In this paper, we will show an unprecedented method to accelerate training and improve performance, which called random gradient (RG). This method can be easier to the training of any model without extra calculation cost, we use Image classification, Semantic segmentation, and GANs to confirm this method can improve speed which is training model in computer vision. The central idea is using the loss multiplied by a random number to random reduce the back-propagation gradient. We can use this method to produce a better result in Pascal VOC, Cifar, Cityscapes datasets.
We observe that gradients computed via the reparameterization trick are in direct correspondence with solutions of the transport equation in the formalism of optimal transport. We use this perspective to compute (approximate) pathwise gradients for probability distributions not directly amenable to the reparameterization trick: Gamma, Beta, and Dirichlet. We further observe that when the reparameterization trick is applied to the Cholesky-factorized multivariate Normal distribution, the resulting gradients are suboptimal in the sense of optimal transport. We derive the optimal gradients and sh…
DiVeQ: Differentiable Vector Quantization Using the Reparameterization Trick
ELLIS Institute Finland & Department of Computer Science, Aalto University, Finland（芬兰ELLIS研究所及阿尔托大学计算机科学系）；Department of Information and Communications Engineering, Aalto University, Finland（芬兰阿尔托大学信息与通信工程系）
Massachusetts Institute of Technology（麻省理工学院）；Harvard University（哈佛大学）
Discovering interaction effects on a response of interest is a fundamental problem faced in biology, medicine, economics, and many other scientific disciplines. In theory, Bayesian methods for discovering pairwise interactions enjoy many benefits such as coherent uncertainty quantification, the ability to incorporate background knowledge, and desirable shrinkage properties. In practice, however, Bayesian methods are often computationally intractable for even moderate-dimensional problems. Our key insight is that many hierarchical models of practical interest admit a particular Gaussian process…
Efficient low-variance gradient estimation enabled by the reparameterization trick (RT) has been essential to the success of variational autoencoders. Doubly-reparameterized gradients (DReGs) improve on the RT for multi-sample variational bounds by applying reparameterization a second time for an additional reduction in variance. Here, we develop two generalizations of the DReGs estimator and show that they can be used to train conditional and hierarchical VAEs on image modelling tasks more effectively. First, we extend the estimator to hierarchical models with several stochastic layers by sho…
ETH Zürich（苏黎世联邦理工学院）；University of Toronto（多伦多大学）；Google Research, Brain Team（谷歌研究院大脑团队）；DeepMind（深度思维公司）；Institute for Advanced Study（高等研究院）
The Gumbel-Max trick is the basis of many relaxed gradient estimators. These estimators are easy to implement and low variance, but the goal of scaling them comprehensively to large combinatorial distributions is still outstanding. Working within the perturbation model framework, we introduce stochastic softmax tricks, which generalize the Gumbel-Softmax trick to combinatorial spaces. Our framework is a unified perspective on existing relaxed estimators for perturbation models, and it contains many novel relaxations. We design structured relaxations for subset selection, spanning trees, arbore…
CSIRO Data61（澳大利亚联邦科学与工业研究组织数据61研究所）；Australian National University（澳大利亚国立大学）；École Polytechnique Paris Saclay（巴黎萨克雷巴黎综合理工学院）；University of Sydney（悉尼大学）；RIKEN（日本理化学研究所）；University of Tokyo（东京大学）
We introduce a family of pairwise stochastic gradient estimators for gradients of expectations, which are related to the log-derivative trick, but involve pairwise interactions between samples. The simplest example of our new estimator, dubbed the fundamental trick estimator, is shown to arise from either a) introducing and approximating an integral representation based on the fundamental theorem of calculus, or b) applying the reparameterisation trick to an implicit parameterisation under infinitesimal perturbation of the parameters. From the former perspective we generalise to a reproducing …
University of Oxford（牛津大学）；Alan Turing Institute for Data Science（艾伦·图灵数据科学研究所）
Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBOs). Combined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the p…
Preferred Networks, Inc.（Preferred Networks公司）；The University of Tokyo（东京大学）
Low-variance gradient estimation is crucial for learning directed graphical models parameterized by neural networks, where the reparameterization trick is widely used for those with continuous variables. While this technique gives low-variance gradient estimates, it has not been directly applicable to discrete variables, the sampling of which inherently requires discontinuous operations. We argue that the discontinuity can be bypassed by marginalizing out the variable of interest, which results in a new reparameterization trick for discrete variables. This reparameterization greatly reduces th…
University of New South Wales（新南威尔士大学）；UNSW Business School（新南威尔士大学商学院）
The reparameterization trick is widely used in variational inference as it yields more accurate estimates of the gradient of the variational objective than alternative approaches such as the score function method. Although there is overwhelming empirical evidence in the literature showing its success, there is relatively little research exploring why the reparameterization trick is so effective. We explore this under the idealized assumptions that the variational approximation is a mean-field Gaussian density and that the log of the joint density of the model parameters and the data is a quadr…
By providing a simple and efficient way of computing low-variance gradients of continuous random variables, the reparameterization trick has become the technique of choice for training a variety of latent variable models. However, it is not applicable to a number of important continuous distributions. We introduce an alternative approach to computing reparameterization gradients based on implicit differentiation and demonstrate its broader applicability by applying it to Gamma, Beta, Dirichlet, and von Mises distributions, which cannot be used with the classic reparameterization trick. Our exp…
Kronecker product kernel provides the standard approach in the kernel methods literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow generalization to such new edges, whose start and end vertices do not appear in the training data, a setting known as zero-shot or zero-data learning. Such a setting occurs in numerous applications, including drug-target interaction prediction, collaborative filtering and information retrieval. Efficient training algorithms based on the so-called vec trick, that ma…
