ICLR 2022 Papers

Recently, post-training quantization (PTQ) has driven much attention to produce efficient neural networks without long-time retraining. Despite the low cost, current PTQ works always fail under the extremely low-bit setting. In this study, we pioneeringly confirm that properly incorporating activation quantization into the PTQ reconstruction benefits the final accuracy. To deeply understand the inherent reason, a theoretical framework is established, which inspires us that the flatness of the optimized low-bit model on calibration and test data is crucial. Based on the conclusion, a simple yet effective approach dubbed as \textsc{QDrop} is proposed, which randomly drops the quantization of activations during reconstruction. Extensive experiments on various tasks including computer vision (image classification, object detection) and natural language processing (text classification and question answering) prove its superiority. With \textsc{QDrop}, the limit of PTQ is pushed to the 2-bit activation for the first time and the accuracy boost can be up to 51.49\%. Without bells and whistles, \textsc{QDrop} establishes a new state of the art for PTQ.

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity method to replicate a forward-backward pass optimisation problem. We propose a new approach which explicates the network's `depth' as a fundamental variable, thus reducing the problem to a system of forward-facing initial value problems. This new method is based on the principal of `Invariant Imbedding' for which we prove a general solution, applicable to all non-linear, vector-valued optimal control problems with both running and terminal loss. Our new architectures provide a tangible tool for inspecting the theoretical--and to a great extent unexplained--properties of network depth. They also constitute a resource of discrete implementations of Neural ODEs comparable to classes of imbedded residual neural networks. Through a series of experiments, we show the competitive performance of the proposed architectures for supervised learning and time series prediction.

Deep equilibrium layers (DEQs) have demonstrated promising performance and are competitive with standard explicit models on many benchmarks. However, little is known about certifying robustness for these models. Inspired by interval bound propagation (IBP), we propose the IBP-MonDEQ layer, a DEQ layer whose robustness can be verified by computing upper and lower interval bounds on the output. Our key insights are that these interval bounds can be obtained as the fixed-point solution to an IBP-inspired equilibrium equation, and furthermore, that this solution always exists and is unique when the layer obeys a certain parameterization. This fixed point can be interpreted as the result of applying IBP to an infinitely deep, weight-tied neural network, which may be of independent interest, as IBP bounds are typically unstable for deeper networks. Our empirical comparison reveals that models with IBP-MonDEQ layers can achieve comparable $\ell_{\infty}$ certified robustness to similarly-sized fully explicit networks.

Our world is full of asymmetries. Gravity and wind can make reaching a place easier than coming back. Social artifacts such as genealogy charts and citation graphs are inherently directed. In reinforcement learning and control, optimal goal-reaching strategies are rarely reversible (symmetrical). Distance functions supported on these asymmetrical structures are called quasimetrics. Despite their common appearance, little research has been done on the learning of quasimetrics. Our theoretical analysis reveals that a common class of learning algorithms, including unconstrained multilayer perceptrons (MLPs), provably fails to learn a quasimetric consistent with training data. In contrast, our proposed Poisson Quasimetric Embedding (PQE) is the first quasimetric learning formulation that both is learnable with gradient-based optimization and enjoys strong performance guarantees. Experiments on random graphs, social graphs, and offline Q-learning demonstrate its effectiveness over many common baselines.

Recent success in cooperative multi-agent reinforcement learning (MARL) relies on centralized training and policy sharing. Centralized training eliminates the issue of non-stationarity MARL yet induces large communication costs, and policy sharing is empirically crucial to efficient learning in certain tasks yet lacks theoretical justification. In this paper, we formally characterize a subclass of cooperative Markov games where agents exhibit a certain form of homogeneity such that policy sharing provably incurs no suboptimality. This enables us to develop the first consensus-based decentralized actor-critic method where the consensus update is applied to both the actors and the critics while ensuring convergence. We also develop practical algorithms based on our decentralized actor-critic method to reduce the communication cost during training, while still yielding policies comparable with centralized training.

