Bo ZHAO, Konda Reddy Mopuri, Hakan Bilen

As the state-of-the-art machine learning methods in many fields rely on larger datasets, storing datasets and training models on them become significantly more expensive. This paper proposes a training set synthesis technique for data-efficient learning, called Dataset Condensation, that learns to condense large dataset into a small set of informative synthetic samples for training deep neural networks from scratch. We formulate this goal as a gradient matching problem between the gradients of deep neural network weights that are trained on the original and our synthetic data. We rigorously evaluate its performance in several computer vision benchmarks and demonstrate that it significantly outperforms the state-of-the-art methods. Finally we explore the use of our method in continual learning and neural architecture search and report promising gains when limited memory and computations are available.

Shuo Yang, Lu Liu, Min Xu

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.

David Klindt, Lukas Schott, Yash Sharma, Ivan Ustyuzhaninov, Wieland Brendel, Matthias Bethge, Dylan Paiton

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 …

Muhammad Khalifa, Hady Elsahar, Marc Dymetman

We propose a Distributional Approach for addressing Controlled Text Generation from pre-trained Language Models (LM). This approach permits to specify, in a single formal framework, both “pointwise’” and “distributional” constraints over the target LM — to our knowledge, the first model with such generality —while minimizing KL divergence from the initial LM distribution. The optimal target distribution is then uniquely determined as an explicit EBM (Energy-BasedModel) representation. From that optimal representation, we then train a target controlled Autoregressive LM through an adaptive distributional variant of PolicyGradient. We conduct a first set of experiments over pointwise constraints showing the advantages of our approach over a set of baselines, in terms of obtaining a controlled LM balancing constraint satisfaction with divergence from the pretrained LM. We then perform experiments over distributional constraints, a unique feature of our approach, demonstrating its potential as a remedy to the problem of Bias in Language Models. Through an ablation study, we show the effectiveness of our adaptive technique for obtaining faster convergence. Code available at https://github.com/naver/gdc

Jingfeng Zhang, Jianing ZHU, Gang Niu, Bo Han, Masashi Sugiyama, Mohan Kankanhalli

In adversarial machine learning, there was a common belief that robustness and accuracy hurt each other. The belief was challenged by recent studies where we can maintain the robustness and improve the accuracy. However, the other direction, whether we can keep the accuracy and improve the robustness, is conceptually and practically more interesting, since robust accuracy should be lower than standard accuracy for any model. In this paper, we show this direction is also promising. Firstly, we find even over-parameterized deep networks may still have insufficient model capacity, because adversarial training has an overwhelming smoothing effect. Secondly, given limited model capacity, we argue adversarial data should have unequal importance: geometrically speaking, a natural data point closer to/farther from the class boundary is less/more robust, and the corresponding adversarial data point should be assigned with larger/smaller weight. Finally, to implement the idea, we propose geometry-aware instance-reweighted adversarial training, where the weights are based on how difficult it is to attack a natural data point. Experiments show that our proposal boosts the robustness of standard adversarial training; combining two directions, we improve both robustness and accuracy of standard adversarial training.

Xingang Pan, Bo DAI, Ziwei Liu, Chen Change Loy, Ping Luo

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 …

Suraj Srinivas, François Fleuret
Current methods for the interpretability of discriminative deep neural networks commonly rely on the model's input-gradients, i.e., the gradients of the output logits w.r.t. the inputs. The common assumption is that these input-gradients contain information regarding $p_{\theta} ( y\mid \mathbf{x} )$, the model's discriminative capabilities, thus justifying their use for interpretability. However, in this work, we show that these input-gradients can be arbitrarily manipulated as a consequence of the shift-invariance of softmax without changing the discriminative function. This leaves an open question: given that input-gradients can be arbitrary, why are they highly structured and explanatory in standard models? In this work, we re-interpret the logits of standard softmax-based classifiers as unnormalized log-densities of the data distribution and show that input-gradients can be viewed as gradients of a class-conditional generative model $p_{\theta}(\mathbf{x} \mid y)$ implicit in the discriminative model. This leads us to hypothesize that the highly structured and explanatory nature of input-gradients may be due to the alignment of this class-conditional model $p_{\theta}(\mathbf{x} \mid y)$ with that of the ground truth data distribution $p_{\text{data}} (\mathbf{x} \mid y)$. We test this hypothesis by studying the effect of density alignment on gradient explanations. To achieve this density alignment, we use an algorithm …
Durmus Alp Emre Acar, Yue Zhao, Ramon Matas, Matthew Mattina, Paul Whatmough, Venkatesh Saligrama

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.

Gobinda Saha, Isha Garg, Kaushik Roy

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.

