arXiv subjects

Pascal Vincent

Publications and source records attributed to Pascal Vincent.

At least 55 records · Page 3Linked to original sources

arXiv2020

Stochastic Hamiltonian Gradient Methods for Smooth Games

The success of adversarial formulations in machine learning has brought renewed motivation for smooth games. In this work, we focus on the class of stochastic Hamiltonian methods and provide the first convergence guarantees for certain classes of stochastic smooth games. We propose a novel unbiased estimator for the stochastic Hamiltonian gradient descent (SHGD) and highlight its benefits. Using tools from the optimization literature we show that SHGD converges linearly to the neighbourhood of a stationary point. To guarantee convergence to the exact solution, we analyze SHGD with a decreasing step-size and we also present the first stochastic variance reduced Hamiltonian method. Our results provide the first global non-asymptotic last-iterate convergence guarantees for the class of stochastic unconstrained bilinear games and for the more general class of stochastic games that satisfy a "sufficiently bilinear" condition, notably including some non-convex non-concave problems. We supplement our analysis with experiments on stochastic bilinear and sufficiently bilinear games, where our theory is shown to be tight, and on simple adversarial machine learning formulations.

cs.LG↗

arXiv2020

Sharp Analysis of Smoothed Bellman Error Embedding

The \textit{Smoothed Bellman Error Embedding} algorithm~\citep{dai2018sbeed}, known as SBEED, was proposed as a provably convergent reinforcement learning algorithm with general nonlinear function approximation. It has been successfully implemented with neural networks and achieved strong empirical results. In this work, we study the theoretical behavior of SBEED in batch-mode reinforcement learning. We prove a near-optimal performance guarantee that depends on the representation power of the used function classes and a tight notion of the distribution shift. Our results improve upon prior guarantees for SBEED in ~\citet{dai2018sbeed} in terms of the dependence on the planning horizon and on the sample size. Our analysis builds on the recent work of ~\citet{Xie2020} which studies a related algorithm MSBO, that could be interpreted as a \textit{non-smooth} counterpart of SBEED.

cs.LG↗

arXiv2020

Revisiting Loss Modelling for Unstructured Pruning

By removing parameters from deep neural networks, unstructured pruning methods aim at cutting down memory footprint and computational cost, while maintaining prediction accuracy. In order to tackle this otherwise intractable problem, many of these methods model the loss landscape using first or second order Taylor expansions to identify which parameters can be discarded. We revisit loss modelling for unstructured pruning: we show the importance of ensuring locality of the pruning steps. We systematically compare first and second order Taylor expansions and empirically show that both can reach similar levels of performance. Finally, we show that better preserving the original network function does not necessarily transfer to better performing networks after fine-tuning, suggesting that only considering the impact of pruning on the loss might not be a sufficient objective to design good pruning criteria.

cs.LG↗

arXiv2020

SVRG for Policy Evaluation with Fewer Gradient Evaluations

Stochastic variance-reduced gradient (SVRG) is an optimization method originally designed for tackling machine learning problems with a finite sum structure. SVRG was later shown to work for policy evaluation, a problem in reinforcement learning in which one aims to estimate the value function of a given policy. SVRG makes use of gradient estimates at two scales. At the slower scale, SVRG computes a full gradient over the whole dataset, which could lead to prohibitive computation costs. In this work, we show that two variants of SVRG for policy evaluation could significantly diminish the number of gradient calculations while preserving a linear convergence speed. More importantly, our theoretical result implies that one does not need to use the entire dataset in every epoch of SVRG when it is applied to policy evaluation with linear function approximation. Our experiments demonstrate large computational savings provided by the proposed methods.

