ICML 2020 Papers

Recent work showed that overparameterized autoencoders can be trained to implement associative memory via iterative maps, when the trained input-output Jacobian of the network has all of its eigenvalue norms strictly below one. Here, we theoretically analyze this phenomenon for sigmoid networks by leveraging recent developments in deep learning theory, especially the correspondence between training neural networks in the infinite-width limit and performing kernel regression with the Neural Tangent Kernel (NTK). We find that overparameterized sigmoid autoencoders can have attractors in the NTK limit for both training with a single example and multiple examples under certain conditions. In particular, for multiple training examples, we find that the norm of the largest Jacobian eigenvalue drops below one with increasing input norm, leading to associative memory.

This paper proposes a new framework for providing approximation guarantees of local search algorithms. Local search is a basic algorithm design technique and is widely used for various combinatorial optimization problems. To analyze local search algorithms for set function maximization, we propose a new notion called \emph{localizability} of set functions, which measures how effective local improvement is. Moreover, we provide approximation guarantees of standard local search algorithms under various combinatorial constraints in terms of localizability. The main application of our framework is sparse optimization, for which we show that restricted strong concavity and restricted smoothness of the objective function imply localizability, and further develop accelerated versions of local search algorithms. We conduct experiments in sparse regression and structure learning of graphical models to confirm the practical efficiency of the proposed local search algorithms.

Recent interest in invertible models and normalizing flows has resulted in new architectures that ensure invertibility of the network model. Neural ODEs and i-ResNets are two recent techniques for constructing models that are invertible, but it is unclear if they can be used to approximate any continuous invertible mapping. Here, we show that out of the box, both of these architectures are limited in their approximation capabilities. We then show how to overcome this limitation: we prove that any homeomorphism on a $p$-dimensional Euclidean space can be approximated by a Neural ODE or an i-ResNet operating on a $2p$-dimensional Euclidean space. We conclude by showing that capping a Neural ODE or an i-ResNet with a single linear layer is sufficient to turn the model into a universal approximator for non-invertible continuous functions.

Recent work has shown that topological enhancements to recurrent neural networks (RNNs) can increase their expressiveness and representational capacity. Two popular enhancements are stacked RNNs, which increases the capacity for learning non-linear functions, and bidirectional processing, which exploits acausal information in a sequence. In this work, we explore the delayed-RNN, which is a single-layer RNN that has a delay between the input and output. We prove that a weight-constrained version of the delayed-RNN is equivalent to a stacked-RNN. We also show that the delay gives rise to partial acausality, much like bidirectional networks. Synthetic experiments confirm that the delayed-RNN can mimic bidirectional networks, solving some acausal tasks similarly, and outperforming them in others. Moreover, we show similar performance to bidirectional networks in a real-world natural language processing task. These results suggest that delayed-RNNs can approximate topologies including stacked RNNs, bidirectional RNNs, and stacked bidirectional RNNs – but with equivalent or faster runtimes for the delayed-RNNs.

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the normalized angular distance between the sample feature embedding and the target classifier to measure sample hardness. We validate this score with an in-depth and extensive scientific study, and observe that CNN models with the highest accuracy also have the best AVH scores. This agrees with an earlier finding that state-of-art models improve on the classification of harder examples. We observe that the training dynamics of AVH is vastly different compared to the training loss. Specifically, AVH quickly reaches a plateau for all samples even though the training loss keeps improving. This suggests the need for designing better loss functions that can target harder examples more effectively. We also find that AVH has a statistically significant correlation with human visual hardness. Finally, we demonstrate the benefit of AVH to a variety of applications such as self-training for domain adaptation and domain generalization.

Anderson acceleration is a well-established and simple technique for speeding up fixed-point computations with countless applications. This work introduces novel methods for adapting Anderson acceleration to proximal gradient algorithms. Under some technical conditions, we extend existing local convergence results of Anderson acceleration for smooth fixed-point mappings to the proposed non-smooth setting. We also prove analytically that it is in general, impossible to guarantee global convergence of native Anderson acceleration. We therefore propose a simple scheme for stabilization that combines the global worst-case guarantees of proximal gradient methods with the local adaptation and practical speed-up of Anderson acceleration. Finally, we provide the first applications of Anderson acceleration to non-Euclidean geometry.

This paper studies a problem of learning surface mesh via implicit functions in an emerging field of deep learning surface reconstruction, where implicit functions are popularly implemented as multi-layer perceptrons (MLPs) with rectified linear units (ReLU). To achieve meshing from the learned implicit functions, existing methods adopt the de-facto standard algorithm of marching cubes; while promising, they suffer from loss of precision learned in the MLPs, due to the discretization nature of marching cubes. Motivated by the knowledge that a ReLU based MLP partitions its input space into a number of linear regions, we identify from these regions analytic cells and faces that are associated with zero-level isosurface of the implicit function, and characterize the conditions under which the identified faces are guaranteed to connect and form a closed, piecewise planar surface. We propose a naturally parallelizable algorithm of analytic marching to exactly recover the mesh captured by a learned MLP. Experiments on deep learning mesh reconstruction verify the advantages of our algorithm over existing ones.

