agents to learn to perform experimental interventions to identify causal relationships. Our results suggest that language description and explanation may be powerful tools for improving agent learning and generalization.

Offline reinforcement learning leverages large datasets to train policies without interactions with the environment. The learned policies may then be deployed in real-world settings where interactions are costly or dangerous. Current algorithms over-fit to the training dataset and as a consequence perform poorly when deployed to out-of-distribution generalizations of the environment. We aim to address these limitations by learning a Koopman latent representation which allows us to infer symmetries of the system's underlying dynamic. The latter is then utilized to extend the otherwise static offline dataset during training; this constitutes a novel data augmentation framework which reflects the system's dynamic and is thus to be interpreted as an exploration of the environments phase space. To obtain the symmetries we employ Koopman theory in which nonlinear dynamics are represented in terms of a linear operator acting on the space of measurement functions of the system. We provide novel theoretical results on the existence and nature of symmetries relevant for control systems such as reinforcement learning settings. Moreover, we empirically evaluate our method on several benchmark offline reinforcement learning tasks and datasets including D4RL, Metaworld and Robosuite and find that by using our framework we consistently improve the state-of-the-art of model-free Q-learning …

We introduce a method for policy improvement that interpolates between the greedy approach of value-based reinforcement learning (RL) and the full planning approach typical of model-based RL. The new method builds on the concept of a geometric horizon model (GHM, also known as a \gamma-model), which models the discounted state-visitation distribution of a given policy. We show that we can evaluate any non-Markov policy that switches between a set of base Markov policies with fixed probability by a careful composition of the base policy GHMs, without any additional learning. We can then apply generalised policy improvement (GPI) to collections of such non-Markov policies to obtain a new Markov policy that will in general outperform its precursors. We provide a thorough theoretical analysis of this approach, develop applications to transfer and standard RL, and empirically demonstrate its effectiveness over standard GPI on a challenging deep RL continuous control task. We also provide an analysis of GHM training methods, proving a novel convergence result regarding previously proposed methods and showing how to train these models stably in deep RL settings.

Meta-reinforcement learning (RL) methods can meta-train policies that adapt to new tasks with orders of magnitude less data than standard RL, but meta-training itself is costly and time-consuming. If we can meta-train on offline data, then we can reuse the same static dataset, labeled once with rewards for different tasks, to meta-train policies that adapt to a variety of new tasks at meta-test time. Although this capability would make meta-RL a practical tool for real-world use, offline meta-RL presents additional challenges beyond online meta-RL or standard offline RL settings. Meta-RL learns an exploration strategy that collects data for adapting, and also meta-trains a policy that quickly adapts to data from a new task. Since this policy was meta-trained on a fixed, offline dataset, it might behave unpredictably when adapting to data collected by the learned exploration strategy, which differs systematically from the offline data and thus induces distributional shift. We propose a hybrid offline meta-RL algorithm, which uses offline data with rewards to meta-train an adaptive policy, and then collects additional unsupervised online data, without any reward labels to bridge this distribution shift. By not requiring reward labels for online collection, this data can be much cheaper to collect. We …

Entropy regularization is a popular method in reinforcement learning (RL). Although it has many advantages, it alters the RL objective and makes the converged policy deviate from the optimal policy of the original Markov Decision Process (MDP). Though divergence regularization has been proposed to settle this problem, it cannot be trivially applied to cooperative multi-agent reinforcement learning (MARL). In this paper, we investigate divergence regularization in cooperative MARL and propose a novel off-policy cooperative MARL framework, divergence-regularized multi-agent actor-critic (DMAC). Theoretically, we derive the update rule of DMAC which is naturally off-policy, guarantees the monotonic policy improvement and convergence in both the original MDP and the divergence-regularized MDP, and is not biased by the regularization. We also give a bound of the discrepancy between the converged policy and the optimal policy in the original MDP. DMAC is a flexible framework and can be combined with many existing MARL algorithms. Empirically, we evaluate DMAC in a didactic stochastic game and StarCraft Multi-Agent Challenge and show that DMAC substantially improves the performance of existing MARL algorithms.

The REINFORCE algorithm \cite{williams1992simple} is popular in policy gradient (PG) for solving reinforcement learning (RL) problems. Meanwhile, the theoretical form of PG is from~\cite{sutton1999policy}. Although both formulae prescribe PG, their precise connections are not yet illustrated. Recently, \citeauthor{nota2020policy} (\citeyear{nota2020policy}) have found that the ambiguity causes implementation errors. Motivated by the ambiguity and implementation incorrectness, we study PG from a perturbation perspective. In particular, we derive PG in a unified framework, precisely clarify the relation between PG implementation and theory, and echos back the findings by \citeauthor{nota2020policy}. Diving into factors contributing to empirical successes of the existing erroneous implementations, we find that small approximation error and the experience replay mechanism play critical roles.

We study deep reinforcement learning (RL) algorithms with delayed rewards. In many real-world tasks, instant rewards are often not readily accessible or even defined immediately after the agent performs actions. In this work, we first formally define the environment with delayed rewards and discuss the challenges raised due to the non-Markovian nature of such environments. Then, we introduce a general off-policy RL framework with a new Q-function formulation that can handle the delayed rewards with theoretical convergence guarantees. For practical tasks with high dimensional state spaces, we further introduce the HC-decomposition rule of the Q-function in our framework which naturally leads to an approximation scheme that helps boost the training efficiency and stability. We finally conduct extensive experiments to demonstrate the superior performance of our algorithms over the existing work and their variants.

The standard formulation of Reinforcement Learning lacks a practical way of specifying what are admissible and forbidden behaviors. Most often, practitioners go about the task of behavior specification by manually engineering the reward function, a counter-intuitive process that requires several iterations and is prone to reward hacking by the agent. In this work, we argue that constrained RL, which has almost exclusively been used for safe RL, also has the potential to significantly reduce the amount of work spent for reward specification in applied RL projects. To this end, we propose to specify behavioral preferences in the CMDP framework and to use Lagrangian methods to automatically weigh each of these behavioral constraints. Specifically, we investigate how CMDPs can be adapted to solve goal-based tasks while adhering to several constraints simultaneously. We evaluate this framework on a set of continuous control tasks relevant to the application of Reinforcement Learning for NPC design in video games.

Several algorithms have been proposed to sample non-uniformly the replay buffer of deep Reinforcement Learning (RL) agents to speed-up learning, but very few theoretical foundations of these sampling schemes have been provided. Among others, Prioritized Experience Replay appears as a hyperparameter sensitive heuristic, even though it can provide good performance. In this work, we cast the replay buffer sampling problem as an importance sampling one for estimating the gradient. This allows deriving the theoretically optimal sampling distribution, yielding the best theoretical convergence speed.Elaborating on the knowledge of the ideal sampling scheme, we exhibit new theoretical foundations of Prioritized Experience Replay. The optimal sampling distribution being intractable, we make several approximations providing good results in practice and introduce, among others, LaBER (Large Batch Experience Replay), an easy-to-code and efficient method for sampling the replay buffer. LaBER, which can be combined with Deep Q-Networks, distributional RL agents or actor-critic methods, yields improved performance over a diverse range of Atari games and PyBullet environments, compared to the base agent it is implemented on and to other prioritization schemes.

