ICLR 2022 Papers

Humans commonly solve complex problems by decomposing them into easier subproblems and then combining the subproblem solutions. This type of compositional reasoning permits reuse of the subproblem solutions when tackling future tasks that share part of the underlying compositional structure. In a continual or lifelong reinforcement learning (RL) setting, this ability to decompose knowledge into reusable components would enable agents to quickly learn new RL tasks by leveraging accumulated compositional structures. We explore a particular form of composition based on neural modules and present a set of RL problems that intuitively admit compositional solutions. Empirically, we demonstrate that neural composition indeed captures the underlying structure of this space of problems. We further propose a compositional lifelong RL method that leverages accumulated neural components to accelerate the learning of future tasks while retaining performance on previous tasks via off-line RL over replayed experiences.

Populations have often been perceived as a structuring component for language to emerge and evolve: the larger the population, the more systematic the language. While this observation is widespread in the sociolinguistic literature, it has not been reproduced in computer simulations with neural agents. In this paper, we thus aim to clarify this apparent contradiction. We explore emergent language properties by varying agent population size in the speaker-listener Lewis Game. After reproducing the experimental paradox, we challenge the simulation assumption that the agent community is homogeneous. We first investigate how speaker-listener asymmetry alters language structure to examine two potential diversity factors: training speed and network capacity. We find out that emergent language properties are only altered by the relative difference of factors between speaker and listener, and not by their absolute values. From then, we leverage this observation to control population heterogeneity without introducing confounding factors. We finally show that introducing such training speed heterogeneities naturally sort out the initial paradox: larger simulated communities start developing more systematic and structured languages.

We study non-convex subgradient flows for training two-layer ReLU neural networks from a convex geometry and duality perspective. We characterize the implicit bias of unregularized non-convex gradient flow as convex regularization of an equivalent convex model. We then show that the limit points of non-convex subgradient flows can be identified via primal-dual correspondence in this convex optimization problem. Moreover, we derive a sufficient condition on the dual variables which ensures that the stationary points of the non-convex objective are the KKT points of the convex objective, thus proving convergence of non-convex gradient flows to the global optimum. For a class of regular training data distributions such as orthogonal separable data, we show that this sufficient condition holds. Therefore, non-convex gradient flows in fact converge to optimal solutions of a convex optimization problem. We present numerical results verifying the predictions of our theory for non-convex subgradient descent.

We present a novel method for 3D shape representation learning using multi-scale wavelet decomposition. Previous works often decompose 3D shapes into complementary components in spatial domain at a single scale. In this work, we study to decompose 3D shapes into sub-bands components in frequency domain at multiple scales, resulting in a hierarchical decomposition tree in a principled manner rooted in multi-resolution wavelet analysis. Specifically, we propose Adaptive Wavelet Transformer Network (AWT-Net) that firstly generates approximation or detail wavelet coefficients per point, classifying each point into high or low sub-bands components, using lifting scheme at multiple scales recursively and hierarchically. Then, AWT-Net exploits Transformer to enhance the original shape features by querying and fusing features from different but integrated sub-bands. The wavelet coefficients can be learned without direct supervision on coefficients, and AWT-Net is fully differentiable and can be learned in an end-to-end fashion. Extensive experiments demonstrate that AWT-Net achieves competitive performance on 3D shape classification and segmentation benchmarks.

Learning hierarchical structures in sequential data -- from simple algorithmic patterns to natural language -- in a reliable, generalizable way remains a challenging problem for neural language models. Past work has shown that recurrent neural networks (RNNs) struggle to generalize on held-out algorithmic or syntactic patterns without supervision or some inductive bias. To remedy this, many papers have explored augmenting RNNs with various differentiable stacks, by analogy with finite automata and pushdown automata (PDAs). In this paper, we improve the performance of our recently proposed Nondeterministic Stack RNN (NS-RNN), which uses a differentiable data structure that simulates a nondeterministic PDA, with two important changes. First, the model now assigns unnormalized positive weights instead of probabilities to stack actions, and we provide an analysis of why this improves training. Second, the model can directly observe the state of the underlying PDA. Our model achieves lower cross-entropy than all previous stack RNNs on five context-free language modeling tasks (within 0.05 nats of the information-theoretic lower bound), including a task on which the NS-RNN previously failed to outperform a deterministic stack RNN baseline. Finally, we propose a restricted version of the NS-RNN that incrementally processes infinitely long sequences, and we present language modeling results on the Penn Treebank.