Xin Yuan, Pedro Henrique Pamplona Savarese, Michael Maire
We develop an approach to growing deep network architectures over the course of training, driven by a principled combination of accuracy and sparsity objectives. Unlike existing pruning or architecture search techniques that operate on full-sized models or supernet architectures, our method can start from a small, simple seed architecture and dynamically grow and prune both layers and filters. By combining a continuous relaxation of discrete network structure optimization with a scheme for sampling sparse subnetworks, we produce compact, pruned networks, while also drastically reducing the computational expense of training. For example, we achieve $49.7\%$ inference FLOPs and $47.4\%$ training FLOPs savings compared to a baseline ResNet-50 on ImageNet, while maintaining $75.2\%$ top-1 validation accuracy --- all without any dedicated fine-tuning stage. Experiments across CIFAR, ImageNet, PASCAL VOC, and Penn Treebank, with convolutional networks for image classification and semantic segmentation, and recurrent networks for language modeling, demonstrate that we both train faster and produce more efficient networks than competing architecture pruning or search methods.
Glen Berseth, Daniel Geng, Coline M Devin, Nicholas Rhinehart, Chelsea Finn, Dinesh Jayaraman, Sergey Levine

Every living organism struggles against disruptive environmental forces to carve out and maintain an orderly niche. We propose that such a struggle to achieve and preserve order might offer a principle for the emergence of useful behaviors in artificial agents. We formalize this idea into an unsupervised reinforcement learning method called surprise minimizing reinforcement learning (SMiRL). SMiRL alternates between learning a density model to evaluate the surprise of a stimulus, and improving the policy to seek more predictable stimuli. The policy seeks out stable and repeatable situations that counteract the environment's prevailing sources of entropy. This might include avoiding other hostile agents, or finding a stable, balanced pose for a bipedal robot in the face of disturbance forces. We demonstrate that our surprise minimizing agents can successfully play Tetris, Doom, control a humanoid to avoid falls, and navigate to escape enemies in a maze without any task-specific reward supervision. We further show that SMiRL can be used together with standard task rewards to accelerate reward-driven learning.

Zhengxian Lin, Kin-Ho Lam, Alan Fern

We investigate a deep reinforcement learning (RL) architecture that supports explaining why a learned agent prefers one action over another. The key idea is to learn action-values that are directly represented via human-understandable properties of expected futures. This is realized via the embedded self-prediction (ESP) model, which learns said properties in terms of human provided features. Action preferences can then be explained by contrasting the future properties predicted for each action. To address cases where there are a large number of features, we develop a novel method for computing minimal sufficient explanations from an ESP. Our case studies in three domains, including a complex strategy game, show that ESP models can be effectively learned and support insightful explanations.

Avi Singh, Huihan Liu, Gaoyue Zhou, Albert Yu, Nicholas Rhinehart, Sergey Levine

Reinforcement learning provides a general framework for flexible decision making and control, but requires extensive data collection for each new task that an agent needs to learn. In other machine learning fields, such as natural language processing or computer vision, pre-training on large, previously collected datasets to bootstrap learning for new tasks has emerged as a powerful paradigm to reduce data requirements when learning a new task. In this paper, we ask the following question: how can we enable similarly useful pre-training for RL agents? We propose a method for pre-training behavioral priors that can capture complex input-output relationships observed in successful trials from a wide range of previously seen tasks, and we show how this learned prior can be used for rapidly learning new tasks without impeding the RL agent's ability to try out novel behaviors. We demonstrate the effectiveness of our approach in challenging robotic manipulation domains involving image observations and sparse reward functions, where our method outperforms prior works by a substantial margin. Additional materials can be found on our project website: https://sites.google.com/view/parrot-rl

Keyulu Xu, Mozhi Zhang, Jingling Li, Simon Du, Ken-Ichi Kawarabayashi, Stefanie Jegelka

We study how neural networks trained by gradient descent extrapolate, i.e., what they learn outside the support of the training distribution. Previous works report mixed empirical results when extrapolating with neural networks: while feedforward neural networks, a.k.a. multilayer perceptrons (MLPs), do not extrapolate well in certain simple tasks, Graph Neural Networks (GNNs) -- structured networks with MLP modules -- have shown some success in more complex tasks. Working towards a theoretical explanation, we identify conditions under which MLPs and GNNs extrapolate well. First, we quantify the observation that ReLU MLPs quickly converge to linear functions along any direction from the origin, which implies that ReLU MLPs do not extrapolate most nonlinear functions. But, they can provably learn a linear target function when the training distribution is sufficiently diverse. Second, in connection to analyzing the successes and limitations of GNNs, these results suggest a hypothesis for which we provide theoretical and empirical evidence: the success of GNNs in extrapolating algorithmic tasks to new data (e.g., larger graphs or edge weights) relies on encoding task-specific non-linearities in the architecture or features. Our theoretical analysis builds on a connection of over-parameterized networks to the neural tangent kernel. Empirically, our theory holds across different …

Jeff Donahue, Sander Dieleman, Mikolaj Binkowski, Erich Elsen, Karen Simonyan

Modern text-to-speech synthesis pipelines typically involve multiple processing stages, each of which is designed or learnt independently from the rest. In this work, we take on the challenging task of learning to synthesise speech from normalised text or phonemes in an end-to-end manner, resulting in models which operate directly on character or phoneme input sequences and produce raw speech audio outputs. Our proposed generator is feed-forward and thus efficient for both training and inference, using a differentiable alignment scheme based on token length prediction. It learns to produce high fidelity audio through a combination of adversarial feedback and prediction losses constraining the generated audio to roughly match the ground truth in terms of its total duration and mel-spectrogram. To allow the model to capture temporal variation in the generated audio, we employ soft dynamic time warping in the spectrogram-based prediction loss. The resulting model achieves a mean opinion score exceeding 4 on a 5 point scale, which is comparable to the state-of-the-art models relying on multi-stage training and additional supervision.