Training generally-capable agents with reinforcement learning (RL) remains a significant challenge. A promising avenue for improving the robustness of RL agents is through the use of curricula. One such class of methods frames environment design as a game between a student and a teacher, using regret-based objectives to produce environment instantiations (or levels) at the frontier of the student agent's capabilities. These methods benefit from theoretical robustness guarantees at equilibrium, yet they often struggle to find effective levels in challenging design spaces in practice. By contrast, evolutionary approaches incrementally alter environment complexity, resulting in potentially open-ended learning, but often rely on domain-specific heuristics and vast amounts of computational resources. This work proposes harnessing the power of evolution in a principled, regret-based curriculum. Our approach, which we call Adversarially Compounding Complexity by Editing Levels (ACCEL), seeks to constantly produce levels at the frontier of an agent's capabilities, resulting in curricula that start simple but become increasingly complex. ACCEL maintains the theoretical benefits of prior regret-based methods, while providing significant empirical gains in a diverse set of environments. An interactive version of this paper is available at https://accelagent.github.io.

Despite considerable advances in deep reinforcement learning, it has been shown to be highly vulnerable to adversarial perturbations to state observations. Recent efforts that have attempted to improve adversarial robustness of reinforcement learning can nevertheless tolerate only very small perturbations, and remain fragile as perturbation size increases. We propose Bootstrapped Opportunistic Adversarial Curriculum Learning (BCL), a novel flexible adversarial curriculum learning framework for robust reinforcement learning. Our framework combines two ideas: conservatively bootstrapping each curriculum phase with highest quality solutions obtained from multiple runs of the previous phase, and opportunistically skipping forward in the curriculum. In our experiments we show that the proposed BCL framework enables dramatic improvements in robustness of learned policies to adversarial perturbations. The greatest improvement is for Pong, where our framework yields robustness to perturbations of up to 25/255; in contrast, the best existing approach can only tolerate adversarial noise up to 5/255. Our code is available at: https://github.com/jlwu002/BCL.

The transformer architecture and variants presented a remarkable success across many machine learning tasks in recent years. This success is intrinsically related to the capability of handling long sequences and the presence of context-dependent weights from the attention mechanism. We argue that these capabilities suit the central role of a Meta-Reinforcement Learning algorithm. Indeed, a meta-RL agent needs to infer the task from a sequence of trajectories. Furthermore, it requires a fast adaptation strategy to adapt its policy for a new task - which can be achieved using the self-attention mechanism. In this work, we present TrMRL (Transformers for Meta-Reinforcement Learning), a meta-RL agent that mimics the memory reinstatement mechanism using the transformer architecture. It associates the recent past of working memories to build an episodic memory recursively through the transformer layers. We show that the self-attention computes a consensus representation that minimizes the Bayes Risk at each layer and provides meaningful features to compute the best actions. We conducted experiments in high-dimensional continuous control environments for locomotion and dexterous manipulation. Results show that TrMRL presents comparable or superior asymptotic performance, sample efficiency, and out-of-distribution generalization compared to the baselines in these environments.

In temporal-difference reinforcement learning algorithms, variance in value estimation can cause instability and overestimation of the maximal target value. Many algorithms have been proposed to reduce overestimation, including several recent ensemble methods, however none have shown success in sample-efficient learning through addressing estimation variance as the root cause of overestimation. In this paper, we propose MeanQ, a simple ensemble method that estimates target values as ensemble means. Despite its simplicity, MeanQ shows remarkable sample efficiency in experiments on the Atari Learning Environment benchmark. Importantly, we find that an ensemble of size 5 sufficiently reduces estimation variance to obviate the lagging target network, eliminating it as a source of bias and further gaining sample efficiency. We justify intuitively and empirically the design choices in MeanQ, including the necessity of independent experience sampling. On a set of 26 benchmark Atari environments, MeanQ outperforms all tested baselines, including the best available baseline, SUNRISE, at 100K interaction steps in 16/26 environments, and by 68% on average. MeanQ also outperforms Rainbow DQN at 500K steps in 21/26 environments, and by 49% on average, and achieves average human-level performance using 200K (±100K) interaction steps. Our implementation is available at https://github.com/indylab/MeanQ.

Safe reinforcement learning (RL) aims to learn policies that satisfy certain constraints before deploying them to safety-critical applications.Previous primal-dual style approaches suffer from instability issues and lack optimality guarantees. This paper overcomes the issues from the perspective of probabilistic inference. We introduce a novel Expectation-Maximization approach to naturally incorporate constraints during the policy learning: 1) a provable optimal non-parametric variational distribution could be computed in closed form after a convex optimization (E-step); 2) the policy parameter is improved within the trust region based on the optimal variational distribution (M-step).The proposed algorithm decomposes the safe RL problem into a convex optimization phase and a supervised learning phase, which yields a more stable training performance.A wide range of experiments on continuous robotic tasks shows that the proposed method achieves significantly better constraint satisfaction performance and better sample efficiency than baselines.The code is available at https://github.com/liuzuxin/cvpo-safe-rl.

We study representation learning for Offline Reinforcement Learning (RL), focusing on the important task of Offline Policy Evaluation (OPE). Recent work shows that, in contrast to supervised learning, realizability of the Q-function is not enough for learning it. Two sufficient conditions for sample-efficient OPE are Bellman completeness and coverage. Prior work often assumes that representations satisfying these conditions are given, with results being mostly theoretical in nature. In this work, we propose BCRL, which directly learns from data an approximately linear Bellman complete representation with good coverage. With this learned representation, we perform OPE using Least Square Policy Evaluation (LSPE) with linear functions in our learned representation. We present an end-to-end theoretical analysis, showing that our two-stage algorithm enjoys polynomial sample complexity provided some representation in the rich class considered is linear Bellman complete. Empirically, we extensively evaluate our algorithm on challenging, image-based continuous control tasks from the Deepmind Control Suite. We show our representation enables better OPE compared to previous representation learning methods developed for off-policy RL (e.g., CURL, SPR). BCRL achieve competitive OPE error with the state-of-the-art method Fitted Q-Evaluation (FQE), and beats FQE when evaluating beyond the initial state distribution. Our ablations show that both linear Bellman …

In constrained reinforcement learning (RL), a learning agent seeks to not only optimize the overall reward but also satisfy the additional safety, diversity, or budget constraints. Consequently, existing constrained RL solutions require several new algorithmic ingredients that are notably different from standard RL. On the other hand, reward-free RL is independently developed in the unconstrained literature, which learns the transition dynamics without using the reward information, and thus naturally capable of addressing RL with multiple objectives under the common dynamics. This paper bridges reward-free RL and constrained RL. Particularly, we propose a simple meta-algorithm such that given any reward-free RL oracle, the approachability and constrained RL problems can be directly solved with negligible overheads in sample complexity. Utilizing the existing reward-free RL solvers, our framework provides sharp sample complexity results for constrained RL in the tabular MDP setting, matching the best existing results up to a factor of horizon dependence; our framework directly extends to a setting of tabular two-player Markov games, and gives a new result for constrained RL with linear function approximation.

