ICLR 2021 Papers

In the mean field regime, neural networks are appropriately scaled so that as the width tends to infinity, the learning dynamics tends to a nonlinear and nontrivial dynamical limit, known as the mean field limit. This lends a way to study large-width neural networks via analyzing the mean field limit. Recent works have successfully applied such analysis to two-layer networks and provided global convergence guarantees. The extension to multilayer ones however has been a highly challenging puzzle, and little is known about the optimization efficiency in the mean field regime when there are more than two layers. In this work, we prove a global convergence result for unregularized feedforward three-layer networks in the mean field regime. We first develop a rigorous framework to establish the mean field limit of three-layer networks under stochastic gradient descent training. To that end, we propose the idea of a neuronal embedding, which comprises of a fixed probability space that encapsulates neural networks of arbitrary sizes. The identified mean field limit is then used to prove a global convergence guarantee under suitable regularity and convergence mode assumptions, which – unlike previous works on two-layer networks – does not rely critically on convexity. Underlying the result is a universal approximation property, natural of neural networks, which importantly is shown to hold at any finite training time (not necessarily at convergence) via an algebraic topology argument.

Learning from a limited number of samples is challenging since the learned model can easily become overfitted based on the biased distribution formed by only a few training examples. In this paper, we calibrate the distribution of these few-sample classes by transferring statistics from the classes with sufficient examples. Then an adequate number of examples can be sampled from the calibrated distribution to expand the inputs to the classifier. We assume every dimension in the feature representation follows a Gaussian distribution so that the mean and the variance of the distribution can borrow from that of similar classes whose statistics are better estimated with an adequate number of samples. Our method can be built on top of off-the-shelf pretrained feature extractors and classification models without extra parameters. We show that a simple logistic regression classifier trained using the features sampled from our calibrated distribution can outperform the state-of-the-art accuracy on three datasets (~5% improvement on miniImageNet compared to the next best). The visualization of these generated features demonstrates that our calibrated distribution is an accurate estimation.

Determinantal point processes (DPPs) have attracted significant attention in machine learning for their ability to model subsets drawn from a large item collection. Recent work shows that nonsymmetric DPP (NDPP) kernels have significant advantages over symmetric kernels in terms of modeling power and predictive performance. However, for an item collection of size $M$, existing NDPP learning and inference algorithms require memory quadratic in $M$ and runtime cubic (for learning) or quadratic (for inference) in $M$, making them impractical for many typical subset selection tasks. In this work, we develop a learning algorithm with space and time requirements linear in $M$ by introducing a new NDPP kernel decomposition. We also derive a linear-complexity NDPP maximum a posteriori (MAP) inference algorithm that applies not only to our new kernel but also to that of prior work. Through evaluation on real-world datasets, we show that our algorithms scale significantly better, and can match the predictive performance of prior work.

Natural images are projections of 3D objects on a 2D image plane. While state-of-the-art 2D generative models like GANs show unprecedented quality in modeling the natural image manifold, it is unclear whether they implicitly capture the underlying 3D object structures. And if so, how could we exploit such knowledge to recover the 3D shapes of objects in the images? To answer these questions, in this work, we present the first attempt to directly mine 3D geometric cues from an off-the-shelf 2D GAN that is trained on RGB images only. Through our investigation, we found that such a pre-trained GAN indeed contains rich 3D knowledge and thus can be used to recover 3D shape from a single 2D image in an unsupervised manner. The core of our framework is an iterative strategy that explores and exploits diverse viewpoint and lighting variations in the GAN image manifold. The framework does not require 2D keypoint or 3D annotations, or strong assumptions on object shapes (e.g. shapes are symmetric), yet it successfully recovers 3D shapes with high precision for human faces, cats, cars, and buildings. The recovered 3D shapes immediately allow high-quality image editing like relighting and object rotation. We quantitatively demonstrate the effectiveness of our approach compared to previous methods in both 3D shape reconstruction and face rotation. Our code is available at https://github.com/XingangPan/GAN2Shape.

Circuits of biological neurons, such as in the functional parts of the brain can be modeled as networks of coupled oscillators. Inspired by the ability of these systems to express a rich set of outputs while keeping (gradients of) state variables bounded, we propose a novel architecture for recurrent neural networks. Our proposed RNN is based on a time-discretization of a system of second-order ordinary differential equations, modeling networks of controlled nonlinear oscillators. We prove precise bounds on the gradients of the hidden states, leading to the mitigation of the exploding and vanishing gradient problem for this RNN. Experiments show that the proposed RNN is comparable in performance to the state of the art on a variety of benchmarks, demonstrating the potential of this architecture to provide stable and accurate RNNs for processing complex sequential data.