cs.LG↗

arXiv2020

Stable Policy Optimization via Off-Policy Divergence Regularization

Trust Region Policy Optimization (TRPO) and Proximal Policy Optimization (PPO) are among the most successful policy gradient approaches in deep reinforcement learning (RL). While these methods achieve state-of-the-art performance across a wide range of challenging tasks, there is room for improvement in the stabilization of the policy learning and how the off-policy data are used. In this paper we revisit the theoretical foundations of these algorithms and propose a new algorithm which stabilizes the policy improvement through a proximity term that constrains the discounted state-action visitation distribution induced by consecutive policies to be close to one another. This proximity term, expressed in terms of the divergence between the visitation distributions, is learned in an off-policy and adversarial manner. We empirically show that our proposed method can have a beneficial effect on stability and improve final performance in benchmark high-dimensional control tasks.

cs.LG↗

arXiv2020

A Closer Look at the Optimization Landscapes of Generative Adversarial Networks

Generative adversarial networks have been very successful in generative modeling, however they remain relatively challenging to train compared to standard deep neural networks. In this paper, we propose new visualization techniques for the optimization landscapes of GANs that enable us to study the game vector field resulting from the concatenation of the gradient of both players. Using these visualization techniques we try to bridge the gap between theory and practice by showing empirically that the training of GANs exhibits significant rotations around Local Stable Stationary Points (LSSP), similar to the one predicted by theory on toy examples. Moreover, we provide empirical evidence that GAN training converge to a stable stationary point which is a saddle point for the generator loss, not a minimum, while still achieving excellent performance.

cs.LG↗

arXiv2020

Stochastic Neural Network with Kronecker Flow

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner that adequately captures the dependencies among the various parameters. In this work, we address this need and present the Kronecker Flow, a generalization of the Kronecker product to invertible mappings designed for stochastic neural networks. We apply our method to variational Bayesian neural networks on predictive tasks, PAC-Bayes generalization bound estimation, and approximate Thompson sampling in contextual bandits. In all setups, our methods prove to be competitive with existing methods and better than the baselines.

cs.LG↗

arXiv2020

A NECTAr-based upgrade for the Cherenkov cameras of the H.E.S.S. 12-meter telescopes

The High Energy Stereoscopic System (H.E.S.S.) is one of the three arrays of imaging atmospheric Cherenkov telescopes (IACTs) currently in operation. It is composed of four 12-meter telescopes and a 28-meter one, and is sensitive to gamma rays in the energy range ~30 GeV - 100 TeV. The cameras of the 12-m telescopes recently underwent a substantial upgrade, with the goal of improving their performance and robustness. The upgrade involved replacing all camera components except for the photomultiplier tubes (PMTs). This meant developing new hardware for the trigger, readout, power, cooling and mechanical systems, and new software for camera control and data acquisition. Several novel technologies were employed in the cameras: the readout is built around the new NECTAr digitizer chip, developed for the next generation of IACTs; the camera electronics is fully controlled and read out via Ethernet using a combination of FPGA and embedded ARM computers; the software uses modern libraries such as Apache Thrift, ZMQ and Protocol buffers. This work describes in detail the design and the performance of the upgraded cameras.

astro-ph.IM↗

arXiv2019

fastMRI: An Open Dataset and Benchmarks for Accelerated MRI

Accelerating Magnetic Resonance Imaging (MRI) by taking fewer measurements has the potential to reduce medical costs, minimize stress to patients and make MRI possible in applications where it is currently prohibitively slow or expensive. We introduce the fastMRI dataset, a large-scale collection of both raw MR measurements and clinical MR images, that can be used for training and evaluation of machine-learning approaches to MR image reconstruction. By introducing standardized evaluation criteria and a freely-accessible dataset, our goal is to help the community make rapid advances in the state of the art for MR image reconstruction. We also provide a self-contained introduction to MRI for machine learning researchers with no medical imaging background.

cs.CV↗

arXiv2019

An Empirical Study of Batch Normalization and Group Normalization in Conditional Computation

