ICLR 2022 Papers

Overparametrized Deep Neural Networks (DNNs) often achieve astounding performances, but may potentially result in severe generalization error. Recently, the relation between the sharpness of the loss landscape and the generalization error has been established by Foret et al. (2020), in which the Sharpness Aware Minimizer (SAM) was proposed to mitigate the degradation of the generalization. Unfortunately, SAM’s computational cost is roughly double that of base optimizers, such as Stochastic Gradient Descent (SGD). This paper thus proposes Efficient Sharpness Aware Minimizer (ESAM), which boosts SAM’s efficiency at no cost to its generalization performance. ESAM includes two novel and efficient training strategies—StochasticWeight Perturbation and Sharpness-Sensitive Data Selection. In the former, the sharpness measure is approximated by perturbing a stochastically chosen set of weights in each iteration; in the latter, the SAM loss is optimized using only a judiciously selected subset of data that is sensitive to the sharpness. We provide theoretical explanations as to why these strategies perform well. We also show, via extensive experiments on the CIFAR and ImageNet datasets, that ESAM enhances the efficiency over SAM from requiring 100% extra computations to 40% vis-`a-vis base optimizers, while test accuracies are preserved or even improved.

The study of provable adversarial robustness for deep neural networks (DNNs) has mainly focused on $\textit{static}$ supervised learning tasks such as image classification. However, DNNs have been used extensively in real-world $\textit{adaptive}$ tasks such as reinforcement learning (RL), making such systems vulnerable to adversarial attacks as well. Prior works in provable robustness in RL seek to certify the behaviour of the victim policy at every time-step against a non-adaptive adversary using methods developed for the static setting. But in the real world, an RL adversary can infer the defense strategy used by the victim agent by observing the states, actions, etc. from previous time-steps and adapt itself to produce stronger attacks in future steps (e.g., by focusing more on states critical to the agent's performance). We present an efficient procedure, designed specifically to defend against an adaptive RL adversary, that can directly certify the total reward without requiring the policy to be robust at each time-step. Focusing on randomized smoothing based defenses, our main theoretical contribution is to prove an $\textit{adaptive version}$ of the Neyman-Pearson Lemma -- a key lemma for smoothing-based certificates -- where the adversarial perturbation at a particular time can be a stochastic function of current and previous observations and states as well as previous actions. Building on this result, we propose $\textit{policy smoothing}$ where the agent adds a Gaussian noise to its observation at each time-step before passing it through the policy function. Our robustness certificates guarantee that the final total reward obtained by policy smoothing remains above a certain threshold, even though the actions at intermediate time-steps may change under the attack. We show that our certificates are $\textit{tight}$ by constructing a worst-case scenario that achieves the bounds derived in our analysis. Our experiments on various environments like Cartpole, Pong, Freeway and Mountain Car show that our method can yield meaningful robustness guarantees in practice.

Turbulence simulation with classical numerical solvers requires high-resolution grids to accurately resolve dynamics. Here we train learned simulators at low spatial and temporal resolutions to capture turbulent dynamics generated at high resolution. We show that our proposed model can simulate turbulent dynamics more accurately than classical numerical solvers at the comparably low resolutions across various scientifically relevant metrics. Our model is trained end-to-end from data and is capable of learning a range of challenging chaotic and turbulent dynamics at low resolution, including trajectories generated by the state-of-the-art Athena++ engine. We show that our simpler, general-purpose architecture outperforms various more specialized, turbulence-specific architectures from the learned turbulence simulation literature. In general, we see that learned simulators yield unstable trajectories; however, we show that tuning training noise and temporal downsampling solves this problem. We also find that while generalization beyond the training distribution is a challenge for learned models, training noise, added loss constraints, and dataset augmentation can help. Broadly, we conclude that our learned simulator outperforms traditional solvers run on coarser grids, and emphasize that simple design choices can offer stability and robust generalization.

Sparse neural networks (NNs) are intensively investigated in literature due to their appeal in saving storage, memory, and computational costs. A recent work (Ramanujan et al., 2020) showed that, different from conventional pruning-and-finetuning pipeline, there exist hidden subnetworks in randomly initialized NNs that have good performance without training the weights. However, such "hidden subnetworks" have mediocre performances and require an expensive edge-popup algorithm to search for them. In this work, we define an extended class of subnetworks in randomly initialized NNs called disguised subnetworks, which are not only "hidden" in the random networks but also "disguised" -- hence can only be "unmasked" with certain transformations on weights. We argue that the unmasking process plays an important role in enlarging the capacity of the subnetworks and thus grants two major benefits: (i) the disguised subnetworks easily outperform the hidden counterparts; (ii) the unmasking process helps to relax the quality requirement on the sparse subnetwork mask so that the expensive edge-popup algorithm can be replaced with more efficient alternatives. On top of this new concept, we propose a novel two-stage algorithm that plays a Peek-a-Boo (PaB) game to identify the disguised subnetworks with a combination of two operations: (1) searching efficiently for a subnetwork at random initialization; (2) unmasking the disguise by learning to transform the resulting subnetwork's remaining weights. Furthermore, we show that the unmasking process can be efficiently implemented (a) without referring to any latent weights or scores; and (b) by only leveraging approximated gradients, so that the whole training algorithm is computationally light. Extensive experiments with several large models (ResNet-18, ResNet-50, and WideResNet-28) and datasets (CIFAR-10, CIFAR-100 and ImageNet) demonstrate the competency of PaB over edge-popup and other counterparts. Our codes are available at: https://github.com/VITA-Group/Peek-a-Boo.