Max B Paulus, Chris Maddison, Andreas Krause

Gradient estimation in models with discrete latent variables is a challenging problem, because the simplest unbiased estimators tend to have high variance. To counteract this, modern estimators either introduce bias, rely on multiple function evaluations, or use learned, input-dependent baselines. Thus, there is a need for estimators that require minimal tuning, are computationally cheap, and have low mean squared error. In this paper, we show that the variance of the straight-through variant of the popular Gumbel-Softmax estimator can be reduced through Rao-Blackwellization without increasing the number of function evaluations. This provably reduces the mean squared error. We empirically demonstrate that this leads to variance reduction, faster convergence, and generally improved performance in two unsupervised latent variable models.

Mike Gartrell, Insu Han, Elvis Dohmatob, Jennifer Gillenwater, Victor-Emmanuel Brunel
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.
Ankit Vani, Max Schwarzer, Yuchen Lu, Eeshan Dhekane, Aaron Courville

Although neural module networks have an architectural bias towards compositionality, they require gold standard layouts to generalize systematically in practice. When instead learning layouts and modules jointly, compositionality does not arise automatically and an explicit pressure is necessary for the emergence of layouts exhibiting the right structure. We propose to address this problem using iterated learning, a cognitive science theory of the emergence of compositional languages in nature that has primarily been applied to simple referential games in machine learning. Considering the layouts of module networks as samples from an emergent language, we use iterated learning to encourage the development of structure within this language. We show that the resulting layouts support systematic generalization in neural agents solving the more complex task of visual question-answering. Our regularized iterated learning method can outperform baselines without iterated learning on SHAPES-SyGeT (SHAPES Systematic Generalization Test), a new split of the SHAPES dataset we introduce to evaluate systematic generalization, and on CLOSURE, an extension of CLEVR also designed to test systematic generalization. We demonstrate superior performance in recovering ground-truth compositional program structure with limited supervision on both SHAPES-SyGeT and CLEVR.

Luca Weihs, Aniruddha Kembhavi, Kiana Ehsani, Sarah M Pratt, Winson Han, Alvaro Herrasti, Eric Kolve, Dustin Schwenk, Roozbeh Mottaghi, Ali Farhadi

A growing body of research suggests that embodied gameplay, prevalent not just in human cultures but across a variety of animal species including turtles and ravens, is critical in developing the neural flexibility for creative problem solving, decision making, and socialization. Comparatively little is known regarding the impact of embodied gameplay upon artificial agents. While recent work has produced agents proficient in abstract games, these environments are far removed the real world and thus these agents can provide little insight into the advantages of embodied play. Hiding games, such as hide-and-seek, played universally, provide a rich ground for studying the impact of embodied gameplay on representation learning in the context of perspective taking, secret keeping, and false belief understanding. Here we are the first to show that embodied adversarial reinforcement learning agents playing Cache, a variant of hide-and-seek, in a high fidelity, interactive, environment, learn generalizable representations of their observations encoding information such as object permanence, free space, and containment. Moving closer to biologically motivated learning strategies, our agents' representations, enhanced by intentionality and memory, are developed through interaction and play. These results serve as a model for studying how facets of vision develop through interaction, provide an experimental framework …

Deniz Oktay, Nick McGreivy, Joshua Aduol, Alex Beatson, Ryan P Adams

The successes of deep learning, variational inference, and many other fields have been aided by specialized implementations of reverse-mode automatic differentiation (AD) to compute gradients of mega-dimensional objectives. The AD techniques underlying these tools were designed to compute exact gradients to numerical precision, but modern machine learning models are almost always trained with stochastic gradient descent. Why spend computation and memory on exact (minibatch) gradients only to use them for stochastic optimization? We develop a general framework and approach for randomized automatic differentiation (RAD), which can allow unbiased gradient estimates to be computed with reduced memory in return for variance. We examine limitations of the general approach, and argue that we must leverage problem specific structure to realize benefits. We develop RAD techniques for a variety of simple neural network architectures, and show that for a fixed memory budget, RAD converges in fewer iterations than using a small batch size for feedforward networks, and in a similar number for recurrent networks. We also show that RAD can be applied to scientific computing, and use it to develop a low-memory stochastic gradient method for optimizing the control parameters of a linear reaction-diffusion PDE representing a fission reactor.