Disentangling the underlying generative factors from complex data has so far been limited to carefully constructed scenarios. We propose a path towards natural data by first showing that the statistics of natural data provide enough structure to enable disentanglement, both theoretically and empirically. Specifically, we provide evidence that objects in natural movies undergo transitions that are typically small in magnitude with occasional large jumps, which is characteristic of a temporally sparse distribution. To address this finding we provide a novel proof that relies on a sparse prior on temporally adjacent observations to recover the true latent variables up to permutations and sign flips, directly providing a stronger result than previous work. We show that equipping practical estimation methods with our prior often surpasses the current state-of-the-art on several established benchmark datasets without any impractical assumptions, such as knowledge of the number of changing generative factors. Furthermore, we contribute two new benchmarks, Natural Sprites and KITTI Masks, which integrate the measured natural dynamics to enable disentanglement evaluation with more realistic datasets. We leverage these benchmarks to test our theory, demonstrating improved performance. We also identify non-obvious challenges for current methods in scaling to more natural domains. Taken together our work addresses key issues in disentanglement research for moving towards more natural settings.

In this paper, we cast fair machine learning as invariant machine learning. We first formulate a version of individual fairness that enforces invariance on certain sensitive sets. We then design a transport-based regularizer that enforces this version of individual fairness and develop an algorithm to minimize the regularizer efficiently. Our theoretical results guarantee the proposed approach trains certifiably fair ML models. Finally, in the experimental studies we demonstrate improved fairness metrics in comparison to several recent fair training procedures on three ML tasks that are susceptible to algorithmic bias.

We propose a novel federated learning method for distributively training neural network models, where the server orchestrates cooperation between a subset of randomly chosen devices in each round. We view Federated Learning problem primarily from a communication perspective and allow more device level computations to save transmission costs. We point out a fundamental dilemma, in that the minima of the local-device level empirical loss are inconsistent with those of the global empirical loss. Different from recent prior works, that either attempt inexact minimization or utilize devices for parallelizing gradient computation, we propose a dynamic regularizer for each device at each round, so that in the limit the global and device solutions are aligned. We demonstrate both through empirical results on real and synthetic data as well as analytical results that our scheme leads to efficient training, in both convex and non-convex settings, while being fully agnostic to device heterogeneity and robust to large number of devices, partial participation and unbalanced data.

The ability to learn continually without forgetting the past tasks is a desired attribute for artificial learning systems. Existing approaches to enable such learning in artificial neural networks usually rely on network growth, importance based weight update or replay of old data from the memory. In contrast, we propose a novel approach where a neural network learns new tasks by taking gradient steps in the orthogonal direction to the gradient subspaces deemed important for the past tasks. We find the bases of these subspaces by analyzing network representations (activations) after learning each task with Singular Value Decomposition (SVD) in a single shot manner and store them in the memory as Gradient Projection Memory (GPM). With qualitative and quantitative analyses, we show that such orthogonal gradient descent induces minimum to no interference with the past tasks, thereby mitigates forgetting. We evaluate our algorithm on diverse image classification datasets with short and long sequences of tasks and report better or on-par performance compared to the state-of-the-art approaches.

We propose a method for meta-learning reinforcement learning algorithms by searching over the space of computational graphs which compute the loss function for a value-based model-free RL agent to optimize. The learned algorithms are domain-agnostic and can generalize to new environments not seen during training. Our method can both learn from scratch and bootstrap off known existing algorithms, like DQN, enabling interpretable modifications which improve performance. Learning from scratch on simple classical control and gridworld tasks, our method rediscovers the temporal-difference (TD) algorithm. Bootstrapped from DQN, we highlight two learned algorithms which obtain good generalization performance over other classical control tasks, gridworld type tasks, and Atari games. The analysis of the learned algorithm behavior shows resemblance to recently proposed RL algorithms that address overestimation in value-based methods.

Prior AI breakthroughs in complex games have focused on either the purely adversarial or purely cooperative settings. In contrast, Diplomacy is a game of shifting alliances that involves both cooperation and competition. For this reason, Diplomacy has proven to be a formidable research challenge. In this paper we describe an agent for the no-press variant of Diplomacy that combines supervised learning on human data with one-step lookahead search via regret minimization. Regret minimization techniques have been behind previous AI successes in adversarial games, most notably poker, but have not previously been shown to be successful in large-scale games involving cooperation. We show that our agent greatly exceeds the performance of past no-press Diplomacy bots, is unexploitable by expert humans, and ranks in the top 2% of human players when playing anonymous games on a popular Diplomacy website.

We study how representation learning can accelerate reinforcement learning from rich observations, such as images, without relying either on domain knowledge or pixel-reconstruction. Our goal is to learn representations that provide for effective downstream control and invariance to task-irrelevant details. Bisimulation metrics quantify behavioral similarity between states in continuous MDPs, which we propose using to learn robust latent representations which encode only the task-relevant information from observations. Our method trains encoders such that distances in latent space equal bisimulation distances in state space. We demonstrate the effectiveness of our method at disregarding task-irrelevant information using modified visual MuJoCo tasks, where the background is replaced with moving distractors and natural videos, while achieving SOTA performance. We also test a first-person highway driving task where our method learns invariance to clouds, weather, and time of day. Finally, we provide generalization results drawn from properties of bisimulation metrics, and links to causal inference.