Differentiable physics has recently been shown as a powerful tool for solving soft-body manipulation tasks. However, the differentiable physics solver often gets stuck when the initial contact points of the end effectors are sub-optimal or when performing multi-stage tasks that require contact point switching, which often leads to local minima. To address this challenge, we propose a contact point discovery approach (CPDeform) that guides the stand-alone differentiable physics solver to deform various soft-body plasticines. The key idea of our approach is to integrate optimal transport-based contact points discovery into the differentiable physics solver to overcome the local minima from initial contact points or contact switching. On single-stage tasks, our method can automatically find suitable initial contact points based on transport priorities. On complex multi-stage tasks, we can iteratively switch the contact points of end-effectors based on transport priorities. To evaluate the effectiveness of our method, we introduce PlasticineLab-M that extends the existing differentiable physics benchmark PlasticineLab to seven new challenging multi-stage soft-body manipulation tasks. Extensive experimental results suggest that: 1) on multi-stage tasks that are infeasible for the vanilla differentiable physics solver, our approach discovers contact points that efficiently guide the solver to completion; 2) on tasks where the vanilla solver performs sub-optimally or near-optimally, our contact point discovery method performs better than or on par with the manipulation performance obtained with handcrafted contact points.

Combinatorial optimization lies at the core of many real-world problems. Especially since the rise of graph neural networks (GNNs), the deep learning community has been developing solvers that derive solutions to NP-hard problems by learning the problem-specific solution structure. However, reproducing the results of these publications proves to be difficult. We make three contributions. First, we present an open-source benchmark suite for the NP-hard Maximum Independent Set problem, in both its weighted and unweighted variants. The suite offers a unified interface to various state-of-the-art traditional and machine learning-based solvers. Second, using our benchmark suite, we conduct an in-depth analysis of the popular guided tree search algorithm by Li et al. [NeurIPS 2018], testing various configurations on small and large synthetic and real-world graphs. By re-implementing their algorithm with a focus on code quality and extensibility, we show that the graph convolution network used in the tree search does not learn a meaningful representation of the solution structure, and can in fact be replaced by random values. Instead, the tree search relies on algorithmic techniques like graph kernelization to find good solutions. Thus, the results from the original publication are not reproducible. Third, we extend the analysis to compare the tree search implementations to other solvers, showing that the classical algorithmic solvers often are faster, while providing solutions of similar quality. Additionally, we analyze a recent solver based on reinforcement learning and observe that for this solver, the GNN is responsible for the competitive solution quality.

In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To simplify the problem, we focus on a prototype elliptic PDE: the Schr\"odinger equation on a hypercube with zero Dirichlet boundary condition, which has wide application in the quantum-mechanical systems. We establish upper and lower bounds for both methods, which improves upon concurrently developed upper bounds for this problem via a fast rate generalization bound. We discover that the current Deep Ritz Methods is sub-optimal and propose a modified version of it. We also prove that PINN and the modified version of DRM can achieve minimax optimal bounds over Sobolev spaces. Empirically, following recent work which has shown that the deep model accuracy will improve with growing training sets according to a power law, we supply computational experiments to show a similar behavior of dimension dependent power law for deep PDE solvers.

Reliable out-of-distribution (OOD) detection is fundamental to implementing safer modern machine learning (ML) systems. In this paper, we introduce Igeood, an effective method for detecting OOD samples. Igeood applies to any pre-trained neural network, works under various degrees of access to the ML model, does not require OOD samples or assumptions on the OOD data but can also benefit (if available) from OOD samples. By building on the geodesic (Fisher-Rao) distance between the underlying data distributions, our discriminator can combine confidence scores from the logits outputs and the learned features of a deep neural network. Empirically, we show that Igeood outperforms competing state-of-the-art methods on a variety of network architectures and datasets.