Yuxuan Zhang, Wenzheng Chen, Huan Ling, Jun Gao, Yinan Zhang, Antonio Torralba, Sanja Fidler

Differentiable rendering has paved the way to training neural networks to perform “inverse graphics” tasks such as predicting 3D geometry from monocular photographs. To train high performing models, most of the current approaches rely on multi-view imagery which are not readily available in practice. Recent Generative Adversarial Networks (GANs) that synthesize images, in contrast, seem to acquire 3D knowledge implicitly during training: object viewpoints can be manipulated by simply manipulating the latent codes. However, these latent codes often lack further physical interpretation and thus GANs cannot easily be inverted to perform explicit 3D reasoning. In this paper, we aim to extract and disentangle 3D knowledge learned by generative models by utilizing differentiable renderers. Key to our approach is to exploit GANs as a multi-view data generator to train an inverse graphics network using an off-the-shelf differentiable renderer, and the trained inverse graphics network as a teacher to disentangle the GAN's latent code into interpretable 3D properties. The entire architecture is trained iteratively using cycle consistency losses. We show that our approach significantly outperforms state-of-the-art inverse graphics networks trained on existing datasets, both quantitatively and via user studies. We further showcase the disentangled GAN as a controllable 3D “neural renderer", complementing …

Matthew Smart, Anton Zilman
Hopfield networks (HNs) and Restricted Boltzmann Machines (RBMs) are two important models at the interface of statistical physics, machine learning, and neuroscience. Recently, there has been interest in the relationship between HNs and RBMs, due to their similarity under the statistical mechanics formalism. An exact mapping between HNs and RBMs has been previously noted for the special case of orthogonal (“uncorrelated”) encoded patterns. We present here an exact mapping in the case of correlated pattern HNs, which are more broadly applicable to existing datasets. Specifically, we show that any HN with $N$ binary variables and $p<N$ potentially correlated binary patterns can be transformed into an RBM with $N$ binary visible variables and $p$ gaussian hidden variables. We outline the conditions under which the reverse mapping exists, and conduct experiments on the MNIST dataset which suggest the mapping provides a useful initialization to the RBM weights. We discuss extensions, the potential importance of this correspondence for the training of RBMs, and for understanding the performance of feature extraction methods which utilize RBMs.
Brenden Petersen, Mikel Landajuela Larma, Terrell N Mundhenk, Claudio Santiago, Soo Kim, Joanne Kim
Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic regression}$. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that leverages deep learning for symbolic regression via a simple idea: use a large model to search the space of small models. Specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions and employ a novel risk-seeking policy gradient to train the network to generate better-fitting expressions. Our algorithm outperforms several baseline methods (including Eureqa, the gold standard for symbolic regression) in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.
Huy Tuan Pham, Phan-Minh Nguyen

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 …

Jang-Hyun Kim, Wonho Choo, Hosan Jeong, Hyun Oh Song

While deep neural networks show great performance on fitting to the training distribution, improving the networks' generalization performance to the test distribution and robustness to the sensitivity to input perturbations still remain as a challenge. Although a number of mixup based augmentation strategies have been proposed to partially address them, it remains unclear as to how to best utilize the supervisory signal within each input data for mixup from the optimization perspective. We propose a new perspective on batch mixup and formulate the optimal construction of a batch of mixup data maximizing the data saliency measure of each individual mixup data and encouraging the supermodular diversity among the constructed mixup data. This leads to a novel discrete optimization problem minimizing the difference between submodular functions. We also propose an efficient modular approximation based iterative submodular minimization algorithm for efficient mixup computation per each minibatch suitable for minibatch based neural network training. Our experiments show the proposed method achieves the state of the art generalization, calibration, and weakly supervised localization results compared to other mixup methods. The source code is available at https://github.com/snu-mllab/Co-Mixup.

Beidi Chen, Zichang Liu, Binghui Peng, Zhaozhuo Xu, Jonathan L Li, Tri Dao, Zhao Song, Anshumali Shrivastava, Christopher Re
Recent advances by practitioners in the deep learning community have breathed new life into Locality Sensitive Hashing (LSH), using it to reduce memory and time bottlenecks in neural network (NN) training. However, while LSH has sub-linear guarantees for approximate near-neighbor search in theory, it is known to have inefficient query time in practice due to its use of random hash functions. Moreover, when model parameters are changing, LSH suffers from update overhead. This work is motivated by an observation that model parameters evolve slowly, such that the changes do not always require an LSH update to maintain performance. This phenomenon points to the potential for a reduction in update time and allows for a modified learnable version of data-dependent LSH to improve query time at a low cost. We use the above insights to build MONGOOSE, an end-to-end LSH framework for efficient NN training. In particular, MONGOOSE is equipped with a scheduling algorithm to adaptively perform LSH updates with provable guarantees and learnable hash functions to improve query efficiency. Empirically, we validate MONGOOSE on large-scale deep learning models for recommendation systems and language modeling. We find that it achieves up to 8% better accuracy compared to previous LSH approaches, with …
Alexey Dosovitskiy, Lucas Beyer, Alexander Kolesnikov, Dirk Weissenborn, Xiaohua Zhai, Thomas Unterthiner, Mostafa Dehghani, Matthias Minderer, Georg Heigold, Sylvain Gelly, Jakob Uszkoreit, Neil Houlsby