We propose State Matching Offline DIstribution Correction Estimation (SMODICE), a novel and versatile regression-based offline imitation learning algorithm derived via state-occupancy matching. We show that the SMODICE objective admits a simple optimization procedure through an application of Fenchel duality and an analytic solution in tabular MDPs. Without requiring access to expert actions, SMODICE can be effectively applied to three offline IL settings: (i) imitation from observations (IfO), (ii) IfO with dynamics or morphologically mismatched expert, and (iii) example-based reinforcement learning, which we show can be formulated as a state-occupancy matching problem. We extensively evaluate SMODICE on both gridworld environments as well as on high-dimensional offline benchmarks. Our results demonstrate that SMODICE is effective for all three problem settings and significantly outperforms prior state-of-art.

Data-driven model predictive control has two key advantages over model-free methods: a potential for improved sample efficiency through model learning, and better performance as computational budget for planning increases. However, it is both costly to plan over long horizons and challenging to obtain an accurate model of the environment. In this work, we combine the strengths of model-free and model-based methods. We use a learned task-oriented latent dynamics model for local trajectory optimization over a short horizon, and use a learned terminal value function to estimate long-term return, both of which are learned jointly by temporal difference learning. Our method, TD-MPC, achieves superior sample efficiency and asymptotic performance over prior work on both state and image-based continuous control tasks from DMControl and Meta-World. Code and videos are available at https://nicklashansen.github.io/td-mpc.

We study the problem of model selection in batch policy optimization: given a fixed, partial-feedback dataset and M model classes, learn a policy with performance that is competitive with the policy derived from the best model class. We formalize the problem in the contextual bandit setting with linear model classes by identifying three sources of error that any model selection algorithm should optimally trade-off in order to be competitive: (1) approximation error, (2) statistical complexity, and (3) coverage. The first two sources are common in model selection for supervised learning, where optimally trading off these two is well-studied. In contrast, the third source is unique to batch policy optimization and is due to dataset shift inherent to the setting. We first show that no batch policy optimization algorithm can achieve a guarantee addressing all three simultaneously, revealing a stark contrast between difficulties in batch policy optimization and the positive results available in supervised learning. Despite this negative result, we show that relaxing any one of the three error sources enables the design of algorithms achieving near-oracle inequalities for the remaining two. We conclude with experiments demonstrating the efficacy of these algorithms.

We propose Adversarially Trained Actor Critic (ATAC), a new model-free algorithm for offline reinforcement learning (RL) under insufficient data coverage, based on the concept of relative pessimism. ATAC is designed as a two-player Stackelberg game framing of offline RL: A policy actor competes against an adversarially trained value critic, who finds data-consistent scenarios where the actor is inferior to the data-collection behavior policy. We prove that, when the actor attains no regret in the two-player game, running ATAC produces a policy that provably 1) outperforms the behavior policy over a wide range of hyperparameters that control the degree of pessimism, and 2) competes with the best policy covered by data with appropriately chosen hyperparameters. Compared with existing works, notably our framework offers both theoretical guarantees for general function approximation and a deep RL implementation scalable to complex environments and large datasets. In the D4RL benchmark, ATAC consistently outperforms state-of-the-art offline RL algorithms on a range of continuous control tasks.

Policy gradient (PG) estimation becomes a challenge when we are not allowed to sample with the target policy but only have access to a dataset generated by some unknown behavior policy. Conventional methods for off-policy PG estimation often suffer from either significant bias or exponentially large variance. In this paper, we propose the double Fitted PG estimation (FPG) algorithm. FPG can work with an arbitrary policy parameterization, assuming access to a Bellman-complete value function class. In the case of linear value function approximation, we provide a tight finite-sample upper bound on policy gradient estimation error, that is governed by the amount of distribution mismatch measured in feature space. We also establish the asymptotic normality of FPG estimation error with a precise covariance characterization, which is further shown to be statistically optimal with a matching Cramer-Rao lower bound. Empirically, we evaluate the performance of FPG on both policy gradient estimation and policy optimization, using either softmax tabular or ReLU policy networks. Under various metrics, our results show that FPG significantly outperforms existing off-policy PG estimation methods based on importance sampling and variance reduction techniques.

We study offline reinforcement learning (RL) for partially observable Markov decision processes (POMDPs) with possibly infinite state and observation spaces. Under the undercompleteness assumption, the optimal policy in such POMDPs are characterized by a class of finite-memory Bellman operators. In the offline setting, estimating these operators directly is challenging due to (i) the large observation space and (ii) insufficient coverage of the offline dataset. To tackle these challenges, we propose a novel algorithm that constructs confidence regions for these Bellman operators via offline estimation of their RKHS embeddings, and returns the final policy via pessimistic planning within the confidence regions. We prove that the proposed algorithm attains an (\epsilon)-optimal policy using an offline dataset containing (\tilde\cO(1 / \epsilon^2)) episodes, provided that the behavior policy has good coverage over the optimal trajectory. To our best knowledge, our algorithm is the first provably sample efficient offline algorithm for POMDPs without uniform coverage assumptions.

Off-Policy Evaluation (OPE) serves as one of the cornerstones in Reinforcement Learning (RL). Fitted Q Evaluation (FQE) with various function approximators, especially deep neural networks, has gained practical success. While statistical analysis has proved FQE to be minimax-optimal with tabular, linear and several nonparametric function families, its practical performance with more general function approximator is less theoretically understood. We focus on FQE with general \textit{differentiable function approximators}, making our theory applicable to neural function approximations. We approach this problem using the Z-estimation theory and establish the following results: The FQE estimation error is asymptotically normal with explicit variance determined jointly by the tangent space of the function class at the ground truth, the reward structure, and the distribution shift due to off-policy learning; The finite-sample FQE error bound is dominated by the same variance term, and it can also be bounded by function class-dependent divergence, which measures how the off-policy distribution shift intertwines with the function approximator. In addition, we study bootstrapping FQE estimators for error distribution inference and estimating confidence intervals, accompanied by a Cramer-Rao lower bound that matches our upper bounds. The Z-estimation analysis provides a generalizable theoretical framework for studying off-policy estimation in RL and provides sharp …

This paper discusses a new approach to the fundamental problem of learning optimal Q-functions. In this approach, optimal Q-functions are formulated as saddle points of a nonlinear Lagrangian function derived from the classic Bellman optimality equation. The paper shows that the Lagrangian enjoys strong duality, in spite of its nonlinearity, which paves the way to a general Lagrangian method to Q-function learning. As a demonstration, the paper develops an imitation learning algorithm based on the duality theory, and applies the algorithm to a state-of-the-art machine translation benchmark. The paper then turns to demonstrate a symmetry breaking phenomenon regarding the optimality of the Lagrangian saddle points, which justifies a largely overlooked direction in developing the Lagrangian method.