Continual learning has been widely studied in recent years to resolve the catastrophic forgetting of deep neural networks. In this paper, we first enforce a low-rank filter subspace by decomposing convolutional filters within each network layer over a small set of filter atoms. Then, we perform continual learning with filter atom swapping. In other words, we learn for each task a new filter subspace for each convolutional layer, i.e., hundreds of parameters as filter atoms, but keep subspace coefficients shared across tasks. By maintaining a small footprint memory of filter atoms, we can easily archive models for past tasks to avoid forgetting. The effectiveness of this simple scheme for continual learning is illustrated both empirically and theoretically. The proposed atom swapping framework further enables flexible and efficient model ensemble with members selected within a task or across tasks to improve the performance in different continual learning settings. Being validated on multiple benchmark datasets with different convolutional network structures, the proposed method outperforms the state-of-the-art methods in both accuracy and scalability.

This paper proposes an algorithm, RMDA, for training neural networks (NNs) with a regularization term for promoting desired structures. RMDA does not incur computation additional to proximal SGD with momentum, and achieves variance reduction without requiring the objective function to be of the finite-sum form. Through the tool of manifold identification from nonlinear optimization, we prove that after a finite number of iterations, all iterates of RMDA possess a desired structure identical to that induced by the regularizer at the stationary point of asymptotic convergence, even in the presence of engineering tricks like data augmentation that complicate the training process. Experiments on training NNs with structured sparsity confirm that variance reduction is necessary for such an identification, and show that RMDA thus significantly outperforms existing methods for this task. For unstructured sparsity, RMDA also outperforms a state-of-the-art pruning method, validating the benefits of training structured NNs through regularization. Implementation of RMDA is available at https://www.github.com/zihsyuan1214/rmda.

The recent success of autoencoders for representation learning can be traced in large part to the addition of a regularization term. Such regularized autoencoders ``constrain" the representation so as to prevent overfitting to the data while producing a parsimonious generative model. A regularized autoencoder should in principle learn not only the data manifold, but also a set of geometry-preserving coordinates for the latent representation space; by geometry-preserving we mean that the latent space representation should attempt to preserve actual distances and angles on the data manifold. In this paper we first formulate a hierarchy for geometry-preserving mappings (isometry, conformal mapping of degree $k$, area-preserving mappings). We then show that a conformal regularization term of degree zero -- i.e., one that attempts to preserve angles and relative distances, instead of angles and exact distances -- produces data representations that are superior to other existing methods. Applying our algorithm to an unsupervised information retrieval task for CelebA data with 40 annotations, we achieve 79\% precision at five retrieved images, an improvement of more than 10\% compared to recent related work. Code is available at https://github.com/Gabe-YHLee/IRVAE-public.

Point cloud obtained from 3D scanning is often sparse, noisy, and irregular. To cope with these issues, recent studies have been separately conducted to densify, denoise, and complete inaccurate point cloud. In this paper, we advocate that jointly solving these tasks leads to significant improvement for point cloud reconstruction. To this end, we propose a deep point cloud reconstruction network consisting of two stages: 1) a 3D sparse stacked-hourglass network as for the initial densification and denoising, 2) a refinement via transformers converting the discrete voxels into continuous 3D points. In particular, we further improve the performance of the transformers by a newly proposed module called amplified positional encoding. This module has been designed to differently amplify the magnitude of positional encoding vectors based on the points' distances for adaptive refinements. Extensive experiments demonstrate that our network achieves state-of-the-art performance among the recent studies in the ScanNet, ICL-NUIM, and ShapeNet datasets. Moreover, we underline the ability of our network to generalize toward real-world and unmet scenes.

Randomized Smoothing (RS) is a promising method for obtaining robustness certificates by evaluating a base model under noise. In this work, we: (i) theoretically motivate why ensembles are a particularly suitable choice as base models for RS, and (ii) empirically confirm this choice, obtaining state-of-the-art results in multiple settings. The key insight of our work is that the reduced variance of ensembles over the perturbations introduced in RS leads to significantly more consistent classifications for a given input. This, in turn, leads to substantially increased certifiable radii for samples close to the decision boundary. Additionally, we introduce key optimizations which enable an up to 55-fold decrease in sample complexity of RS for predetermined radii, thus drastically reducing its computational overhead. Experimentally, we show that ensembles of only 3 to 10 classifiers consistently improve on their strongest constituting model with respect to their average certified radius (ACR) by 5% to 21% on both CIFAR10 and ImageNet, achieving a new state-of-the-art ACR of 0.86 and 1.11, respectively. We release all code and models required to reproduce our results at https://github.com/eth-sri/smoothing-ensembles.