We study neural contextual bandits, a general class of contextual bandits, where each context-action pair is associated with a raw feature vector, but the specific reward generating function is unknown. We propose a novel learning algorithm that transforms the raw feature vector using the last hidden layer of a deep ReLU neural network (deep representation learning), and uses an upper confidence bound (UCB) approach to explore in the last linear layer (shallow exploration). We prove that under standard assumptions, our proposed algorithm achieves $\tilde{O}(\sqrt{T})$ finite-time regret, where $T$ is the learning time horizon. Compared with existing neural contextual bandit algorithms, our approach is computationally much more efficient since it only needs to explore in the last layer of the deep neural network.

Recent self-supervised methods for image representation learning maximize the agreement between embedding vectors produced by encoders fed with different views of the same image. The main challenge is to prevent a collapse in which the encoders produce constant or non-informative vectors. We introduce VICReg (Variance-Invariance-Covariance Regularization), a method that explicitly avoids the collapse problem with two regularizations terms applied to both embeddings separately: (1) a term that maintains the variance of each embedding dimension above a threshold, (2) a term that decorrelates each pair of variables. Unlike most other approaches to the same problem, VICReg does not require techniques such as: weight sharing between the branches, batch normalization, feature-wise normalization, output quantization, stop gradient, memory banks, etc., and achieves results on par with the state of the art on several downstream tasks. In addition, we show that our variance regularization term stabilizes the training of other methods and leads to performance improvements.

Isotropic Gaussian priors are the de facto standard for modern Bayesian neural network inference. However, it is unclear whether these priors accurately reflect our true beliefs about the weight distributions or give optimal performance. To find better priors, we study summary statistics of neural network weights in networks trained using stochastic gradient descent (SGD). We find that convolutional neural network (CNN) and ResNet weights display strong spatial correlations, while fully connected networks (FCNNs) display heavy-tailed weight distributions. We show that building these observations into priors can lead to improved performance on a variety of image classification datasets. Surprisingly, these priors mitigate the cold posterior effect in FCNNs, but slightly increase the cold posterior effect in ResNets.

Deep neural networks (DNNs) are effective in solving many real-world problems. Larger DNN models usually exhibit better quality (e.g., accuracy) but their excessive computation results in long inference time. Model sparsification can reduce the computation and memory cost while maintaining model quality. Most existing sparsification algorithms unidirectionally remove weights, while others randomly or greedily explore a small subset of weights in each layer for pruning. The limitations of these algorithms reduce the level of achievable sparsity. In addition, many algorithms still require pre-trained dense models and thus suffer from large memory footprint. In this paper, we propose a novel scheduled grow-and-prune (GaP) methodology without having to pre-train a dense model. It addresses the shortcomings of the previous works by repeatedly growing a subset of layers to dense and then pruning them back to sparse after some training. Experiments show that the models pruned using the proposed methods match or beat the quality of the highly optimized dense models at 80% sparsity on a variety of tasks, such as image classification, objective detection, 3D object part segmentation, and translation. They also outperform other state-of-the-art (SOTA) methods for model sparsification. As an example, a 90% non-uniform sparse ResNet-50 model obtained via GaP achieves 77.9% top-1 accuracy on ImageNet, improving the previous SOTA results by 1.5%. Code available at: https://github.com/boone891214/GaP.

Stochastic differential equations provide a rich class of flexible generative models, capable of describing a wide range of spatio-temporal processes. A host of recent work looks to learn data-representing SDEs, using neural networks and other flexible function approximators. Despite these advances, learning remains computationally expensive due to the sequential nature of SDE integrators. In this work, we propose an importance-sampling estimator for probabilities of observations of SDEs for the purposes of learning. Crucially, the approach we suggest does not rely on such integrators. The proposed method produces lower-variance gradient estimates compared to algorithms based on SDE integrators and has the added advantage of being embarrassingly parallelizable. This facilitates the effective use of large-scale parallel hardware for massive decreases in computation time.