In this contribution, we augment the metric learning setting by introducing a parametric pseudo-distance, trained jointly with the encoder. Several interpretations are thus drawn for the learned distance-like model’s output. We first show it approximates a likelihood ratio which can be used for hypothesis tests, and that it further induces a large divergence across the joint distributions of pairs of examples from the same and from different classes. Evaluation is performed under the verification setting consisting of determining whether sets of examples belong to the same class, even if such classes are novel and were never presented to the model during training. Empirical evaluation shows such method defines an end-to-end approach for the verification problem, able to attain better performance than simple scorers such as those based on cosine similarity and further outperforming widely used downstream classifiers. We further observe training is much simplified under the proposed approach compared to metric learning with actual distances, requiring no complex scheme to harvest pairs of examples.

We provide an end-to-end differentially private spectral algorithm for learning LDA, based on matrix/tensor decompositions, and establish theoretical guarantees on utility/consistency of the estimated model parameters. We represent the spectral algorithm as a computational graph. Noise can be injected along the edges of this graph to obtain differential privacy. We identify subsets of edges, named “configurations”, such that adding noise to all edges in such a subset guarantees differential privacy of the end-to-end spectral algorithm. We characterize the sensitivity of the edges with respect to the input and thus estimate the amount of noise to be added to each edge for any required privacy level. We then characterize the utility loss for each configuration as a function of injected noise. Overall, by combining the sensitivity and utility characterization, we obtain an end-to-end differentially private spectral algorithm for LDA and identify which configurations outperform others under specific regimes. We are the first to achieve utility guarantees under a required level of differential privacy for learning in LDA. We additionally show that our method systematically outperforms differentially private variational inference.

Off-policy reinforcement learning (RL) using a fixed offline dataset of logged interactions is an important consideration in real world applications. This paper studies offline RL using the DQN replay dataset comprising the entire replay experience of a DQN agent on 60 Atari 2600 games. We demonstrate that recent off-policy deep RL algorithms, even when trained solely on this fixed dataset, outperform the fully trained DQN agent. To enhance generalization in the offline setting, we present Random Ensemble Mixture (REM), a robust Q-learning algorithm that enforces optimal Bellman consistency on random convex combinations of multiple Q-value estimates. Offline REM trained on the DQN replay dataset surpasses strong RL baselines. Ablation studies highlight the role of offline dataset size and diversity as well as the algorithm choice in our positive results. Overall, the results here present an optimistic view that robust RL algorithms trained on sufficiently large and diverse offline datasets can lead to high quality policies. The DQN replay dataset can serve as an offline RL benchmark and is open-sourced.

We study why overparameterization—increasing model size well beyond the point of zero training error—can hurt test error on minority groups despite improving average test error when there are spurious correlations in the data. Through simulations and experiments on two image datasets, we identify two key properties of the training data that drive this behavior: the proportions of majority versus minority groups, and the signal-to-noise ratio of the spurious correlations. We then analyze a linear setting and theoretically show how the inductive bias of models towards “memorizing” fewer examples can cause overparameterization to hurt. Our analysis leads to a counterintuitive approach of subsampling the majority group, which empirically achieves low minority error in the overparameterized regime, even though the standard approach of upweighting the minority fails. Overall, our results suggest a tension between using overparameterized models versus using all the training data for achieving low worst-group error.

Program execution speed critically depends on increasing cache hits, as cache hits are orders of magnitude faster than misses. To increase cache hits, we focus on the problem of cache replacement: choosing which cache line to evict upon inserting a new line. This is challenging because it requires planning far ahead and currently there is no known practical solution. As a result, current replacement policies typically resort to heuristics designed for specific common access patterns, which fail on more diverse and complex access patterns. In contrast, we propose an imitation learning approach to automatically learn cache access patterns by leveraging Belady’s, an oracle policy that computes the optimal eviction decision given the future cache accesses. While directly applying Belady’s is infeasible since the future is unknown, we train a policy conditioned only on past accesses that accurately approximates Belady’s even on diverse and complex access patterns, and call this approach Parrot. When evaluated on 13 of the most memory-intensive SPEC applications, Parrot increases cache miss rates by 20% over the current state of the art. In addition, on a large-scale web search benchmark, Parrot increases cache hit rates by 61% over a conventional LRU policy. We release a Gym environment to facilitate research in this area, as data is plentiful, and further advancements can have significant real-world impact.

With a view to bridging the gap between deep learning and symbolic AI, we present a novel end-to-end neural network architecture that learns to form propositional representations with an explicitly relational structure from raw pixel data. In order to evaluate and analyse the architecture, we introduce a family of simple visual relational reasoning tasks of varying complexity. We show that the proposed architecture, when pre-trained on a curriculum of such tasks, learns to generate reusable representations that better facilitate subsequent learning on previously unseen tasks when compared to a number of baseline architectures. The workings of a successfully trained model are visualised to shed some light on how the architecture functions.