Transformer architectures are now central to sequence modeling tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied in the computer vision domain, where 2D images are first segmented into patches and then treated as 1D sequences. Such linearization, however, impairs the notion of spatial locality in images, which bears important visual clues. To bridge the gap, we propose \emph{ripple attention}, a sub-quadratic attention mechanism for vision transformers. Built upon the recent kernel-based efficient attention mechanisms, we design a novel dynamic programming algorithm that weights contributions of different tokens to a query with respect to their relative spatial distances in the 2D space in linear observed time.Extensive experiments and analyses demonstrate the effectiveness of ripple attention on various visual tasks.

Transformers have shown remarkable progress on computer vision tasks in the past year. Compared to their CNN counterparts, transformers usually need the help of distillation to achieve comparable results on middle or small sized datasets. Meanwhile, recent researches discover that when transformers are trained with supervised and self-supervised manner respectively, the captured patterns are quite different both qualitatively and quantitatively. These findings motivate us to introduce an self-supervised teaching assistant (SSTA) besides the commonly used supervised teacher to improve the performance of transformers. Specifically, we propose a head-level knowledge distillation method that selects the most important head of the supervised teacher and self-supervised teaching assistant, and let the student mimic the attention distribution of these two heads, so as to make the student focus on the relationship between tokens deemed by the teacher and the teacher assistant. Extensive experiments verify the effectiveness of SSTA and demonstrate that the proposed SSTA is a good compensation to the supervised teacher. Meanwhile, some analytical experiments towards multiple perspectives (e.g. prediction, shape bias, robustness, and transferability to downstream tasks) with supervised teachers, self-supervised teaching assistants and students are inductive and may inspire future researches.

Existing techniques for model inversion typically rely on hard-to-tune regularizers, such as total variation or feature regularization, which must be individually calibrated for each network in order to produce adequate images. In this work, we introduce Plug-In Inversion, which relies on a simple set of augmentations and does not require excessive hyper-parameter tuning. Under our proposed augmentation-based scheme, the same set of augmentation hyper-parameters can be used for inverting a wide range of image classification models, regardless of input dimensions or the architecture. We illustrate the practicality of our approach by inverting Vision Transformers (ViTs) and Multi-Layer Perceptrons (MLPs) trained on the ImageNet dataset, tasks which to the best of our knowledge have not been successfully accomplished by any previous works.

Transformer-based models such as BERT have proven successful in information retrieval problem, which seek to identify relevant documents for a given query. There are two broad flavours of such models: cross-attention (CA) models, which learn a joint embedding for the query and document, and dual-encoder (DE) models, which learn separate embeddings for the query and document. Empirically, CA models are often found to be more accurate, which has motivated a series of works seeking to bridge this gap. However, a more fundamental question remains less explored: does this performance gap reflect an inherent limitation in the capacity of DE models, or a limitation in the training of such models? And does such an understanding suggest a principled means of improving DE models? In this paper, we study these questions, with three contributions. First, we establish theoretically that with a sufficiently large embedding dimension, DE models have the capacity to model a broad class of score distributions. Second, we show empirically that on real-world problems, DE models may overfit to spurious correlations in the training set, and thus under-perform on test samples. To mitigate this behaviour, we propose a suitable distillation strategy, and confirm its practical efficacy on the MSMARCO-Passage and …

In this paper we provide, to the best of our knowledge, the first comprehensive approach for incorporating various masking mechanisms into Transformers architectures in a scalable way. We show that recent results on linear causal attention (Choromanski et al., 2021) and log-linear RPE-attention (Luo et al., 2021) are special cases of this general mechanism. However by casting the problem as a topological (graph-based) modulation of unmasked attention, we obtain several results unknown before, including efficient d-dimensional RPE-masking and graph-kernel masking. We leverage many mathematical techniques ranging from spectral analysis through dynamic programming and random walks to new algorithms for solving Markov processes on graphs. We provide a corresponding empirical evaluation.

Recently, random feature attentions (RFAs) are proposed to approximate the softmax attention in linear time and space complexity by linearizing the exponential kernel. In this paper, we first propose a novel perspective to understand the bias in such approximation by recasting RFAs as self-normalized importance samplers. This perspective further sheds light on an \emph{unbiased} estimator for the whole softmax attention, called randomized attention (RA). RA constructs positive random features via query-specific distributions and enjoys greatly improved approximation fidelity, albeit exhibiting quadratic complexity. By combining the expressiveness in RA and the efficiency in RFA, we develop a novel linear complexity self-attention mechanism called linear randomized attention (LARA). Extensive experiments across various domains demonstrate that RA and LARA significantly improve the performance of RFAs by a substantial margin.

Self-attention mechanisms model long-range context by using pairwise attention between all input tokens. In doing so, they assume a fixed attention granularity defined by the individual tokens (e.g., text characters or image pixels), which may not be optimal for modeling complex dependencies at higher levels. In this paper, we propose ContextPool to address this problem by adapting the attention granularity for each token. Inspired by the success of ConvNets that are combined with pooling to capture long-range dependencies, we learn to pool neighboring features for each token before computing attention in a given attention layer. The pooling weights and support size are adaptively determined, allowing the pooled features to encode meaningful context with varying scale. We show that ContextPool makes attention models more expressive, achieving strong performance often with fewer layers and thus significantly reduced cost. Experiments validate that our ContextPool module, when plugged into transformer models, matches or surpasses state-of-the-art performance using less compute on several language and image benchmarks, outperforms recent works with learned context sizes or sparse attention patterns, and is also applicable to ConvNets for efficient feature learning.

Compositional generalization is a critical ability in learning and decision-making. We focus on the setting of reinforcement learning in object-oriented environments to study compositional generalization in world modeling. We (1) formalize the compositional generalization problem with an algebraic approach and (2) study how a world model can achieve that. We introduce a conceptual environment, Object Library, and two instances, and deploy a principled pipeline to measure the generalization ability. Motivated by the formulation, we analyze several methods with exact or no compositional generalization ability using our framework, and design a differentiable approach, Homomorphic Object-oriented World Model (HOWM), that achieves soft but more efficient compositional generalization.

Training populations of agents has demonstrated great promise in Reinforcement Learning for stabilizing training, improving exploration and asymptotic performance, and generating a diverse set of solutions. However, population-based training is often not considered by practitioners as it is perceived to be either prohibitively slow (when implemented sequentially), or computationally expensive (if agents are trained in parallel on independent accelerators). In this work, we compare implementations and revisit previous studies to show that the judicious use of compilation and vectorization allows population-based training to be performed on a single machine with one accelerator with minimal overhead compared to training a single agent. We also show that, when provided with a few accelerators, our protocols extend to large population sizes for applications such as hyperparameter tuning. We hope that this work and the public release of our code will encourage practitioners to use population-based learning techniques more frequently for their research and applications.