Batch normalization has been widely used to improve optimization in deep neural networks. While the uncertainty in batch statistics can act as a regularizer, using these dataset statistics specific to the training set impairs generalization in certain tasks. Recently, alternative methods for normalizing feature activations in neural networks have been proposed. Among them, group normalization has been shown to yield similar, in some domains even superior performance to batch normalization. All these methods utilize a learned affine transformation after the normalization operation to increase representational power. Methods used in conditional computation define the parameters of these transformations as learnable functions of conditioning information. In this work, we study whether and where the conditional formulation of group normalization can improve generalization compared to conditional batch normalization. We evaluate performances on the tasks of visual question answering, few-shot learning, and conditional image generation.

cs.CV↗

arXiv2019

Randomized Value Functions via Multiplicative Normalizing Flows

Randomized value functions offer a promising approach towards the challenge of efficient exploration in complex environments with high dimensional state and action spaces. Unlike traditional point estimate methods, randomized value functions maintain a posterior distribution over action-space values. This prevents the agent's behavior policy from prematurely exploiting early estimates and falling into local optima. In this work, we leverage recent advances in variational Bayesian neural networks and combine these with traditional Deep Q-Networks (DQN) and Deep Deterministic Policy Gradient (DDPG) to achieve randomized value functions for high-dimensional domains. In particular, we augment DQN and DDPG with multiplicative normalizing flows in order to track a rich approximate posterior distribution over the parameters of the value function. This allows the agent to perform approximate Thompson sampling in a computationally efficient manner via stochastic gradient methods. We demonstrate the benefits of our approach through an empirical comparison in high dimensional environments.

cs.LG↗

arXiv2019

Reducing Uncertainty in Undersampled MRI Reconstruction with Active Acquisition

The goal of MRI reconstruction is to restore a high fidelity image from partially observed measurements. This partial view naturally induces reconstruction uncertainty that can only be reduced by acquiring additional measurements. In this paper, we present a novel method for MRI reconstruction that, at inference time, dynamically selects the measurements to take and iteratively refines the prediction in order to best reduce the reconstruction error and, thus, its uncertainty. We validate our method on a large scale knee MRI dataset, as well as on ImageNet. Results show that (1) our system successfully outperforms active acquisition baselines; (2) our uncertainty estimates correlate with error maps; and (3) our ResNet-based architecture surpasses standard pixel-to-pixel models in the task of MRI reconstruction. The proposed method not only shows high-quality reconstructions but also paves the road towards more applicable solutions for accelerating MRI.

cs.CV↗

arXiv2018

Improving Landmark Localization with Semi-Supervised Learning

We present two techniques to improve landmark localization in images from partially annotated datasets. Our primary goal is to leverage the common situation where precise landmark locations are only provided for a small data subset, but where class labels for classification or regression tasks related to the landmarks are more abundantly available. First, we propose the framework of sequential multitasking and explore it here through an architecture for landmark localization where training with class labels acts as an auxiliary signal to guide the landmark localization on unlabeled data. A key aspect of our approach is that errors can be backpropagated through a complete landmark localization model. Second, we propose and explore an unsupervised learning technique for landmark localization based on having a model predict equivariant landmarks with respect to transformations applied to the image. We show that these techniques, improve landmark prediction considerably and can learn effective detectors even when only a small fraction of the dataset has landmark labels. We present results on two toy datasets and four real datasets, with hands and faces, and report new state-of-the-art on two datasets in the wild, e.g. with only 5\% of labeled images we outperform previous state-of-the-art trained on the AFLW dataset.

cs.CV↗

arXiv2018

Convergent Tree Backup and Retrace with Function Approximation

Off-policy learning is key to scaling up reinforcement learning as it allows to learn about a target policy from the experience generated by a different behavior policy. Unfortunately, it has been challenging to combine off-policy learning with function approximation and multi-step bootstrapping in a way that leads to both stable and efficient algorithms. In this work, we show that the \textsc{Tree Backup} and \textsc{Retrace} algorithms are unstable with linear function approximation, both in theory and in practice with specific examples. Based on our analysis, we then derive stable and efficient gradient-based algorithms using a quadratic convex-concave saddle-point formulation. By exploiting the problem structure proper to these algorithms, we are able to provide convergence guarantees and finite-sample bounds. The applicability of our new analysis also goes beyond \textsc{Tree Backup} and \textsc{Retrace} and allows us to provide new convergence rates for the GTD and GTD2 algorithms without having recourse to projections or Polyak averaging.