Most set prediction models in deep learning use set-equivariant operations, but they actually operate on multisets. We show that set-equivariant functions cannot represent certain functions on multisets, so we introduce the more appropriate notion of multiset-equivariance. We identify that the existing Deep Set Prediction Network (DSPN) can be multiset-equivariant without being hindered by set-equivariance and improve it with approximate implicit differentiation, allowing for better optimization while being faster and saving memory. In a range of toy experiments, we show that the perspective of multiset-equivariance is beneficial and that our changes to DSPN achieve better results in most cases. On CLEVR object property prediction, we substantially improve over the state-of-the-art Slot Attention from 8% to 77% in one of the strictest evaluation metrics because of the benefits made possible by implicit differentiation.

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we show that the OT map itself can be used as a generative model, providing comparable performance. Previous analogous approaches consider OT maps as generative models only in the latent spaces due to their poor performance in the original high-dimensional ambient space. In contrast, we apply OT maps directly in the ambient space, e.g., a space of high-dimensional images. First, we derive a min-max optimization algorithm to efficiently compute OT maps for the quadratic cost (Wasserstein-2 distance). Next, we extend the approach to the case when the input and output distributions are located in the spaces of different dimensions and derive error bounds for the computed OT map. We evaluate the algorithm on image generation and unpaired image restoration tasks. In particular, we consider denoising, colorization, and inpainting, where the optimality of the restoration map is a desired attribute, since the output (restored) image is expected to be close to the input (degraded) one.

Multilingual machine translation aims to develop a single model for multiple language directions. However, existing multilingual models based on Transformer are limited in terms of both translation performance and inference speed. In this paper, we propose switch-GLAT, a non-autoregressive multilingual machine translation model with a code-switch decoder. It can generate contextual code-switched translations for a given source sentence, and perform code-switch back-translation, greatly boosting multilingual translation performance. In addition, its inference is highly efficient thanks to its parallel decoder. Experiments show that our proposed switch-GLAT outperform the multilingual Transformer with as much as 0.74 BLEU improvement and 6.2x faster decoding speed in inference.

Multiple views of data, both naturally acquired (e.g., image and audio) and artificially produced (e.g., via adding different noise to data samples), have proven useful in enhancing representation learning. Natural views are often handled by multiview analysis tools, e.g., (deep) canonical correlation analysis [(D)CCA], while the artificial ones are frequently used in self-supervised learning (SSL) paradigms, e.g., BYOL and Barlow Twins. Both types of approaches often involve learning neural feature extractors such that the embeddings of data exhibit high cross-view correlations. Although intuitive, the effectiveness of correlation-based neural embedding is mostly empirically validated. This work aims to understand latent correlation maximization-based deep multiview learning from a latent component identification viewpoint. An intuitive generative model of multiview data is adopted, where the views are different nonlinear mixtures of shared and private components. Since the shared components are view/distortion-invariant, representing the data using such components is believed to reveal the identity of the samples effectively and robustly. Under this model, latent correlation maximization is shown to guarantee the extraction of the shared components across views (up to certain ambiguities). In addition, it is further shown that the private information in each view can be provably disentangled from the shared using proper regularization design. A finite sample analysis, which has been rare in nonlinear mixture identifiability study, is also presented. The theoretical results and newly designed regularization are tested on a series of tasks.

Most convergence guarantees for stochastic gradient descent with momentum (SGDm) rely on iid sampling. Yet, SGDm is often used outside this regime, in settings with temporally correlated input samples such as continual learning and reinforcement learning. Existing work has shown that SGDm with a decaying step-size can converge under Markovian temporal correlation. In this work, we show that SGDm under covariate shift with a fixed step-size can be unstable and diverge. In particular, we show SGDm under covariate shift is a parametric oscillator, and so can suffer from a phenomenon known as resonance. We approximate the learning system as a time varying system of ordinary differential equations, and leverage existing theory to characterize the system's divergence/convergence as resonant/nonresonant modes. The theoretical result is limited to the linear setting with periodic covariate shift, so we empirically supplement this result to show that resonance phenomena persist even under non-periodic covariate shift, nonlinear dynamics with neural networks, and optimizers other than SGDm.

