ICLR 2022 Papers

The Koopman operator theory linearly describes nonlinear dynamical systems in a high-dimensional functional space and it allows to apply linear control methods to highly nonlinear systems. However, the Koopman operator does not account for any uncertainty in dynamical systems, causing it to perform poorly in real-world applications. Therefore, we propose a deep stochastic Koopman operator (DeSKO) model in a robust learning control framework to guarantee stability of nonlinear stochastic systems. The DeSKO model captures a dynamical system's uncertainty by inferring a distribution of observables. We use the inferred distribution to design a robust, stabilizing closed-loop controller for a dynamical system. Modeling and control experiments on several advanced control benchmarks show that our framework is more robust and scalable than state-of-the-art deep Koopman operators and reinforcement learning methods. Tested control benchmarks include a soft robotic arm, a legged robot, and a biological gene regulatory network. We also demonstrate that this robust control method resists previously unseen uncertainties, such as external disturbances, with a magnitude of up to five times the maximum control input. Our approach opens up new possibilities in learning control for high-dimensional nonlinear systems while robustly managing internal or external uncertainty.

Molecular chirality, a form of stereochemistry most often describing relative spatial arrangements of bonded neighbors around tetrahedral carbon centers, influences the set of 3D conformers accessible to the molecule without changing its 2D graph connectivity. Chirality can strongly alter (bio)chemical interactions, particularly protein-drug binding. Most 2D graph neural networks (GNNs) designed for molecular property prediction at best use atomic labels to naïvely treat chirality, while E(3)-invariant 3D GNNs are invariant to chirality altogether. To enable representation learning on molecules with defined stereochemistry, we design an SE(3)-invariant model that processes torsion angles of a 3D molecular conformer. We explicitly model conformational flexibility by integrating a novel type of invariance to rotations about internal molecular bonds into the architecture, mitigating the need for multi-conformer data augmentation. We test our model on four benchmarks: contrastive learning to distinguish conformers of different stereoisomers in a learned latent space, classification of chiral centers as R/S, prediction of how enantiomers rotate circularly polarized light, and ranking enantiomers by their docking scores in an enantiosensitive protein pocket. We compare our model, Chiral InterRoto-Invariant Neural Network (ChIRo), with 2D and 3D GNNs to demonstrate that our model achieves state of the art performance when learning chiral-sensitive functions from molecular structures.

Common wisdom in the graph neural network (GNN) community dictates that anisotropic models---in which messages sent between nodes are a function of both the source and target node---are required to achieve state-of-the-art performance. Benchmarks to date have demonstrated that these models perform better than comparable isotropic models---where messages are a function of the source node only. In this work we provide empirical evidence challenging this narrative: we propose an isotropic GNN, which we call Efficient Graph Convolution (EGC), that consistently outperforms comparable anisotropic models, including the popular GAT or PNA architectures by using spatially-varying adaptive filters. In addition to raising important questions for the GNN community, our work has significant real-world implications for efficiency. EGC achieves higher model accuracy, with lower memory consumption and latency, along with characteristics suited to accelerator implementation, while being a drop-in replacement for existing architectures. As an isotropic model, it requires memory proportional to the number of vertices in the graph ($\mathcal{O}(V)$); in contrast, anisotropic models require memory proportional to the number of edges ($\mathcal{O}(E)$). We demonstrate that EGC outperforms existing approaches across 6 large and diverse benchmark datasets, and conclude by discussing questions that our work raise for the community going forward. Code and pretrained models for our experiments are provided at https://github.com/shyam196/egc.

Modern deep reinforcement learning (DRL) has been successful in solving a range of challenging sequential decision-making problems. Most of these algorithms use an ensemble of neural networks as their backbone structure and benefit from the diversity among the neural networks to achieve optimal results. Unfortunately, the members of the ensemble can converge to the same point either the parametric space or representation space during the training phase, therefore, losing all the leverage of an ensemble. In this paper, we describe Maximize Ensemble Diversity in Reinforcement Learning (MED-RL), a set of regularization methods inspired from the economics and consensus optimization to improve diversity in the ensemble-based deep reinforcement learning methods by encouraging inequality between the networks during training. We integrated MED-RL in five of the most common ensemble-based deep RL algorithms for both continuous and discrete control tasks and evaluated on six Mujoco environments and six Atari games. Our results show that MED-RL augmented algorithms outperform their un-regularized counterparts significantly and in some cases achieved more than 300$\%$ in performance gains.