cs.LG↗

arXiv2018

Learning to Compute Word Embeddings On the Fly

Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the "long tail" of this distribution requires enormous amounts of data. Representations of rare words trained directly on end tasks are usually poor, requiring us to pre-train embeddings on external data, or treat all rare words as out-of-vocabulary words with a unique representation. We provide a method for predicting embeddings of rare words on the fly from small amounts of auxiliary data with a network trained end-to-end for the downstream task. We show that this improves results against baselines where embeddings are trained on the end task for reading comprehension, recognizing textual entailment and language modeling.

cs.LG↗

arXiv2017

Learning to Generate Samples from Noise through Infusion Training

In this work, we investigate a novel training procedure to learn a generative model as the transition operator of a Markov chain, such that, when applied repeatedly on an unstructured random noise sample, it will denoise it into a sample that matches the target distribution from the training set. The novel training procedure to learn this progressive denoising operation involves sampling from a slightly different chain than the model chain used for generation in the absence of a denoising target. In the training chain we infuse information from the training target example that we would like the chains to reach with a high probability. The thus learned transition operator is able to produce quality and varied samples in a small number of steps. Experiments show competitive results compared to the samples generated with a basic Generative Adversarial Net

stat.ML↗

arXiv2016

A Cheap Linear Attention Mechanism with Fast Lookups and Fixed-Size Representations

The softmax content-based attention mechanism has proven to be very beneficial in many applications of recurrent neural networks. Nevertheless it suffers from two major computational limitations. First, its computations for an attention lookup scale linearly in the size of the attended sequence. Second, it does not encode the sequence into a fixed-size representation but instead requires to memorize all the hidden states. These two limitations restrict the use of the softmax attention mechanism to relatively small-scale applications with short sequences and few lookups per sequence. In this work we introduce a family of linear attention mechanisms designed to overcome the two limitations listed above. We show that removing the softmax non-linearity from the traditional attention formulation yields constant-time attention lookups and fixed-size representations of the attended sequences. These properties make these linear attention mechanisms particularly suitable for large-scale applications with extreme query loads, real-time requirements and memory constraints. Early experiments on a question answering task show that these linear mechanisms yield significantly better accuracy results than no attention, but obviously worse than their softmax alternative.

cs.LG↗

arXiv2016

Exact gradient updates in time independent of output size for the spherical loss family

An important class of problems involves training deep neural networks with sparse prediction targets of very high dimension D. These occur naturally in e.g. neural language models or the learning of word-embeddings, often posed as predicting the probability of next words among a vocabulary of size D (e.g. 200,000). Computing the equally large, but typically non-sparse D-dimensional output vector from a last hidden layer of reasonable dimension d (e.g. 500) incurs a prohibitive O(Dd) computational cost for each example, as does updating the $D \times d$ output weight matrix and computing the gradient needed for backpropagation to previous layers. While efficient handling of large sparse network inputs is trivial, the case of large sparse targets is not, and has thus so far been sidestepped with approximate alternatives such as hierarchical softmax or sampling-based approximations during training. In this work we develop an original algorithmic approach which, for a family of loss functions that includes squared error and spherical softmax, can compute the exact loss, gradient update for the output weights, and gradient for backpropagation, all in $O(d^{2})$ per example instead of $O(Dd)$, remarkably without ever computing the D-dimensional output. The proposed algorithm yields a speedup of up to $D/4d$ i.e. two orders of magnitude for typical sizes, for that critical part of the computations that often dominates the training time in this kind of network architecture.

cs.NE↗