Drawing inspiration from gradient-based meta-learning methods with infinitely small gradient steps, we introduce Continuous-Time Meta-Learning (COMLN), a meta-learning algorithm where adaptation follows the dynamics of a gradient vector field. Specifically, representations of the inputs are meta-learned such that a task-specific linear classifier is obtained as a solution of an ordinary differential equation (ODE). Treating the learning process as an ODE offers the notable advantage that the length of the trajectory is now continuous, as opposed to a fixed and discrete number of gradient steps. As a consequence, we can optimize the amount of adaptation necessary to solve a new task using stochastic gradient descent, in addition to learning the initial conditions as is standard practice in gradient-based meta-learning. Importantly, in order to compute the exact meta-gradients required for the outer-loop updates, we devise an efficient algorithm based on forward mode differentiation, whose memory requirements do not scale with the length of the learning trajectory, thus allowing longer adaptation in constant memory. We provide analytical guarantees for the stability of COMLN, we show empirically its efficiency in terms of runtime and memory usage, and we illustrate its effectiveness on a range of few-shot image classification problems.

Federated learning (FL) enables distributed optimization of machine learning models while protecting privacy by independently training local models on each client and then aggregating parameters on a central server, thereby producing an effective global model. Although a variety of FL algorithms have been proposed, their training efficiency remains low when the data are not independently and identically distributed (non-i.i.d.) across different clients. We observe that the slow convergence rates of the existing methods are (at least partially) caused by the catastrophic forgetting issue during the local training stage on each individual client, which leads to a large increase in the loss function concerning the previous training data provided at other clients. Here, we propose FedReg, an algorithm to accelerate FL with alleviated knowledge forgetting in the local training stage by regularizing locally trained parameters with the loss on generated pseudo data, which encode the knowledge of previous training data learned by the global model. Our comprehensive experiments demonstrate that FedReg not only significantly improves the convergence rate of FL, especially when the neural network architecture is deep and the clients' data are extremely non-i.i.d., but is also able to protect privacy better in classification problems and more robust against gradient inversion attacks.

This article considers the popular MCMC method of unadjusted Langevin Monte Carlo (LMC) and provides a non-asymptotic analysis of its sampling error in 2-Wasserstein distance. The proof is based on a refinement of mean-square analysis in Li et al. (2019), and this refined framework automates the analysis of a large class of sampling algorithms based on discretizations of contractive SDEs. Using this framework, we establish an $\tilde{O}(\sqrt{d}/\epsilon)$ mixing time bound for LMC, without warm start, under the common log-smooth and log-strongly-convex conditions, plus a growth condition on the 3rd-order derivative of the potential of target measures. This bound improves the best previously known $\tilde{O}(d/\epsilon)$ result and is optimal (in terms of order) in both dimension $d$ and accuracy tolerance $\epsilon$ for target measures satisfying the aforementioned assumptions. Our theoretical analysis is further validated by numerical experiments.

Multi-hop logical reasoning is an established problem in the field of representation learning on knowledge graphs (KGs). It subsumes both one-hop link prediction as well as other more complex types of logical queries. Existing algorithms operate only on classical, triple-based graphs, whereas modern KGs often employ a hyper-relational modeling paradigm. In this paradigm, typed edges may have several key-value pairs known as qualifiers that provide fine-grained context for facts. In queries, this context modifies the meaning of relations, and usually reduces the answer set. Hyper-relational queries are often observed in real-world KG applications, and existing approaches for approximate query answering cannot make use of qualifier pairs. In this work, we bridge this gap and extend the multi-hop reasoning problem to hyper-relational KGs allowing to tackle this new type of complex queries. Building upon recent advancements in Graph Neural Networks and query embedding techniques, we study how to embed and answer hyper-relational conjunctive queries. Besides that, we propose a method to answer such queries and demonstrate in our experiments that qualifiers improve query answering on a diverse set of query patterns.