Autoregressive (AR) models have been the dominating approach to conditional sequence generation, but are suffering from the issue of high inference latency. Non-autoregressive (NAR) models have been recently proposed to reduce the latency by generating all output tokens in parallel but could only achieve inferior accuracy compared to their autoregressive counterparts, primarily due to a difficulty in dealing with the multi-modality in sequence generation. This paper proposes a new approach that jointly optimizes both AR and NAR models in a unified Expectation-Maximization (EM) framework. In the E-step, an AR model learns to approximate the regularized posterior of the NAR model. In the M-step, the NAR model is updated on the new posterior and selects the training examples for the next AR model. This iterative process can effectively guide the system to remove the multi-modality in the output sequences. To our knowledge, this is the first EM approach to NAR sequence generation. We evaluate our method on the task of machine translation. Experimental results on benchmark data sets show that the proposed approach achieves competitive, if not better, performance with existing NAR models and significantly reduces the inference latency.

Derivative-free optimization (DFO) has recently gained a lot of momentum in machine learning, spawning interest in the community to design faster methods for problems where gradients are not accessible. While some attention has been given to the concept of acceleration in the DFO literature, existing stochastic algorithms for objective functions with a finite-sum structure have not been shown theoretically to achieve an accelerated rate of convergence. Algorithms that use acceleration in such a setting are prone to instabilities, making it difficult to reach convergence. In this work, we exploit the finite-sum structure of the objective in order to design a variance-reduced DFO algorithm that provably yields acceleration. We prove rates of convergence for both smooth convex and strongly-convex finite-sum objective functions. Finally, we validate our theoretical results empirically on several tasks and datasets.

We develop amortized population Gibbs (APG) samplers, a class of scalable methods that frame structured variational inference as adaptive importance sampling. APG samplers construct high-dimensional proposals by iterating over updates to lower-dimensional blocks of variables. We train each conditional proposal by minimizing the inclusive KL divergence with respect to the conditional posterior. To appropriately account for the size of the input data, we develop a new parameterization in terms of neural sufficient statistics. Experiments show that APG samplers can be used to train highly-structured deep generative models in an unsupervised manner, and achieve substantial improvements in inference accuracy relative to standard autoencoding variational methods.

Optimizing the parameters of partial differential equations (PDEs), i.e., PDE-constrained optimization (PDE-CO), allows us to model natural systems from observations or perform rational design of structures with complicated mechanical, thermal, or electromagnetic properties. However, PDE-CO is often computationally prohibitive due to the need to solve the PDE—typically via finite element analysis (FEA)—at each step of the optimization procedure. In this paper we propose amortized finite element analysis (AmorFEA), in which a neural network learns to produce accurate PDE solutions, while preserving many of the advantages of traditional finite element methods. This network is trained to directly minimize the potential energy from which the PDE and finite element method are derived, avoiding the need to generate costly supervised training data by solving PDEs with traditional FEA. As FEA is a variational procedure, AmorFEA is a direct analogue to popular amortized inference approaches in latent variable models, with the finite element basis acting as the variational family. AmorFEA can perform PDE-CO without the need to repeatedly solve the associated PDE, accelerating optimization when compared to a traditional workflow using FEA and the adjoint method.

Models that employ latent variables to capture structure in observed data lie at the heart of many current unsupervised learning algorithms, but exact maximum-likelihood learning for powerful and flexible latent-variable models is almost always intractable. Thus, state-of-the-art approaches either abandon the maximum-likelihood framework entirely, or else rely on a variety of variational approximations to the posterior distribution over the latents. Here, we propose an alternative approach that we call amortised learning. Rather than computing an approximation to the posterior over latents, we use a wake-sleep Monte-Carlo strategy to learn a function that directly estimates the maximum-likelihood parameter updates. Amortised learning is possible whenever samples of latents and observations can be simulated from the generative model, treating the model as a “black box”. We demonstrate its effectiveness on a wide range of complex models, including those with latents that are discrete or supported on non-Euclidean spaces.

The variance reduction class of algorithms including the representative ones, SVRG and SARAH, have well documented merits for empirical risk minimization problems. However, they require grid search to tune parameters (step size and the number of iterations per inner loop) for optimal performance. This work introduces ‘almost tune-free’ SVRG and SARAH schemes equipped with i) Barzilai-Borwein (BB) step sizes; ii) averaging; and, iii) the inner loop length adjusted to the BB step sizes. In particular, SVRG, SARAH, and their BB variants are first reexamined through an ‘estimate sequence’ lens to enable new averaging methods that tighten their convergence rates theoretically, and improve their performance empirically when the step size or the inner loop length is chosen large. Then a simple yet effective means to adjust the number of iterations per inner loop is developed to enhance the merits of the proposed averaging schemes and BB step sizes. Numerical tests corroborate the proposed methods.