While the Transformer architecture has become the de-facto standard for natural language processing tasks, its applications to computer vision remain limited. In vision, attention is either applied in conjunction with convolutional networks, or used to replace certain components of convolutional networks while keeping their overall structure in place. We show that this reliance on CNNs is not necessary and a pure transformer applied directly to sequences of image patches can perform very well on image classification tasks. When pre-trained on large amounts of data and transferred to multiple mid-sized or small image recognition benchmarks (ImageNet, CIFAR-100, VTAB, etc.), Vision Transformer (ViT) attains excellent results compared to state-of-the-art convolutional networks while requiring substantially fewer computational resources to train.

Krzysztof Choromanski, Valerii Likhosherstov, David Dohan, Richard Song, Georgiana-Andreea Gane, Tamas Sarlos, Peter Hawkins, Jared Q Davis, Afroz Mohiuddin, Lukasz Kaiser, David Belanger, Lucy J Colwell, Adrian Weller

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can also be used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

Biao Zhang, Ankur Bapna, Rico Sennrich, Orhan Firat

Using a mix of shared and language-specific (LS) parameters has shown promise in multilingual neural machine translation (MNMT), but the question of when and where LS capacity matters most is still under-studied. We offer such a study by proposing conditional language-specific routing (CLSR). CLSR employs hard binary gates conditioned on token representations to dynamically select LS or shared paths. By manipulating these gates, it can schedule LS capacity across sub-layers in MNMT subject to the guidance of translation signals and budget constraints. Moreover, CLSR can easily scale up to massively multilingual settings. Experiments with Transformer on OPUS-100 and WMT datasets show that: 1) MNMT is sensitive to both the amount and the position of LS modeling: distributing 10%-30% LS computation to the top and/or bottom encoder/decoder layers delivers the best performance; and 2) one-to-many translation benefits more from CLSR compared to many-to-one translation, particularly with unbalanced training data. Our study further verifies the trade-off between the shared capacity and LS capacity for multilingual translation. We corroborate our analysis by confirming the soundness of our findings as foundation of our improved multilingual Transformers. Source code and models are available at https://github.com/googleinterns/cct-m4.

Javier Antorán, Umang Bhatt, Tameem Adel, Adrian Weller, José Miguel Hernández Lobato

Both uncertainty estimation and interpretability are important factors for trustworthy machine learning systems. However, there is little work at the intersection of these two areas. We address this gap by proposing a novel method for interpreting uncertainty estimates from differentiable probabilistic models, like Bayesian Neural Networks (BNNs). Our method, Counterfactual Latent Uncertainty Explanations (CLUE), indicates how to change an input, while keeping it on the data manifold, such that a BNN becomes more confident about the input's prediction. We validate CLUE through 1) a novel framework for evaluating counterfactual explanations of uncertainty, 2) a series of ablation experiments, and 3) a user study. Our experiments show that CLUE outperforms baselines and enables practitioners to better understand which input patterns are responsible for predictive uncertainty.

Qiang Zhang, Tete Xiao, Alyosha Efros, Lerrel Pinto, Xiaolong Wang

At the heart of many robotics problems is the challenge of learning correspondences across domains. For instance, imitation learning requires obtaining correspondence between humans and robots; sim-to-real requires correspondence between physics simulators and real hardware; transfer learning requires correspondences between different robot environments. In this paper, we propose to learn correspondence across such domains emphasizing on differing modalities (vision and internal state), physics parameters (mass and friction), and morphologies (number of limbs). Importantly, correspondences are learned using unpaired and randomly collected data from the two domains. We propose dynamics cycles that align dynamic robotic behavior across two domains using a cycle consistency constraint. Once this correspondence is found, we can directly transfer the policy trained on one domain to the other, without needing any additional fine-tuning on the second domain. We perform experiments across a variety of problem domains, both in simulation and on real robots. Our framework is able to align uncalibrated monocular video of a real robot arm to dynamic state-action trajectories of a simulated arm without paired data. Video demonstrations of our results are available at: https://sites.google.com/view/cycledynamics .

Jonathan Gray, Adam Lerer, Anton Bakhtin, Noam Brown

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.