Learning the principal eigenfunctions of an integral operator defined by a kernel and a data distribution is at the core of many machine learning problems. Traditional nonparametric solutions based on the Nystrom formula suffer from scalability issues. Recent work has resorted to a parametric approach, i.e., training neural networks to approximate the eigenfunctions. However, the existing method relies on an expensive orthogonalization step and is difficult to implement. We show that these problems can be fixed by using a new series of objective functions that generalizes the EigenGame to function space. We test our method on a variety of supervised and unsupervised learning problems and show it provides accurate approximations to the eigenfunctions of polynomial, radial basis, neural network Gaussian process, and neural tangent kernels. Finally, we demonstrate our method can scale up linearised Laplace approximation of deep neural networks to modern image classification datasets through approximating the Gauss-Newton matrix. Code is available at https://github.com/thudzj/neuraleigenfunction.

Visual attention helps achieve robust perception under noise, corruption, and distribution shifts in human vision, which are areas where modern neural networks still fall short. We present VARS, Visual Attention from Recurrent Sparse reconstruction, a new attention formulation built on two prominent features of the human visual attention mechanism: recurrency and sparsity. Related features are grouped together via recurrent connections between neurons, with salient objects emerging via sparse regularization. VARS adopts an attractor network with recurrent connections that converges toward a stable pattern over time.Network layers are represented as ordinary differential equations (ODEs), formulating attention as a recurrent attractor network that equivalently optimizes the sparse reconstruction of input using a dictionary of ``templates'' encodingunderlying patterns of data. We show that self-attention is a special case of VARS with a single-step optimization and no sparsity constraint. VARS can be readily used as a replacement for self-attention in popular vision transformers, consistently improving their robustness across various benchmarks.

We revisit the design choices in Transformers, and propose methods to address their weaknesses in handling long sequences. First, we propose a simple layer named gated attention unit, which allows the use of a weaker single-head attention with minimal quality loss. We then propose a linear approximation method complementary to this new layer, which is accelerator-friendly and highly competitive in quality. The resulting model, named FLASH, matches the perplexity of improved Transformers over both short (512) and long (8K) context lengths, achieving training speedups of up to 4.9x on Wiki-40B and 12.1x on PG-19 for auto-regressive language modeling, and 4.8x on C4 for masked language modeling.

A key concern in integrating machine learning models in medicine is the ability to interpret their reasoning. Popular explainability methods have demonstrated satisfactory results in natural image recognition, yet in medical image analysis, many of these approaches provide partial and noisy explanations. Recently, attention mechanisms have shown compelling results both in their predictive performance and in their interpretable qualities. A fundamental trait of attention is that it leverages salient parts of the input which contribute to the model's prediction. To this end, our work focuses on the explanatory value of attention weight distributions. We propose a multi-layer attention mechanism that enforces consistent interpretations between attended convolutional layers using convex optimization. We apply duality to decompose the consistency constraints between the layers by reparameterizing their attention probability distributions. We further suggest learning the dual witness by optimizing with respect to our objective; thus, our implementation uses standard back-propagation, hence it is highly efficient. While preserving predictive performance, our proposed method leverages weakly annotated medical imaging data and provides complete and faithful explanations to the model's prediction.

Transformers have emerged as a preferred model for many tasks in natural langugage processing and vision. Recent efforts on training and deploying Transformers more efficiently have identified many strategies to approximate the self-attention matrix, a key module in a Transformer architecture. Effective ideas include various prespecified sparsity patterns, low-rank basis expansions and combinations thereof. In this paper, we revisit classical Multiresolution Analysis (MRA) concepts such as Wavelets, whose potential value in this setting remains underexplored thus far. We show that simple approximations based on empirical feedback and design choices informed by modern hardware and implementation challenges, eventually yield a MRA-based approach for self-attention with an excellent performance profile across most criteria of interest. We undertake an extensive set of experiments and demonstrate that this multi-resolution scheme outperforms most efficient self-attention proposals and is favorable for both short and long sequences. Code is available at \url{https://github.com/mlpen/mra-attention}.

While unbiased machine learning models are essential for many applications, bias is a human-defined concept that can vary across tasks. Given only input-label pairs, algorithms may lack sufficient information to distinguish stable (causal) features from unstable (spurious) features. However, related tasks often share similar biases -- an observation we may leverage to develop stable classifiers in the transfer setting. In this work, we explicitly inform the target classifier about unstable features in the source tasks. Specifically, we derive a representation that encodes the unstable features by contrasting different data environments in the source task. We achieve robustness by clustering data of the target task according to this representation and minimizing the worst-case risk across these clusters. We evaluate our method on both text and image classifications. Empirical results demonstrate that our algorithm is able to maintain robustness on the target task for both synthetically generated environments and real-world environments. Our code is available at https://github.com/YujiaBao/Tofu.

Pre-training serves as a broadly adopted starting point for transfer learning on various downstream tasks. Recent investigations of lottery tickets hypothesis (LTH) demonstrate such enormous pre-trained models can be replaced by extremely sparse subnetworks (a.k.a. matching subnetworks) without sacrificing transferability. However, practical security-crucial applications usually pose more challenging requirements beyond standard transfer, which also demand these subnetworks to overcome adversarial vulnerability. In this paper, we formulate a more rigorous concept, Double-Win Lottery Tickets, in which a located subnetwork from a pre-trained model can be independently transferred on diverse downstream tasks, to reach BOTH the same standard and robust generalization, under BOTH standard and adversarial training regimes, as the full pre-trained model can do. We comprehensively examine various pre-training mechanisms and find that robust pre-training tends to craft sparser double-win lottery tickets with superior performance over the standard counterparts. For example, on downstream CIFAR-10/100 datasets, we identify double-win matching subnetworks with the standard, fast adversarial, and adversarial pre-training from ImageNet, at 89.26%/73.79%, 89.26%/79.03%, and 91.41%/83.22% sparsity, respectively. Furthermore, we observe the obtained double-win lottery tickets can be more data-efficient to transfer, under practical data-limited (e.g., 1% and 10%) downstream schemes. Our results show that the benefits from robust pre-training are amplified …

Polythetic classifications, based on shared patterns of features that need neither be universal nor constant among members of a class, are common in the natural world and greatly outnumber monothetic classifications over a set of features. We show that threshold meta-learners, such as Prototypical Networks, require an embedding dimension that is exponential in the number of task-relevant features to emulate these functions. In contrast, attentional classifiers, such as Matching Networks, are polythetic by default and able to solve these problems with a linear embedding dimension. However, we find that in the presence of task-irrelevant features, inherent to meta-learning problems, attentional models are susceptible to misclassification. To address this challenge, we propose a self-attention feature-selection mechanism that adaptively dilutes non-discriminative features. We demonstrate the effectiveness of our approach in meta-learning Boolean functions, and synthetic and real-world few-shot learning tasks.