The randomized singular value decomposition (SVD) is a popular and effective algorithm for computing a near-best rank $k$ approximation of a matrix $A$ using matrix-vector products with standard Gaussian vectors. Here, we generalize the theory of randomized SVD to multivariate Gaussian vectors, allowing one to incorporate prior knowledge of $A$ into the algorithm. This enables us to explore the continuous analogue of the randomized SVD for Hilbert--Schmidt (HS) operators using operator-function products with functions drawn from a Gaussian process (GP). We then construct a new covariance kernel for GPs, based on weighted Jacobi polynomials, which allows us to rapidly sample the GP and control the smoothness of the randomly generated functions. Numerical examples on matrices and HS operators demonstrate the applicability of the algorithm.

Machine learning training methods depend plentifully and intricately on hyperparameters, motivating automated strategies for their optimisation. Many existing algorithms restart training for each new hyperparameter choice, at considerable computational cost. Some hypergradient-based one-pass methods exist, but these either cannot be applied to arbitrary optimiser hyperparameters (such as learning rates and momenta) or take several times longer to train than their base models. We extend these existing methods to develop an approximate hypergradient-based hyperparameter optimiser which is applicable to any continuous hyperparameter appearing in a differentiable model weight update, yet requires only one training episode, with no restarts. We also provide a motivating argument for convergence to the true hypergradient, and perform tractable gradient-based optimisation of independent learning rates for each model parameter. Our method performs competitively from varied random hyperparameter initialisations on several UCI datasets and Fashion-MNIST (using a one-layer MLP), Penn Treebank (using an LSTM) and CIFAR-10 (using a ResNet-18), in time only 2-3x greater than vanilla training.

Adversarial Propagation (AdvProp) is an effective way to improve recognition models, leveraging adversarial examples. Nonetheless, AdvProp suffers from the extremely slow training speed, mainly because: a) extra forward and backward passes are required for generating adversarial examples; b) both original samples and their adversarial counterparts are used for training (i.e., 2X data). In this paper, we introduce Fast AdvProp, which aggressively revamps AdvProp's costly training components, rendering the method nearly as cheap as the vanilla training. Specifically, our modifications in Fast AdvProp are guided by the hypothesis that disentangled learning with adversarial examples is the key for performance improvements, while other training recipes (e.g., paired clean and adversarial training samples, multi-step adversarial attackers) could be largely simplified. Our empirical results show that, compared to the vanilla training baseline, Fast AdvProp is able to further model performance on a spectrum of visual benchmarks, without incurring extra training cost. Additionally, our ablations find Fast AdvProp scales better if larger models are used, is compatible with existing data augmentation methods (i.e., Mixup and CutMix), and can be easily adapted to other recognition tasks like object detection. The code is available here: https://github.com/meijieru/fast_advprop.

We present Reward-Switching Policy Optimization (RSPO), a paradigm to discover diverse strategies in complex RL environments by iteratively finding novel policies that are both locally optimal and sufficiently different from existing ones. To encourage the learning policy to consistently converge towards a previously undiscovered local optimum, RSPO switches between extrinsic and intrinsic rewards via a trajectory-based novelty measurement during the optimization process. When a sampled trajectory is sufficiently distinct, RSPO performs standard policy optimization with extrinsic rewards. For trajectories with high likelihood under existing policies, RSPO utilizes an intrinsic diversity reward to promote exploration. Experiments show that RSPO is able to discover a wide spectrum of strategies in a variety of domains, ranging from single-agent navigation tasks and MuJoCo control to multi-agent stag-hunt games and the StarCraft II Multi-Agent Challenge.

Recent attempts at image steganography make use of advances in deep learning to train an encoder-decoder network pair to hide and retrieve secret messages in images. These methods are able to hide large amounts of data, but they also incur high decoding error rates (around 20%). In this paper, we propose a novel algorithm for steganography that takes advantage of the fact that neural networks are sensitive to tiny perturbations. Our method, Fixed Neural Network Steganography (FNNS), yields significantly lower error rates when compared to prior state-of-the-art methods and achieves 0% error reliably for hiding up to 3 bits per pixel (bpp) of secret information in images. FNNS also successfully evades existing statistical steganalysis systems and can be modified to evade neural steganalysis systems as well. Recovering every bit correctly, up to 3 bpp, enables novel applications that requires encryption. We introduce one specific use case for facilitating anonymized and safe image sharing. Our code is available at https://github.com/varshakishore/FNNS.