We present a novel methodology for repairing neural networks that use ReLU activation functions. Unlike existing methods that rely on modifying the weights of a neural network which can induce a global change in the function space, our approach applies only a localized change in the function space while still guaranteeing the removal of the buggy behavior. By leveraging the piecewise linear nature of ReLU networks, our approach can efficiently construct a patch network tailored to the linear region where the buggy input resides, which when combined with the original network, provably corrects the behavior on the buggy input. Our method is both sound and complete -- the repaired network is guaranteed to fix the buggy input, and a patch is guaranteed to be found for any buggy input. Moreover, our approach preserves the continuous piecewise linear nature of ReLU networks, automatically generalizes the repair to all the points including other undetected buggy inputs inside the repair region, is minimal in terms of changes in the function space, and guarantees that outputs on inputs away from the repair region are unaltered. On several benchmarks, we show that our approach significantly outperforms existing methods in terms of locality and limiting negative side effects.

Molecular graph representation learning is a fundamental problem in modern drug and material discovery. Molecular graphs are typically modeled by their 2D topological structures, but it has been recently discovered that 3D geometric information plays a more vital role in predicting molecular functionalities. However, the lack of 3D information in real-world scenarios has significantly impeded the learning of geometric graph representation. To cope with this challenge, we propose the Graph Multi-View Pre-training (GraphMVP) framework where self-supervised learning (SSL) is performed by leveraging the correspondence and consistency between 2D topological structures and 3D geometric views. GraphMVP effectively learns a 2D molecular graph encoder that is enhanced by richer and more discriminative 3D geometry. We further provide theoretical insights to justify the effectiveness of GraphMVP. Finally, comprehensive experiments show that GraphMVP can consistently outperform existing graph SSL methods. Code is available on GitHub: https://github.com/chao1224/GraphMVP.

Cross-domain imitation learning studies how to leverage expert demonstrations of one agent to train an imitation agent with a different embodiment or morphology. Comparing trajectories and stationary distributions between the expert and imitation agents is challenging because they live on different systems that may not even have the same dimensionality. We propose Gromov-Wasserstein Imitation Learning (GWIL), a method for cross-domain imitation that uses the Gromov-Wasserstein distance to align and compare states between the different spaces of the agents. Our theory formally characterizes the scenarios where GWIL preserves optimality, revealing its possibilities and limitations. We demonstrate the effectiveness of GWIL in non-trivial continuous control domains ranging from simple rigid transformation of the expert domain to arbitrary transformation of the state-action space.

We investigate whether three types of post hoc model explanations–feature attribution, concept activation, and training point ranking–are effective for detecting a model’s reliance on spurious signals in the training data. Specifically, we consider the scenario where the spurious signal to be detected is unknown, at test-time, to the user of the explanation method. We design an empirical methodology that uses semi-synthetic datasets along with pre-specified spurious artifacts to obtain models that verifiably rely on these spurious training signals. We then provide a suite of metrics that assess an explanation method’s reliability for spurious signal detection under various conditions. We find that the post hoc explanation methods tested are ineffective when the spurious artifact is unknown at test-time especially for non-visible artifacts like a background blur. Further, we find that feature attribution methods are susceptible to erroneously indicating dependence on spurious signals even when the model being explained does not rely on spurious artifacts. This finding casts doubt on the utility of these approaches, in the hands of a practitioner, for detecting a model’s reliance on spurious signals.

Humans show language-biased image recognition for a word-embedded image, known as picture-word interference. Such interference depends on hierarchical semantic categories and reflects that human language processing highly interacts with visual processing. Similar to humans, recent artificial models jointly trained on texts and images, e.g., OpenAI CLIP, show language-biased image classification. Exploring whether the bias leads to interference similar to those observed in humans can contribute to understanding how much the model acquires hierarchical semantic representations from joint learning of language and vision. The present study introduces methodological tools from the cognitive science literature to assess the biases of artificial models. Specifically, we introduce a benchmark task to test whether words superimposed on images can distort the image classification across different category levels and, if it can, whether the perturbation is due to the shared semantic representation between language and vision. Our dataset is a set of word-embedded images and consists of a mixture of natural image datasets and hierarchical word labels with superordinate/basic category levels. Using this benchmark test, we evaluate the CLIP model. We show that presenting words distorts the image classification by the model across different category levels, but the effect does not depend on the semantic relationship between images and embedded words. This suggests that the semantic word representation in the CLIP visual processing is not shared with the image representation, although the word representation strongly dominates for word-embedded images.