Creating labeled training sets has become one of the major roadblocks in machine learning. To address this, recent Weak Supervision (WS) frameworks synthesize training labels from multiple potentially noisy supervision sources. However, existing frameworks are restricted to supervision sources that share the same output space as the target task. To extend the scope of usable sources, we formulate Weak Indirect Supervision (WIS), a new research problem for automatically synthesizing training labels based on indirect supervision sources that have different output label spaces. To overcome the challenge of mismatched output spaces, we develop a probabilistic modeling approach, PLRM, which uses user-provided label relations to model and leverage indirect supervision sources. Moreover, we provide a theoretically-principled test of the distinguishability of PLRM for unseen labels, along with an generalization bound. On both image and text classification tasks as well as an industrial advertising application, we demonstrate the advantages of PLRM by outperforming baselines by a margin of 2%-9%.

Synthesizing optimal controllers for dynamical systems often involves solving optimization problems with hard real-time constraints. These constraints determine the class of numerical methods that can be applied: computationally expensive but accurate numerical routines are replaced by fast and inaccurate methods, trading inference time for solution accuracy. This paper provides techniques to improve the quality of optimized control policies given a fixed computational budget. We achieve the above via a hypersolvers approach, which hybridizes a differential equation solver and a neural network. The performance is evaluated in direct and receding-horizon optimal control tasks in both low and high dimensions, where the proposed approach shows consistent Pareto improvements in solution accuracy and control performance.

In distribution compression, one aims to accurately summarize a probability distribution $\mathbb{P}$ using a small number of representative points. Near-optimal thinning procedures achieve this goal by sampling $n$ points from a Markov chain and identifying $\sqrt{n}$ points with $\widetilde{\mathcal{O}}(1/\sqrt{n})$ discrepancy to $\mathbb{P}$. Unfortunately, these algorithms suffer from quadratic or super-quadratic runtime in the sample size $n$. To address this deficiency, we introduce Compress++, a simple meta-procedure for speeding up any thinning algorithm while suffering at most a factor of $4$ in error. When combined with the quadratic-time kernel halving and kernel thinning algorithms of Dwivedi and Mackey (2021), Compress++ delivers $\sqrt{n}$ points with $\mathcal{O}(\sqrt{\log n/n})$ integration error and better-than-Monte-Carlo maximum mean discrepancy in $\mathcal{O}(n \log^3 n)$ time and $\mathcal{O}( \sqrt{n} \log^2 n )$ space. Moreover, Compress++ enjoys the same near-linear runtime given any quadratic-time input and reduces the runtime of super-quadratic algorithms by a square-root factor. In our benchmarks with high-dimensional Monte Carlo samples and Markov chains targeting challenging differential equation posteriors, Compress++ matches or nearly matches the accuracy of its input algorithm in orders of magnitude less time.

Learning to infer the conditional posterior model is a key step for robust meta-learning. This paper presents a new Bayesian meta-learning approach called Neural Variational Dropout Processes (NVDPs). NVDPs model the conditional posterior distribution based on a task-specific dropout; a low-rank product of Bernoulli experts meta-model is utilized for a memory-efficient mapping of dropout rates from a few observed contexts. It allows for a quick reconfiguration of a globally learned and shared neural network for new tasks in multi-task few-shot learning. In addition, NVDPs utilize a novel prior conditioned on the whole task data to optimize the conditional dropout posterior in the amortized variational inference. Surprisingly, this enables the robust approximation of task-specific dropout rates that can deal with a wide range of functional ambiguities and uncertainties. We compared the proposed method with other meta-learning approaches in the few-shot learning tasks such as 1D stochastic regression, image inpainting, and classification. The results show the excellent performance of NVDPs.

In this paper, we introduce Target-Aware Weighted Training (TAWT), a weighted training algorithm for cross-task learning based on minimizing a representation-based task distance between the source and target tasks. We show that TAWT is easy to implement, is computationally efficient, requires little hyperparameter tuning, and enjoys non-asymptotic learning-theoretic guarantees. The effectiveness of TAWT is corroborated through extensive experiments with BERT on four sequence tagging tasks in natural language processing (NLP), including part-of-speech (PoS) tagging, chunking, predicate detection, and named entity recognition (NER). As a byproduct, the proposed representation-based task distance allows one to reason in a theoretically principled way about several critical aspects of cross-task learning, such as the choice of the source data and the impact of fine-tuning.

The empirical success of deep convolutional networks on tasks involving high-dimensional data such as images or audio suggests that they can efficiently approximate certain functions that are well-suited for such tasks. In this paper, we study this through the lens of kernel methods, by considering simple hierarchical kernels with two or three convolution and pooling layers, inspired by convolutional kernel networks. These achieve good empirical performance on standard vision datasets, while providing a precise description of their functional space that yields new insights on their inductive bias. We show that the RKHS consists of additive models of interaction terms between patches, and that its norm encourages spatial similarities between these terms through pooling layers. We then provide generalization bounds which illustrate how pooling and patches yield improved sample complexity guarantees when the target function presents such regularities.