Combinatorial optimization problems with parameters to be predicted from side information are commonly seen in a variety of problems during the paradigm shift from reactive decision making to proactive decision making. Due to the misalignment between the continuous prediction results and the discrete decisions in optimization problems, it is hard to achieve a satisfactory prediction result with the ordinary $l_2$ loss in the prediction phase. To properly connect the prediction loss with the optimization goal, in this paper we propose a total group preorder (TGP) loss and its differential version called approximated total group preorder (ATGP) loss for predict-then-optimize (PTO) problems with strong ranking property. These new losses are provably more robust than the usual $l_2$ loss in a linear regression setting and have great potential to extend to other settings. We also propose an automatic searching algorithm that adapts the ATGP loss to PTO problems with different combinatorial structures. Extensive experiments on the ranking problem, the knapsack problem, and the shortest path problem have demonstrated that our proposed method can achieve a significant performance compared to the other methods designed for PTO problems.

We present an empirical study of scaling properties of encoder-decoder Transformer models used in neural machine translation (NMT). We show that cross-entropy loss as a function of model size follows a certain scaling law. Specifically (i) We propose a formula which describes the scaling behavior of cross-entropy loss as a bivariate function of encoder and decoder size, and show that it gives accurate predictions under a variety of scaling approaches and languages; we show that the total number of parameters alone is not sufficient for such purposes. (ii) We observe different power law exponents when scaling the decoder vs scaling the encoder, and provide recommendations for optimal allocation of encoder/decoder capacity based on this observation. (iii) We also report that the scaling behavior of the model is acutely influenced by composition bias of the train/test sets, which we define as any deviation from naturally generated text (either via machine generated or human translated text). We observe that natural text on the target side enjoys scaling, which manifests as successful reduction of the cross-entropy loss. (iv) Finally, we investigate the relationship between the cross-entropy loss and the quality of the generated translations. We find two different behaviors, depending on the nature of the test data. For test sets which were originally translated from target language to source language, both loss and BLEU score improve as model size increases. In contrast, for test sets originally translated from source language to target language, the loss improves, but the BLEU score stops improving after a certain threshold. We release generated text from all models used in this study.

Intrinsic interpretability of graph neural networks (GNNs) is to find a small subset of the input graph's features --- rationale --- which guides the model prediction. Unfortunately, the leading rationalization models often rely on data biases, especially shortcut features, to compose rationales and make predictions without probing the critical and causal patterns. Moreover, such data biases easily change outside the training distribution. As a result, these models suffer from a huge drop in interpretability and predictive performance on out-of-distribution data. In this work, we propose a new strategy of discovering invariant rationale (DIR) to construct intrinsically interpretable GNNs. It conducts interventions on the training distribution to create multiple interventional distributions. Then it approaches the causal rationales that are invariant across different distributions while filtering out the spurious patterns that are unstable. Experiments on both synthetic and real-world datasets validate the superiority of our DIR in terms of interpretability and generalization ability on graph classification over the leading baselines. Code and datasets are available at https://github.com/Wuyxin/DIR-GNN.

Although DALL-E has shown an impressive ability of composition-based systematic generalization in image generation, it requires the dataset of text-image pairs and the compositionality is provided by the text. In contrast, object-centric representation models like the Slot Attention model learn composable representations without the text prompt. However, unlike DALL-E, its ability to systematically generalize for zero-shot generation is significantly limited. In this paper, we propose a simple but novel slot-based autoencoding architecture, called SLATE, for combining the best of both worlds: learning object-centric representations that allow systematic generalization in zero-shot image generation without text. As such, this model can also be seen as an illiterate DALL-E model. Unlike the pixel-mixture decoders of existing object-centric representation models, we propose to use the Image GPT decoder conditioned on the slots for capturing complex interactions among the slots and pixels. In experiments, we show that this simple and easy-to-implement architecture not requiring a text prompt achieves significant improvement in in-distribution and out-of-distribution (zero-shot) image generation and qualitatively comparable or better slot-attention structure than the models based on mixture decoders.

It has been well recognized that neural network based image classifiers are easily fooled by images with tiny perturbations crafted by an adversary. There has been a vast volume of research to generate and defend such adversarial attacks. However, the following problem is left unexplored: How to reverse-engineer adversarial perturbations from an adversarial image? This leads to a new adversarial learning paradigm—Reverse Engineering of Deceptions (RED). If successful, RED allows us to estimate adversarial perturbations and recover the original images. However, carefully crafted, tiny adversarial perturbations are difficult to recover by optimizing a unilateral RED objective. For example, the pure image denoising method may overfit to minimizing the reconstruction error but hardly preserve the classification properties of the true adversarial perturbations. To tackle this challenge, we formalize the RED problem and identify a set of principles crucial to the RED approach design. Particularly, we find that prediction alignment and proper data augmentation (in terms of spatial transformations) are two criteria to achieve a generalizable RED approach. By integrating these RED principles with image denoising, we propose a new Class-Discriminative Denoising based RED framework, termed CDD-RED. Extensive experiments demonstrate the effectiveness of CDD-RED under different evaluation metrics (ranging from the pixel-level, prediction-level to the attribution-level alignment) and a variety of attack generation methods (e.g., FGSM, PGD, CW, AutoAttack, and adaptive attacks).