Hypergraphs are a common model for multiway relationships in data, and hypergraph semi-supervised learning is the problem of assigning labels to all nodes in a hypergraph, given labels on just a few nodes. Diffusions and label spreading are classical techniques for semi-supervised learning in the graph setting, and there are some standard ways to extend them to hypergraphs.However, these methods are linear models, and do not offer an obvious way of incorporating node features for making predictions.Here, we develop a nonlinear diffusion process on hypergraphs that spreads both features and labels following the hypergraph structure. Even though the process is nonlinear, we show global convergence to a unique limiting point for a broad class of nonlinearities and we show that such limit is the global minimum of a new regularized semi-supervised learning loss function which aims at reducing a generalized form of variance of the nodes across the hyperedges.The limiting point serves as a node embedding from which we make predictions with a linear model. Our approach is competitive with state-of-the-art graph and hypergraph neural networks, and also takes less time to train.

Compositional data analysis with a high proportion of zeros has gained increasing popularity, especially in chemometrics and human gut microbiomes research. Statistical analyses of this type of data are typically carried out via a log-ratio transformation after replacing zeros with small positive values. We should note, however, that this procedure is geometrically improper, as it causes anomalous distortions through the transformation. We propose a radial transformation that does not require zero substitutions and more importantly results in essential equivalence between domains before and after the transformation. We show that a rich class of kernels on hyperspheres can successfully define a kernel embedding for compositional data based on this equivalence. To the best of our knowledge, this is the first work that theoretically establishes the availability of the extensive library of kernel-based machine learning methods for compositional data. The applicability of the proposed approach is demonstrated with kernel principal component analysis.

We study offline meta-reinforcement learning, a practical reinforcement learning paradigm that learns from offline data to adapt to new tasks. The distribution of offline data is determined jointly by the behavior policy and the task. Existing offline meta-reinforcement learning algorithms cannot distinguish these factors, making task representations unstable to the change of behavior policies. To address this problem, we propose a contrastive learning framework for task representations that are robust to the distribution mismatch of behavior policies in training and test. We design a bi-level encoder structure, use mutual information maximization to formalize task representation learning, derive a contrastive learning objective, and introduce several approaches to approximate the true distribution of negative pairs. Experiments on a variety of offline meta-reinforcement learning benchmarks demonstrate the advantages of our method over prior methods, especially on the generalization to out-of-distribution behavior policies.

Recent work highlights the role of causality in designing equitable decision-making algorithms. It is not immediately clear, however, how existing causal conceptions of fairness relate to one another, or what the consequences are of using these definitions as design principles. Here, we first assemble and categorize popular causal definitions of algorithmic fairness into two broad families: (1) those that constrain the effects of decisions on counterfactual disparities; and (2) those that constrain the effects of legally protected characteristics, like race and gender, on decisions. We then show, analytically and empirically, that both families of definitions \emph{almost always}---in a measure theoretic sense---result in strongly Pareto dominated decision policies, meaning there is an alternative, unconstrained policy favored by every stakeholder with preferences drawn from a large, natural class. For example, in the case of college admissions decisions, policies constrained to satisfy causal fairness definitions would be disfavored by every stakeholder with neutral or positive preferences for both academic preparedness and diversity.Indeed, under a prominent definition of causal fairness, we prove the resulting policies require admitting all students with the same probability, regardless of academic qualifications or group membership. Our results highlight formal limitations and potential adverse consequences of common mathematical notions of …

Fairness is now an important issue in machine learning. There are arising concerns that automated decision-making systems reflect real-world biases. Although a wide range of fairness-related methods have been proposed in recent years, the under-representation problem has been less studied. Due to the uneven distribution of samples from different populations, machine learning models tend to be biased against minority groups when trained by minimizing the average empirical risk across all samples. In this paper, we propose a novel adaptive reweighing method to address representation bias. The goal of our method is to achieve group-level balance among different demographic groups by learning adaptive weights for each sample. Our approach emphasizes more on error-prone samples in prediction and enhances adequate representation of minority groups for fairness. We derive a closed-form solution for adaptive weight assignment and propose an efficient algorithm with theoretical convergence guarantees. We theoretically analyze the fairness of our model and empirically verify that our method strikes a balance between fairness and accuracy. In experiments, our method achieves comparable or better performance than state-of-the-art methods in both classification and regression tasks. Furthermore, our method exhibits robustness to label noise on various benchmark datasets.

A variety of fairness constraints have been proposed in the literature to mitigate group-level statistical bias. Their impacts have been largely evaluated for different groups of populations corresponding to a set of sensitive attributes, such as race or gender. Nonetheless, the community has not observed sufficient explorations for how imposing fairness constraints fare at an instance level. Building on the concept of influence function, a measure that characterizes the impact of a training example on the target model and its predictive performance, this work studies the influence of training examples when fairness constraints are imposed. We find out that under certain assumptions, the influence function with respect to fairness constraints can be decomposed into a kernelized combination of training examples. One promising application of the proposed fairness influence function is to identify suspicious training examples that may cause model discrimination by ranking their influence scores. We demonstrate with extensive experiments that training on a subset of weighty data examples leads to lower fairness violations with a trade-off of accuracy.

With the fast development of algorithmic governance, fairness has become a compulsory property for machine learning models to suppress unintentional discrimination. In this paper, we focus on the pre-processing aspect for achieving fairness, and propose a data reweighing approach that only adjusts the weight for samples in the training phase. Different from most previous reweighing methods which usually assign a uniform weight for each (sub)group, we granularly model the influence of each training sample with regard to fairness-related quantity and predictive utility, and compute individual weights based on influence under the constraints from both fairness and utility. Experimental results reveal that previous methods achieve fairness at a non-negligible cost of utility, while as a significant advantage, our approach can empirically release the tradeoff and obtain cost-free fairness for equal opportunity. We demonstrate the cost-free fairness through vanilla classifiers and standard training processes, compared to baseline methods on multiple real-world tabular datasets. Code available at https://github.com/brandeis-machine-learning/influence-fairness.

In spite of the high performance and reliability of deep learning algorithms in a wide range of everyday applications, many investigations tend to show that a lot of models exhibit biases, discriminating against specific subgroups of the population (e.g. gender, ethnicity). This urges the practitioner to develop fair systems with a uniform/comparable performance across sensitive groups. In this work, we investigate the gender bias of deep Face Recognition networks. In order to measure this bias, we introduce two new metrics, BFAR and BFRR, that better reflect the inherent deployment needs of Face Recognition systems. Motivated by geometric considerations, we mitigate gender bias through a new post-processing methodology which transforms the deep embeddings of a pre-trained model to give more representation power to discriminated subgroups. It consists in training a shallow neural network by minimizing a Fair von Mises-Fisher loss whose hyperparameters account for the intra-class variance of each gender. Interestingly, we empirically observe that these hyperparameters are correlated with our fairness metrics. In fact, extensive numerical experiments on a variety of datasets show that a careful selection significantly reduces gender bias.