Dibya Ghosh, Abhishek Gupta, Ashwin D Reddy, Justin Fu, Coline M Devin, Ben Eysenbach, Sergey Levine

Current reinforcement learning (RL) algorithms can be brittle and difficult to use, especially when learning goal-reaching behaviors from sparse rewards. Although supervised imitation learning provides a simple and stable alternative, it requires access to demonstrations from a human supervisor. In this paper, we study RL algorithms that use imitation learning to acquire goal reaching policies from scratch, without the need for expert demonstrations or a value function. In lieu of demonstrations, we leverage the property that any trajectory is a successful demonstration for reaching the final state in that same trajectory. We propose a simple algorithm in which an agent continually relabels and imitates the trajectories it generates to progressively learn goal-reaching behaviors from scratch. Each iteration, the agent collects new trajectories using the latest policy, and maximizes the likelihood of the actions along these trajectories under the goal that was actually reached, so as to improve the policy. We formally show that this iterated supervised learning procedure optimizes a bound on the RL objective, derive performance bounds of the learned policy, and empirically demonstrate improved goal-reaching performance and robustness over current RL algorithms in several benchmark tasks.

Amy Zhang, Rowan T McAllister, Roberto Calandra, Yarin Gal, Sergey Levine

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.

John Co-Reyes, Yingjie Miao, Daiyi Peng, Esteban Real, Quoc V Le, Sergey Levine, Honglak Lee, Aleksandra Faust

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.

T. Konstantin Rusch, Siddhartha Mishra

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.

Alexander Richard, Dejan Markovic, Israel Gebru, Steven Krenn, Gladstone A Butler, Fernando Torre, Yaser Sheikh

We present a neural rendering approach for binaural sound synthesis that can produce realistic and spatially accurate binaural sound in realtime. The network takes, as input, a single-channel audio source and synthesizes, as output, two-channel binaural sound, conditioned on the relative position and orientation of the listener with respect to the source. We investigate deficiencies of the l2-loss on raw waveforms in a theoretical analysis and introduce an improved loss that overcomes these limitations. In an empirical evaluation, we establish that our approach is the first to generate spatially accurate waveform outputs (as measured by real recordings) and outperforms existing approaches by a considerable margin, both quantitatively and in a perceptual study. Dataset and code are available online.

Ian Gemp, Brian McWilliams, Claire Vernade, Thore Graepel

We present a novel view on principal components analysis as a competitive game in which each approximate eigenvector is controlled by a player whose goal is to maximize their own utility function. We analyze the properties of this PCA game and the behavior of its gradient based updates. The resulting algorithm---which combines elements from Oja's rule with a generalized Gram-Schmidt orthogonalization---is naturally decentralized and hence parallelizable through message passing. We demonstrate the scalability of the algorithm with experiments on large image datasets and neural network activations. We discuss how this new view of PCA as a differentiable game can lead to further algorithmic developments and insights.

Yang Song, Jascha Sohl-Dickstein, Durk Kingma, Abhishek Kumar, Stefano Ermon, Ben Poole
Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (a.k.a., score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking …
Chenlin Meng, Jiaming Song, Yang Song, Shengjia Zhao, Stefano Ermon

While autoregressive models excel at image compression, their sample quality is often lacking. Although not realistic, generated images often have high likelihood according to the model, resembling the case of adversarial examples. Inspired by a successful adversarial defense method, we incorporate randomized smoothing into autoregressive generative modeling. We first model a smoothed version of the data distribution, and then reverse the smoothing process to recover the original data distribution. This procedure drastically improves the sample quality of existing autoregressive models on several synthetic and real-world image datasets while obtaining competitive likelihoods on synthetic datasets.

Xizhou Zhu, Weijie Su, Lewei Lu, Bin Li, Xiaogang Wang, Jifeng Dai
DETR has been recently proposed to eliminate the need for many hand-designed components in object detection while demonstrating good performance. However, it suffers from slow convergence and limited feature spatial resolution, due to the limitation of Transformer attention modules in processing image feature maps. To mitigate these issues, we proposed Deformable DETR, whose attention modules only attend to a small set of key sampling points around a reference. Deformable DETR can achieve better performance than DETR (especially on small objects) with 10$\times$ less training epochs. Extensive experiments on the COCO benchmark demonstrate the effectiveness of our approach. Code is released at https://github.com/fundamentalvision/Deformable-DETR.
Ruochen Wang, Minhao Cheng, Xiangning Chen, Xiaocheng Tang, Cho-Jui Hsieh

Differentiable Neural Architecture Search is one of the most popular Neural Architecture Search (NAS) methods for its search efficiency and simplicity, accomplished by jointly optimizing the model weight and architecture parameters in a weight-sharing supernet via gradient-based algorithms. At the end of the search phase, the operations with the largest architecture parameters will be selected to form the final architecture, with the implicit assumption that the values of architecture parameters reflect the operation strength. While much has been discussed about the supernet's optimization, the architecture selection process has received little attention. We provide empirical and theoretical analysis to show that the magnitude of architecture parameters does not necessarily indicate how much the operation contributes to the supernet's performance. We propose an alternative perturbation-based architecture selection that directly measures each operation's influence on the supernet. We re-evaluate several differentiable NAS methods with the proposed architecture selection and find that it is able to extract significantly improved architectures from the underlying supernets consistently. Furthermore, we find that several failure modes of DARTS can be greatly alleviated with the proposed selection method, indicating that much of the poor generalization observed in DARTS can be attributed to the failure of magnitude-based architecture selection rather …