Time-series data are ubiquitous these days, but lack of the labels in time-series data is regarded as a hurdle for its broad applicability. Meanwhile, active learning has been successfully adopted to reduce the labeling efforts in various tasks. Thus, this paper addresses an important issue, time-series active learning. Inspired by the temporal coherence in time-series data, where consecutive data points tend to have the same label, our label propagation framework, called TCLP, automatically assigns a queried label to the data points within an accurately estimated time-series segment, thereby significantly boosting the impact of an individual query. Compared with traditional time-series active learning, TCLP is shown to improve the classification accuracy by up to 7.1 times when only 0.8% of data points in the entire time series are queried for their labels.

We consider representation learning of 3D molecular graphs in which each atom is associated with a spatial position in 3D. This is an under-explored area of research, and a principled message passing framework is currently lacking. In this work, we conduct analyses in the spherical coordinate system (SCS) for the complete identification of 3D graph structures. Based on such observations, we propose the spherical message passing (SMP) as a novel and powerful scheme for 3D molecular learning. SMP dramatically reduces training complexity, enabling it to perform efficiently on large-scale molecules. In addition, SMP is capable of distinguishing almost all molecular structures, and the uncovered cases may not exist in practice. Based on meaningful physically-based representations of 3D information, we further propose the SphereNet for 3D molecular learning. Experimental results demonstrate that the use of meaningful 3D information in SphereNet leads to significant performance improvements in prediction tasks. Our results also demonstrate the advantages of SphereNet in terms of capability, efficiency, and scalability.

Information sharing is key in building team cognition and enables coordination and cooperation. High-performing human teams also benefit from acting strategically with hierarchical levels of iterated communication and rationalizability, meaning a human agent can reason about the actions of their teammates in their decision-making. Yet, the majority of prior work in Multi-Agent Reinforcement Learning (MARL) does not support iterated rationalizability and only encourage inter-agent communication, resulting in a suboptimal equilibrium cooperation strategy. In this work, we show that reformulating an agent's policy to be conditional on the policies of its neighboring teammates inherently maximizes Mutual Information (MI) lower-bound when optimizing under Policy Gradient (PG). Building on the idea of decision-making under bounded rationality and cognitive hierarchy theory, we show that our modified PG approach not only maximizes local agent rewards but also implicitly reasons about MI between agents without the need for any explicit ad-hoc regularization terms. Our approach, InfoPG, outperforms baselines in learning emergent collaborative behaviors and sets the state-of-the-art in decentralized cooperative MARL tasks. Our experiments validate the utility of InfoPG by achieving higher sample efficiency and significantly larger cumulative reward in several complex cooperative multi-agent domains.

Potential games are arguably one of the most important and widely studied classes of normal form games. They define the archetypal setting of multi-agent coordination in which all agents utilities are perfectly aligned via a common potential function. Can this intuitive framework be transplanted in the setting of Markov games? What are the similarities and differences between multi-agent coordination with and without state dependence? To answer these questions, we study a natural class of Markov Potential Games (MPGs) that generalize prior attempts at capturing complex stateful multi-agent coordination. Counter-intuitively, insights from normal-form potential games do not carry over as MPGs involve settings where state-games can be zero-sum games. In the opposite direction, Markov games where every state-game is a potential game are not necessarily MPGs. Nevertheless, MPGs showcase standard desirable properties such as the existence of deterministic Nash policies. In our main technical result, we prove convergence of independent policy gradient and its stochastic counterpart to Nash policies (polynomially fast in the approximation error) by adapting recent gradient dominance property arguments developed for single-agent Markov decision processes to multi-agent learning settings.

Modeling dynamical systems combining prior physical knowledge and machine learning (ML) is promising in scientific problems when the underlying processes are not fully understood, e.g. when the dynamics is partially known. A common practice to identify the respective parameters of the physical and ML components is to formulate the problem as supervised learning on observed trajectories. However, this formulation leads to an infinite number of possible decompositions. To solve this ill-posedness, we reformulate the learning problem by introducing an upper bound on the prediction error of a physical-statistical model. This allows us to control the contribution of both the physical and statistical components to the overall prediction. This framework generalizes several existing hybrid schemes proposed in the literature. We provide theoretical guarantees on the well-posedness of our formulation along with a proof of convergence in a simple affine setting. For more complex dynamics, we validate our framework experimentally.