Graph Neural Networks (GNNs) are popular for graph machine learning and have shown great results on wide node classification tasks. Yet, they are less popular for practical deployments in the industry owing to their scalability challenges incurred by data dependency. Namely, GNN inference depends on neighbor nodes multiple hops away from the target, and fetching them burdens latency-constrained applications. Existing inference acceleration methods like pruning and quantization can speed up GNNs by reducing Multiplication-and-ACcumulation (MAC) operations, but the improvements are limited given the data dependency is not resolved. Conversely, multi-layer perceptrons (MLPs) have no graph dependency and infer much faster than GNNs, even though they are less accurate than GNNs for node classification in general. Motivated by these complementary strengths and weaknesses, we bring GNNs and MLPs together via knowledge distillation (KD). Our work shows that the performance of MLPs can be improved by large margins with GNN KD. We call the distilled MLPs Graph-less Neural Networks (GLNNs) as they have no inference graph dependency. We show that GLNNs with competitive accuracy infer faster than GNNs by 146X-273X and faster than other acceleration methods by 14X-27X. Under a production setting involving both transductive and inductive predictions across 7 datasets, GLNN accuracies improve over stand-alone MLPs by 12.36% on average and match GNNs on 6/7 datasets. Comprehensive analysis shows when and why GLNNs can achieve competitive accuracies to GNNs and suggests GLNN as a handy choice for latency-constrained applications.

The literature has proposed several methods to finetune pretrained GANs on new datasets, which typically results in higher performance compared to training from scratch, especially in the limited-data regime. However, despite the apparent empirical benefits of GAN pretraining, its inner mechanisms were not analyzed in-depth, and understanding of its role is not entirely clear. Moreover, the essential practical details, e.g., selecting a proper pretrained GAN checkpoint, currently do not have rigorous grounding and are typically determined by trial and error. This work aims to dissect the process of GAN finetuning. First, we show that initializing the GAN training process by a pretrained checkpoint primarily affects the model's coverage rather than the fidelity of individual samples. Second, we explicitly describe how pretrained generators and discriminators contribute to the finetuning process and explain the previous evidence on the importance of pretraining both of them. Finally, as an immediate practical benefit of our analysis, we describe a simple recipe to choose an appropriate GAN checkpoint that is the most suitable for finetuning to a particular target task. Importantly, for most of the target tasks, Imagenet-pretrained GAN, despite having poor visual quality, appears to be an excellent starting point for finetuning, resembling the typical pretraining scenario of discriminative computer vision models.

This paper studies Associate Learning (AL), an alternative methodology to the end-to-end backpropagation (BP). We introduce the workflow to convert a neural network into a proper structure such that AL can be used to learn the weights for various types of neural networks. We compared AL and BP on some of the most successful types of neural networks -- Convolutional Neural Network (CNN), Recurrent Neural Network (RNN), and Transformer. Experimental results show that AL consistently outperforms BP on various open datasets. We discuss possible reasons for AL's success and its limitations.

Deep Reinforcement Learning (RL) is mainly studied in a setting where the training and the testing environments are similar. But in many practical applications, these environments may differ. For instance, in control systems, the robot(s) on which a policy is learned might differ from the robot(s) on which a policy will run. It can be caused by different internal factors (e.g., calibration issues, system attrition, defective modules) or also by external changes (e.g., weather conditions). There is a need to develop RL methods that generalize well to variations of the training conditions. In this article, we consider the simplest yet hard to tackle generalization setting where the test environment is unknown at train time, forcing the agent to adapt to the system's new dynamics. This online adaptation process can be computationally expensive (e.g., fine-tuning) and cannot rely on meta-RL techniques since there is just a single train environment. To do so, we propose an approach where we learn a subspace of policies within the parameter space. This subspace contains an infinite number of policies that are trained to solve the training environment while having different parameter values. As a consequence, two policies in that subspace process information differently and exhibit different behaviors when facing variations of the train environment. Our experiments carried out over a large variety of benchmarks compare our approach with baselines, including diversity-based methods. In comparison, our approach is simple to tune, does not need any extra component (e.g., discriminator) and learns policies able to gather a high reward on unseen environments.

Learning energy-based model (EBM) requires MCMC sampling of the learned model as an inner loop of the learning algorithm. However, MCMC sampling of EBMs in high-dimensional data space is generally not mixing, because the energy function, which is usually parametrized by deep network, is highly multi-modal in the data space. This is a serious handicap for both theory and practice of EBMs. In this paper, we propose to learn EBM with a flow-based model (or in general latent variable model) serving as a backbone, so that the EBM is a correction or an exponential tilting of the flow-based model. We show that the model has a particularly simple form in the space of the latent variables of the generative model, and MCMC sampling of the EBM in the latent space mixes well and traverses modes in the data space. This enables proper sampling and learning of EBMs.