Conventional representation learning algorithms for knowledge graphs (KG) map each entity to a unique embedding vector. Such a shallow lookup results in a linear growth of memory consumption for storing the embedding matrix and incurs high computational costs of working with real-world KGs. Drawing parallels with subword tokenization commonly used in NLP, we explore the landscape of more parameter-efficient node embedding strategies with possibly sublinear memory requirements. To this end, we propose NodePiece, an anchor-based approach to learn a fixed-size entity vocabulary. In NodePiece, a vocabulary of subword/sub-entity units is constructed from anchor nodes in a graph with known relation types. Given such a fixed-size vocabulary, it is possible to bootstrap an encoding and embedding for any entity, including those unseen during training. Experiments show that NodePiece performs competitively in node classification, link prediction, and relation prediction tasks retaining less than 10% of explicit nodes in a graph as anchors and often having 10x fewer parameters. To this end, we show that a NodePiece-enabled model outperforms existing shallow models on a large OGB WikiKG 2 graph having 70x fewer parameters.

Valuation problems, such as feature interpretation, data valuation and model valuation for ensembles, become increasingly more important in many machine learning applications. Such problems are commonly solved by well-known game-theoretic criteria, such as Shapley value or Banzhaf value. In this work, we present a novel energy-based treatment for cooperative games, with a theoretical justification by the maximum entropy framework. Surprisingly, by conducting variational inference of the energy-based model, we recover various game-theoretic valuation criteria through conducting one-step fixed point iteration for maximizing the mean-field ELBO objective. This observation also verifies the rationality of existing criteria, as they are all attempting to decouple the correlations among the players through the mean-field approach. By running fixed point iteration for multiple steps, we achieve a trajectory of the valuations, among which we define the valuation with the best conceivable decoupling error as the Variational Index. We prove that under uniform initializations, these variational valuations all satisfy a set of game-theoretic axioms. We experimentally demonstrate that the proposed Variational Index enjoys lower decoupling error and better valuation performance on certain synthetic and real-world valuation problems.

A desirable property of autonomous agents is the ability to both solve long-horizon problems and generalize to unseen tasks. Recent advances in data-driven skill learning have shown that extracting behavioral priors from offline data can enable agents to solve challenging long-horizon tasks with reinforcement learning. However, generalization to tasks unseen during behavioral prior training remains an outstanding challenge. To this end, we present Few-shot Imitation with Skill Transition Models (FIST), an algorithm that extracts skills from offline data and utilizes them to generalize to unseen tasks given a few downstream demonstrations. FIST learns an inverse skill dynamics model, a distance function, and utilizes a semi-parametric approach for imitation. We show that FIST is capable of generalizing to new tasks and substantially outperforms prior baselines in navigation experiments requiring traversing unseen parts of a large maze and 7-DoF robotic arm experiments requiring manipulating previously unseen objects in a kitchen.

Identifying the status of individual network units is critical for understanding the mechanism of convolutional neural networks (CNNs). However, it is still challenging to reliably give a general indication of unit status, especially for units in different network models. To this end, we propose a novel method for quantitatively clarifying the status of single unit in CNN using algebraic topological tools. Unit status is indicated via the calculation of a defined topological-based entropy, called feature entropy, which measures the degree of chaos of the global spatial pattern hidden in the unit for a category. In this way, feature entropy could provide an accurate indication of status for units in different networks with diverse situations like weight-rescaling operation. Further, we show that feature entropy decreases as the layer goes deeper and shares almost simultaneous trend with loss during training. We show that by investigating the feature entropy of units on only training data, it could give discrimination between networks with different generalization ability from the view of the effectiveness of feature representations.