The minimization of the loss function is of paramount importance in deep neural networks. On the other hand, many popular optimization algorithms have been shown to correspond to some evolution equation of gradient flow type. Inspired by the numerical schemes used for general evolution equations we introduce a second order stochastic Runge Kutta method and show that it yields a consistent procedure for the minimization of the loss function. In addition it can be coupled, in an adaptive framework, with a Stochastic Gradient Descent (SGD) to adjust automatically the learning rate of the SGD, without the need of any additional information on the Hessian of the loss functional. The adaptive SGD, called SGD-G2, is successfully tested on standard datasets.

If NAS methods are solutions, what is the problem? Most existing NAS methods require two-stage parameter optimization. However, performance of the same architecture in the two stages correlates poorly. In this work, we propose a new problem definition for NAS, task-specific end-to-end, based on this observation. We argue that given a computer vision task for which a NAS method is expected, this definition can reduce the vaguely-defined NAS evaluation to i) accuracy of this task and ii) the total computation consumed to finally obtain a model with satisfying accuracy. Seeing that most existing methods do not solve this problem directly, we propose DSNAS, an efficient differentiable NAS framework that simultaneously optimizes architecture and parameters with a low-biased Monte Carlo estimate. Child networks derived from DSNAS can be deployed directly without parameter retraining. Comparing with two-stage methods, DSNAS successfully discovers networks with comparable accuracy (74.4%) on ImageNet in 420 GPU hours, reducing the total time by more than 34%.

Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibrium solutions in the GAN zero-sum game. In this work, we show through several theoretical and numerical results that indeed GAN zero-sum games may not have any local Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We discuss several numerical experiments demonstrating the existence of proximal equilibrium solutions in GAN minimax problems.

We propose a class of kernel-based two-sample tests, which aim to determine whether two sets of samples are drawn from the same distribution. Our tests are constructed from kernels parameterized by deep neural nets, trained to maximize test power. These tests adapt to variations in distribution smoothness and shape over space, and are especially suited to high dimensions and complex data. By contrast, the simpler kernels used in prior kernel testing work are spatially homogeneous, and adaptive only in lengthscale. We explain how this scheme includes popular classifier-based two-sample tests as a special case, but improves on them in general. We provide the first proof of consistency for the proposed adaptation method, which applies both to kernels on deep features and to simpler radial basis kernels or multiple kernel learning. In experiments, we establish the superior performance of our deep kernels in hypothesis testing on benchmark and real-world data. The code of our deep-kernel-based two sample tests is available at https://github.com/fengliu90/DK-for-TST.

Test-time data augmentation---averaging the predictions of a machine learning model across multiple augmented samples of data---is a widely used technique that improves the predictive performance. While many advanced learnable data augmentation techniques have emerged in recent years, they are focused on the training phase. Such techniques are not necessarily optimal for test-time augmentation and can be outperformed by a policy consisting of simple crops and flips. The primary goal of this paper is to demonstrate that test-time augmentation policies can be successfully learned too. We~introduce \emph{greedy policy search} (GPS), a simple but high-performing method for learning a policy of test-time augmentation. We demonstrate that augmentation policies learned with GPS achieve superior predictive performance on image classification problems, provide better in-domain uncertainty estimation, and improve the robustness to domain shift.

This paper presents an inverted-file k-means clustering algorithm (IVF) suitable for a large-scale sparse data set with potentially numerous classes. Given such a data set, IVF efficiently works at high-speed and with low memory consumption, which keeps the same solution as a standard Lloyd's algorithm. The high performance arises from two distinct data representations. One is a sparse expression for both the object and mean feature vectors. The other is an inverted-file data structure for a set of the mean feature vectors. To confirm the effect of these representations, we design three algorithms using distinct data structures and expressions for comparison. We experimentally demonstrate that IVF achieves better performance than the designed algorithms when they are applied to large-scale real document data sets in a modern computer system equipped with superscalar out-of-order processors and a deep hierarchical memory system. We also introduce a simple yet practical clock-cycle per instruction (CPI) model for speed-performance analysis. Analytical results reveal that IVF suppresses three performance degradation factors: the numbers of cache misses, branch mispredictions, and the completed instructions.