Selective regression allows abstention from prediction if the confidence to make an accurate prediction is not sufficient. In general, by allowing a reject option, one expects the performance of a regression model to increase at the cost of reducing coverage (i.e., by predicting on fewer samples). However, as we show, in some cases, the performance of a minority subgroup can decrease while we reduce the coverage, and thus selective regression can magnify disparities between different sensitive subgroups. Motivated by these disparities, we propose new fairness criteria for selective regression requiring the performance of every subgroup to improve with a decrease in coverage. We prove that if a feature representation satisfies the \textit{sufficiency} criterion or is \textit{calibrated for mean and variance}, then the proposed fairness criteria is met. Further, we introduce two approaches to mitigate the performance disparity across subgroups: (a) by regularizing an upper bound of conditional mutual information under a Gaussian assumption and (b) by regularizing a contrastive loss for conditional mean and conditional variance prediction. The effectiveness of these approaches is demonstrated on synthetic and real-world datasets.

Only recently, researchers attempt to provide classification algorithms with provable group fairness guarantees. Most of these algorithms suffer from harassment caused by the requirement that the training and deployment data follow the same distribution. This paper proposes an input-agnostic certified group fairness algorithm, FairSmooth, for improving the fairness of classification models while maintaining the remarkable prediction accuracy. A Gaussian parameter smoothing method is developed to transform base classifiers into their smooth versions. An optimal individual smooth classifier is learnt for each group with only the data regarding the group and an overall smooth classifier for all groups is generated by averaging the parameters of all the individual smooth ones. By leveraging the theory of nonlinear functional analysis, the smooth classifiers are reformulated as output functions of a Nemytskii operator. Theoretical analysis is conducted to derive that the Nemytskii operator is smooth and induces a Frechet differentiable smooth manifold. We theoretically demonstrate that the smooth manifold has a global Lipschitz constant that is independent of the domain of the input data, which derives the input-agnostic certified group fairness.

Recently, deep neural networks have gained increasing popularity in the field of time series forecasting. A primary reason for their success is their ability to effectively capture complex temporal dynamics across multiple related time series. The advantages of these deep forecasters only start to emerge in the presence of a sufficient amount of data. This poses a challenge for typical forecasting problems in practice, where there is a limited number of time series or observations per time series, or both. To cope with this data scarcity issue, we propose a novel domain adaptation framework, Domain Adaptation Forecaster (DAF). DAF leverages statistical strengths from a relevant domain with abundant data samples (source) to improve the performance on the domain of interest with limited data (target). In particular, we use an attention-based shared module with a domain discriminator across domains and private modules for individual domains. We induce domain-invariant latent features (queries and keys) and retrain domain-specific features (values) simultaneously to enable joint training of forecasters on source and target domains. A main insight is that our design of aligning keys allows the target domain to leverage source time series even with different characteristics. Extensive experiments on various domains demonstrate that our …

Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare by assisting decision-makers to answer "what-if" questions. Existing causal inference approaches typically consider regular, discrete-time intervals between observations and treatment decisions and hence are unable to naturally model irregularly sampled data, which is the common setting in practice. To handle arbitrary observation patterns, we interpret the data as samples from an underlying continuous-time process and propose to model its latent trajectory explicitly using the mathematics of controlled differential equations. This leads to a new approach, the Treatment Effect Neural Controlled Differential Equation (TE-CDE), that allows the potential outcomes to be evaluated at any time point. In addition, adversarial training is used to adjust for time-dependent confounding which is critical in longitudinal settings and is an added challenge not encountered in conventional time series. To assess solutions to this problem, we propose a controllable simulation environment based on a model of tumor growth for a range of scenarios with irregular sampling reflective of a variety of clinical scenarios. TE-CDE consistently outperforms existing approaches in all scenarios with irregular sampling.

Disease-related representations play a crucial role in image-based disease prediction such as cancer diagnosis, due to its considerable generalization capacity. However, it is still a challenge to identify lesion characteristics in obscured images, as many lesions are obscured by other tissues. In this paper, to learn the representations for identifying obscured lesions, we propose a disentanglement learning strategy under the guidance of alpha blending generation in an encoder-decoder framework (DAB-Net). Specifically, we take mammogram mass benign/malignant classification as an example. In our framework, composite obscured mass images are generated by alpha blending and then explicitly disentangled into disease-related mass features and interference glands features. To achieve disentanglement learning, features of these two parts are decoded to reconstruct the mass and the glands with corresponding reconstruction losses, and only disease-related mass features are fed into the classifier for disease prediction. Experimental results on one public dataset DDSM and three in-house datasets demonstrate that the proposed strategy can achieve state-of-the-art performance. DAB-Net achieves substantial improvements of 3.9%∼4.4% AUC in obscured cases. Besides, the visualization analysis shows the model can better disentangle the mass and glands in the obscured image, suggesting the effectiveness of our solution in exploring the hidden characteristics in this …

Black-box model-based optimization (MBO) problems, where the goal is to find a design input that maximizes an unknown objective function, are ubiquitous in a wide range of domains, such as the design of proteins, DNA sequences, aircraft, and robots. Solving model-based optimization problems typically requires actively querying the unknown objective function on design proposals, which means physically building the candidate molecule, aircraft, or robot, testing it, and storing the result. This process can be expensive and time consuming, and one might instead prefer to optimize for the best design using only the data one already has. This setting---called offline MBO---poses substantial and different algorithmic challenges than more commonly studied online techniques. A number of recent works have demonstrated success with offline MBO for high-dimensional optimization problems using high-capacity deep neural networks. However, the lack of standardized benchmarks in this emerging field is making progress difficult to track. To address this, we present Design-Bench, a benchmark for offline MBO with a unified evaluation protocol and reference implementations of recent methods. Our benchmark includes a suite of diverse and realistic tasks derived from real-world optimization problems in biology, materials science, and robotics that present distinct challenges for offline MBO. Our benchmark and …

Assembly of multi-part physical structures is both a valuable end product for autonomous robotics, as well as a valuable diagnostic task for open-ended training of embodied intelligent agents. We introduce a naturalistic physics-based environment with a set of connectable magnet blocks inspired by children’s toy kits. The objective is to assemble blocks into a succession of target blueprints. Despite the simplicity of this objective, the compositional nature of building diverse blueprints from a set of blocks leads to an explosion of complexity in structures that agents encounter. Furthermore, assembly stresses agents' multi-step planning, physical reasoning, and bimanual coordination. We find that the combination of large-scale reinforcement learning and graph-based policies-- surprisingly without any additional complexity -- is an effective recipe for training agents that not only generalize to complex unseen blueprints in a zero-shot manner, but even operate in a reset-free setting without being trained to do so. Through extensive experiments, we highlight the importance of large-scale training, structured representations, contributions of multi-task vs. single-task learning, as well as the effects of curriculums, and discuss qualitative behaviors of trained agents. Our accompanying project webpage can be found at: https://sites.google.com/view/learning-direct-assembly/home