Erik Arakelyan, Daniel Daza, Pasquale Minervini, Michael Cochez
Neural link predictors are immensely useful for identifying missing edges in large scale Knowledge Graphs. However, it is still not clear how to use these models for answering more complex queries that arise in a number of domains, such as queries using logical conjunctions ($\land$), disjunctions ($\lor$) and existential quantifiers ($\exists$), while accounting for missing edges. In this work, we propose a framework for efficiently answering complex queries on incomplete Knowledge Graphs. We translate each query into an end-to-end differentiable objective, where the truth value of each atom is computed by a pre-trained neural link predictor. We then analyse two solutions to the optimisation problem, including gradient-based and combinatorial search. In our experiments, the proposed approach produces more accurate results than state-of-the-art methods --- black-box neural models trained on millions of generated queries --- without the need of training on a large and diverse set of complex queries. Using orders of magnitude less training data, we obtain relative improvements ranging from 8% up to 40% in Hits@3 across different knowledge graphs containing factual information. Finally, we demonstrate that it is possible to explain the outcome of our model in terms of the intermediate solutions identified for each of the complex …
Atsushi Nitanda, Taiji Suzuki

We analyze the convergence of the averaged stochastic gradient descent for overparameterized two-layer neural networks for regression problems. It was recently found that a neural tangent kernel (NTK) plays an important role in showing the global convergence of gradient-based methods under the NTK regime, where the learning dynamics for overparameterized neural networks can be almost characterized by that for the associated reproducing kernel Hilbert space (RKHS). However, there is still room for a convergence rate analysis in the NTK regime. In this study, we show that the averaged stochastic gradient descent can achieve the minimax optimal convergence rate, with the global convergence guarantee, by exploiting the complexities of the target function and the RKHS associated with the NTK. Moreover, we show that the target function specified by the NTK of a ReLU network can be learned at the optimal convergence rate through a smooth approximation of a ReLU network under certain conditions.

Marcin Andrychowicz, Anton Raichuk, Piotr Stanczyk, Manu Orsini, Sertan Girgin, Raphaël Marinier, Hussenot Hussenot-Desenonges, Matthieu Geist, Olivier Pietquin, Marcin Michalski, Sylvain Gelly, Olivier Bachem

In recent years, reinforcement learning (RL) has been successfully applied to many different continuous control tasks. While RL algorithms are often conceptually simple, their state-of-the-art implementations take numerous low- and high-level design decisions that strongly affect the performance of the resulting agents. Those choices are usually not extensively discussed in the literature, leading to discrepancy between published descriptions of algorithms and their implementations. This makes it hard to attribute progress in RL and slows down overall progress [Engstrom'20]. As a step towards filling that gap, we implement >50 such ``"choices" in a unified on-policy deep actor-critic framework, allowing us to investigate their impact in a large-scale empirical study. We train over 250'000 agents in five continuous control environments of different complexity and provide insights and practical recommendations for the training of on-policy deep actor-critic RL agents.

Yuan Yin, Vincent Le Guen, Jérémie DONA, Emmanuel d Bezenac, Ibrahim Ayed, Nicolas THOME, patrick gallinari

Forecasting complex dynamical phenomena in settings where only partial knowledge of their dynamics is available is a prevalent problem across various scientific fields. While purely data-driven approaches are arguably insufficient in this context, standard physical modeling based approaches tend to be over-simplistic, inducing non-negligible errors. In this work, we introduce the APHYNITY framework, a principled approach for augmenting incomplete physical dynamics described by differential equations with deep data-driven models. It consists in decomposing the dynamics into two components: a physical component accounting for the dynamics for which we have some prior knowledge, and a data-driven component accounting for errors of the physical model. The learning problem is carefully formulated such that the physical model explains as much of the data as possible, while the data-driven component only describes information that cannot be captured by the physical model, no more, no less. This not only provides the existence and uniqueness for this decomposition, but also ensures interpretability and benefits generalization. Experiments made on three important use cases, each representative of a different family of phenomena, i.e. reaction-diffusion equations, wave equations and the non-linear damped pendulum, show that APHYNITY can efficiently leverage approximate physical models to accurately forecast the evolution of the …

Lizhen Nie, Mao Ye, Qiang Liu, Dan Nicolae

Motivated by the rising abundance of observational data with continuous treatments, we investigate the problem of estimating the average dose-response curve (ADRF). Available parametric methods are limited in their model space, and previous attempts in leveraging neural network to enhance model expressiveness relied on partitioning continuous treatment into blocks and using separate heads for each block; this however produces in practice discontinuous ADRFs. Therefore, the question of how to adapt the structure and training of neural network to estimate ADRFs remains open. This paper makes two important contributions. First, we propose a novel varying coefficient neural network (VCNet) that improves model expressiveness while preserving continuity of the estimated ADRF. Second, to improve finite sample performance, we generalize targeted regularization to obtain a doubly robust estimator of the whole ADRF curve.