Bayesian reward learning from demonstrations enables rigorous safety and uncertainty analysis when performing imitation learning. However, Bayesian reward learning methods are typically computationally intractable for complex control problems. We propose a highly efficient Bayesian reward learning algorithm that scales to high-dimensional imitation learning problems by first pre-training a low-dimensional feature encoding via self-supervised tasks and then leveraging preferences over demonstrations to perform fast Bayesian inference. We evaluate our proposed approach on the task of learning to play Atari games from demonstrations, without access to the game score. For Atari games our approach enables us to generate 100,000 samples from the posterior over reward functions in only 5 minutes using a personal laptop. Furthermore, our proposed approach achieves comparable or better imitation learning performance than state-of-the-art methods that only find a point estimate of the reward function. Finally, we show that our approach enables efficient high-confidence policy performance bounds. We show that these high-confidence performance bounds can be used to rank the performance and risk of a variety of evaluation policies, despite not having samples of the reward function. We also show evidence that high-confidence performance bounds can be used to detect reward hacking in complex imitation learning problems.

The development of personalized human head models from medical images has become an important topic in the electromagnetic dosimetry field, including the optimization of electrostimulation, safety assessments, etc. Human head models are commonly generated via the segmentation of magnetic resonance images into different anatomical tissues. This process is time consuming and requires special experience for segmenting a relatively large number of tissues. Thus, it is challenging to accurately compute the electric field in different specific brain regions. Recently, deep learning has been applied for the segmentation of the human brain. However, most studies have focused on the segmentation of brain tissue only and little attention has been paid to other tissues, which are considerably important for electromagnetic dosimetry. In this study, we propose a new architecture for a convolutional neural network, named ForkNet, to perform the segmentation of whole human head structures, which is essential for evaluating the electrical field distribution in the brain. The proposed network can be used to generate personalized head models and applied for the evaluation of the electric field in the brain during transcranial magnetic stimulation. Our computational results indicate that the head models generated using the proposed network exhibit strong matching with those created via manual segmentation in an intra-scanner segmentation task.

The Column Subset Selection Problem (CSSP) and the Nystr\"om method are among the leading tools for constructing small low-rank approximations of large datasets in machine learning and scientific computing. A fundamental question in this area is: how well can a data subset of size k compete with the best rank k approximation? We develop techniques which exploit spectral properties of the data matrix to obtain improved approximation guarantees which go beyond the standard worst-case analysis. Our approach leads to significantly better bounds for datasets with known rates of singular value decay, e.g., polynomial or exponential decay. Our analysis also reveals an intriguing phenomenon: the approximation factor as a function of k may exhibit multiple peaks and valleys, which we call a multiple-descent curve. A lower bound we establish shows that this behavior is not an artifact of our analysis, but rather it is an inherent property of the CSSP and Nystr\"om tasks. Finally, using the example of a radial basis function (RBF) kernel, we show that both our improved bounds and the multiple-descent curve can be observed on real datasets simply by varying the RBF parameter.

An important problem that arises in reinforcement learning and Monte Carlo methods is estimating quantities defined by the stationary distribution of a Markov chain. In many real-world applications, access to the underlying transition operator is limited to a fixed set of data that has already been collected, without additional interaction with the environment being available. We show that consistent estimation remains possible in this challenging scenario, and that effective estimation can still be achieved in important applications. Our approach is based on estimating a ratio that corrects for the discrepancy between the stationary and empirical distributions, derived from fundamental properties of the stationary distribution, and exploiting constraint reformulations based on variational divergence minimization. The resulting algorithm, GenDICE, is straightforward and effective. We prove its consistency under general conditions, provide an error analysis, and demonstrate strong empirical performance on benchmark problems, including off-line PageRank and off-policy policy evaluation.