The recent availability of Electronic Health Records (EHR) has allowed for the development of algorithms predicting inpatient risk of deterioration and trajectory evolution. However, prediction of disease progression with EHR is challenging since these data are sparse, heterogeneous, multi-dimensional, and multi-modal time-series. As such, clustering is regularly used to identify similar groups within the patient cohort to improve prediction. Current models have shown some success in obtaining cluster representations of patient trajectories. However, they i) fail to obtain clinical interpretability for each cluster, and ii) struggle to learn meaningful cluster numbers in the context of imbalanced distribution of disease outcomes. We propose a supervised deep learning model to cluster EHR data based on the identification of clinically understandable phenotypes with regard to both outcome prediction and patient trajectory. We introduce novel loss functions to address the problems of class imbalance and cluster collapse, and furthermore propose a feature-time attention mechanism to identify cluster-based phenotype importance across time and feature dimensions. We tested our model in two datasets corresponding to distinct medical settings. Our model yielded added interpretability to cluster formation and outperformed benchmarks by at least 4% in relevant metrics.

Uncertainty quantification of predictive models is crucial in decision-making problems. Conformal prediction is a general and theoretically sound answer. However, it requires exchangeable data, excluding time series. While recent works tackled this issue, we argue that Adaptive Conformal Inference (ACI, Gibbs & Candès, 2021), developed for distribution-shift time series, is a good procedure for time series with general dependency. We theoretically analyse the impact of the learning rate on its efficiency in the exchangeable and auto-regressive case. We propose a parameter-free method, AgACI, that adaptively builds upon ACI based on online expert aggregation. We lead extensive fair simulations against competing methods that advocate for ACI's use in time series. We conduct a real case study: electricity price forecasting. The proposed aggregation algorithm provides efficient prediction intervals for day-ahead forecasting. All the code and data to reproduce the experiments are made available on GitHub.

Can world knowledge learned by large language models (LLMs) be used to act in interactive environments? In this paper, we investigate the possibility of grounding high-level tasks, expressed in natural language (e.g. “make breakfast”), to a chosen set of actionable steps (e.g. “open fridge”). While prior work focused on learning from explicit step-by-step examples of how to act, we surprisingly find that if pre-trained LMs are large enough and prompted appropriately, they can effectively decompose high-level tasks into mid-level plans without any further training. However, the plans produced naively by LLMs often cannot map precisely to admissible actions. We propose a procedure that conditions on existing demonstrations and semantically translates the plans to admissible actions. Our evaluation in the recent VirtualHome environment shows that the resulting method substantially improves executability over the LLM baseline. The conducted human evaluation reveals a trade-off between executability and correctness but shows a promising sign towards extracting actionable knowledge from language models.

Graph Neural Networks (GNNs) are widely applied for graph anomaly detection. As one of the key components for GNN design is to select a tailored spectral filter, we take the first step towards analyzing anomalies via the lens of the graph spectrum. Our crucial observation is the existence of anomalies will lead to the right-shift' phenomenon, that is, the spectral energy distribution concentrates less on low frequencies and more on high frequencies. This fact motivates us to propose the Beta Wavelet Graph Neural Network (BWGNN). Indeed, BWGNN has spectral and spatial localized band-pass filters to better handle theright-shift' phenomenon in anomalies. We demonstrate the effectiveness of BWGNN on four large-scale anomaly detection datasets. Our code and data are released at https://github.com/squareRoot3/Rethinking-Anomaly-Detection.

Aquatic locomotion is a classic fluid-structure interaction (FSI) problem of interest to biologists and engineers. Solving the fully coupled FSI equations for incompressible Navier-Stokes and finite elasticity is computationally expensive. Optimizing robotic swimmer design within such a system generally involves cumbersome, gradient-free procedures on top of the already costly simulation.To address this challenge we present a novel, fully differentiable hybrid approach to FSI that combines a 2D direct numerical simulation for the deformable solid structure of the swimmer and a physics-constrained neural network surrogate to capture hydrodynamic effects of the fluid.For the deformable solid simulation of the swimmer's body, we use state-of-the-art techniques from the field of computer graphics to speed up the finite-element method (FEM). For the fluid simulation, we use a U-Net architecture trained with a physics-based loss function to predict the flow field at each time step. The pressure and velocity field outputs from the neural network are sampled around the boundary of our swimmer using an immersed boundary method (IBM) to compute its swimming motion accurately and efficiently.We demonstrate the computational efficiency and differentiability of our hybrid simulator on a 2D carangiform swimmer. Due to differentiability, the simulator can be used for computational design of controls …

Traditional automated theorem proving systems for first-order logic depend on speed-optimized search and many handcrafted heuristics designed to work over a wide range of domains. Machine learning approaches in the literature either depend on these traditional provers to bootstrap themselves, by leveraging these heuristics, or can struggle due to limited existing proof data. The latter issue can be explained by the lack of a smooth difficulty gradient in theorem proving datasets; large gaps in difficulty between different theorems can make training harder or even impossible. In this paper, we adapt the idea of hindsight experience replay from reinforcement learning to the automated theorem proving domain, so as to use the intermediate data generated during unsuccessful proof attempts. We build a first-order logic prover by disabling all the smart clause-scoring heuristics of the state-of-the-art E prover and replacing them with a clause-scoring neural network learned by using hindsight experience replay in an incremental learning setting. Clauses are represented as graphs and presented to transformer networks with spectral features. We show that provers trained in this way can outperform previous machine learning approaches and compete with the state of the art heuristic-based theorem prover E in its best configuration, on the popular …

In this work, we consider one-shot imitation learning for object rearrangement tasks, where an AI agent needs to watch a single expert demonstration and learn to perform the same task in different environments. To achieve a strong generalization, the AI agent must infer the spatial goal specification for the task. However, there can be multiple goal specifications that fit the given demonstration. To address this, we propose a reward learning approach, Graph-based Equivalence Mappings (GEM), that can discover spatial goal representations that are aligned with the intended goal specification, enabling successful generalization in unseen environments. Specifically, GEM represents a spatial goal specification by a reward function conditioned on i) a graph indicating important spatial relationships between objects and ii) state equivalence mappings for each edge in the graph indicating invariant properties of the corresponding relationship. GEM combines inverse reinforcement learning and active reward learning to efficiently improve the reward function by utilizing the graph structure and domain randomization enabled by the equivalence mappings. We conducted experiments with simulated oracles and with human subjects. The results show that GEM can drastically improve the generalizability of the learned goal representations over strong baselines.