Mikhail Yurochkin, Yuekai Sun

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.

Xiaoxia (Shirley) Wu, Ethan Dyer, Behnam Neyshabur

Inspired by human learning, researchers have proposed ordering examples during training based on their difficulty. Both curriculum learning, exposing a network to easier examples early in training, and anti-curriculum learning, showing the most difficult examples first, have been suggested as improvements to the standard i.i.d. training. In this work, we set out to investigate the relative benefits of ordered learning. We first investigate the implicit curricula resulting from architectural and optimization bias and find that samples are learned in a highly consistent order. Next, to quantify the benefit of explicit curricula, we conduct extensive experiments over thousands of orderings spanning three kinds of learning: curriculum, anti-curriculum, and random-curriculum -- in which the size of the training dataset is dynamically increased over time, but the examples are randomly ordered. We find that for standard benchmark datasets, curricula have only marginal benefits, and that randomly ordered samples perform as well or better than curricula and anti-curricula, suggesting that any benefit is entirely due to the dynamic training set size. Inspired by common use cases of curriculum learning in practice, we investigate the role of limited training time budget and noisy data in the success of curriculum learning. Our experiments demonstrate that curriculum, …

Zhiyuan Li, Yi Zhang, Sanjeev Arora
Convolutional neural networks often dominate fully-connected counterparts in generalization performance, especially on image classification tasks. This is often explained in terms of \textquotedblleft better inductive bias.\textquotedblright\ However, this has not been made mathematically rigorous, and the hurdle is that the sufficiently wide fully-connected net can always simulate the convolutional net. Thus the training algorithm plays a role. The current work describes a natural task on which a provable sample complexity gap can be shown, for standard training algorithms. We construct a single natural distribution on $\mathbb{R}^d\times\{\pm 1\}$ on which any orthogonal-invariant algorithm (i.e. fully-connected networks trained with most gradient-based methods from gaussian initialization) requires $\Omega(d^2)$ samples to generalize while $O(1)$ samples suffice for convolutional architectures. Furthermore, we demonstrate a single target function, learning which on all possible distributions leads to an $O(1)$ vs $\Omega(d^2/\varepsilon)$ gap. The proof relies on the fact that SGD on fully-connected network is orthogonal equivariant. Similar results are achieved for $\ell_2$ regression and adaptive training algorithms, e.g. Adam and AdaGrad, which are only permutation equivariant.
Zhifeng Kong, Wei Ping, Jiaji Huang, Kexin Zhao, Bryan Catanzaro

In this work, we propose DiffWave, a versatile diffusion probabilistic model for conditional and unconditional waveform generation. The model is non-autoregressive, and converts the white noise signal into structured waveform through a Markov chain with a constant number of steps at synthesis. It is efficiently trained by optimizing a variant of variational bound on the data likelihood. DiffWave produces high-fidelity audios in different waveform generation tasks, including neural vocoding conditioned on mel spectrogram, class-conditional generation, and unconditional generation. We demonstrate that DiffWave matches a strong WaveNet vocoder in terms of speech quality (MOS: 4.44 versus 4.43), while synthesizing orders of magnitude faster. In particular, it significantly outperforms autoregressive and GAN-based waveform models in the challenging unconditional generation task in terms of audio quality and sample diversity from various automatic and human evaluations.

Cheng Phoo, Bharath Hariharan

Most few-shot learning techniques are pre-trained on a large, labeled “base dataset”. In problem domains where such large labeled datasets are not available for pre-training (e.g., X-ray, satellite images), one must resort to pre-training in a different “source” problem domain (e.g., ImageNet), which can be very different from the desired target task. Traditional few-shot and transfer learning techniques fail in the presence of such extreme differences between the source and target tasks. In this paper, we present a simple and effective solution to tackle this extreme domain gap: self-training a source domain representation on unlabeled data from the target domain. We show that this improves one-shot performance on the target domain by 2.9 points on average on the challenging BSCD-FSL benchmark consisting of datasets from multiple domains.

Colin Wei, Kendrick Shen, Yining Chen, Tengyu Ma

Self-training algorithms, which train a model to fit pseudolabels predicted by another previously-learned model, have been very successful for learning with unlabeled data using neural networks. However, the current theoretical understanding of self-training only applies to linear models. This work provides a unified theoretical analysis of self-training with deep networks for semi-supervised learning, unsupervised domain adaptation, and unsupervised learning. At the core of our analysis is a simple but realistic “expansion” assumption, which states that a low-probability subset of the data must expand to a neighborhood with large probability relative to the subset. We also assume that neighborhoods of examples in different classes have minimal overlap. We prove that under these assumptions, the minimizers of population objectives based on self-training and input-consistency regularization will achieve high accuracy with respect to ground-truth labels. By using off-the-shelf generalization bounds, we immediately convert this result to sample complexity guarantees for neural nets that are polynomial in the margin and Lipschitzness. Our results help explain the empirical successes of recently proposed self-training algorithms which use input consistency regularization.