We present a new algorithm for stochastic variational inference that targets at models with non-differentiable densities. One of the key challenges in stochastic variational inference is to come up with a low-variance estimator of the gradient of a variational objective. We tackle the challenge by generalizing the reparameterization trick, one of the most effective techniques for addressing the variance issue for differentiable models, so that the trick works for non-differentiable models as well. Our algorithm splits the space of latent variables into regions where the density of the variable…
The reparameterization trick has become one of the most useful tools in the field of variational inference. However, the reparameterization trick is based on the standardization transformation which restricts the scope of application of this method to distributions that have tractable inverse cumulative distribution functions or are expressible as deterministic transformations of such distributions. In this paper, we generalized the reparameterization trick by allowing a general transformation. We discover that the proposed model is a special case of control variate indicating that the propose…
University of Amsterdam（阿姆斯特丹大学）；Aiconic；UC Berkeley（加州大学伯克利分校）
Reparameterizable densities are an important way to learn probability distributions in a deep learning setting. For many distributions it is possible to create low-variance gradient estimators by utilizing a `reparameterization trick'. Due to the absence of a general reparameterization trick, much research has recently been devoted to extend the number of reparameterizable distributional families. Unfortunately, this research has primarily focused on distributions defined in Euclidean space, ruling out the usage of one of the most influential class of spaces with non-trivial topologies: Lie gr…
Within many machine learning algorithms, a fundamental problem concerns efficient calculation of an unbiased gradient wrt parameters $\gammav$ for expectation-based objectives $\Ebb_{q_{\gammav} (\yv)} [f(\yv)]$. Most existing methods either (i) suffer from high variance, seeking help from (often) complicated variance-reduction techniques; or (ii) they only apply to reparameterizable continuous random variables and employ a reparameterization trick. To address these limitations, we propose a General and One-sample (GO) gradient that (i) applies to many distributions associated with non-reparam…
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face increasingly complex tasks. Traditional policy gradient algorithms use the likelihood-ratio trick, which is known to produce unbiased but high variance estimates. More modern approaches exploit the reparametrization trick, which gives lower variance gradient estimates but requires differentiable value function approximators. In this work, we study a different type of s…
EWHA Womans University（梨花女子大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）
Estimating the gradients of stochastic nodes in stochastic computational graphs is one of the crucial research questions in the deep generative modeling community, which enables the gradient descent optimization on neural network parameters. Stochastic gradient estimators of discrete random variables are widely explored, for example, Gumbel-Softmax reparameterization trick for Bernoulli and categorical distributions. Meanwhile, other discrete distribution cases such as the Poisson, geometric, binomial, multinomial, negative binomial, etc. have not been explored. This paper proposes a generaliz…
National University of Ireland Maynooth（爱尔兰国立梅努斯大学）；University of Oxford（牛津大学）；Purdue University（普渡大学）
The deep learning community has devised a diverse set of methods to make gradient optimization, using large datasets, of large and highly complex models with deeply cascaded nonlinearities, practical. Taken as a whole, these methods constitute a breakthrough, allowing computational structures which are quite wide, very deep, and with an enormous number and variety of free parameters to be effectively optimized. The result now dominates much of practical machine learning, with applications in machine translation, computer vision, and speech recognition. Many of these methods, viewed through the…
Technische Universität Darmstadt（达姆施塔特工业大学）；Honda Research Institute Europe（欧洲本田研究院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Reinforcement learning methods for robotics are increasingly successful due to the constant development of better policy gradient techniques. A precise (low variance) and accurate (low bias) gradient estimator is crucial to face increasingly complex tasks. Traditional policy gradient algorithms use the likelihood-ratio trick, which is known to produce unbiased but high variance estimates. More modern approaches exploit the reparametrization trick, which gives lower variance gradient estimates but requires differentiable value function approximators. In this work, we study a different type of s…
Double Variance Reduction: A Smoothing Trick for Composite Optimization Problems without First-Order Gradient
School of Management, Xi’an Jiaotong University（西安交通大学管理学院）；State Grid Corporation of China（中国国家电网有限公司）；International Business School, Beijing Foreign Studies University（北京外国语大学国际商学院）；Agency for Science, Technology and Research (A*STAR)（新加坡科技研究局）；College of Computing and Data Science, NTU（南洋理工大学计算机与数据科学学院）
The reparameterization trick enables optimizing large scale stochastic computation graphs via gradient descent. The essence of the trick is to refactor each stochastic node into a differentiable function of its parameters and a random variable with fixed distribution. After refactoring, the gradients of the loss propagated by the chain rule through the graph are low variance unbiased estimators of the gradients of the expected loss. While many continuous random variables have such reparameterizations, discrete random variables lack useful reparameterizations due to the discontinuous nature of …
This paper studies the performance of a recently proposed preconditioned stochastic gradient descent (PSGD) algorithm on recurrent neural network (RNN) training. PSGD adaptively estimates a preconditioner to accelerate gradient descent, and is designed to be simple, general and easy to use, as stochastic gradient descent (SGD). RNNs, especially the ones requiring extremely long term memories, are difficult to train. We have tested PSGD on a set of synthetic pathological RNN learning problems and the real world MNIST handwritten digit recognition task. Experimental results suggest that PSGD is …
Xi’an Jiaotong University（西安交通大学）；Shenzhen Research Institute of Xi’an Jiaotong University（西安交通大学深圳研究院）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Tsinghua University（清华大学）
The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a nonnegative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ (or a Gumbel-Max variable $i$) in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and graph embedding require to ge…
The well-known Gumbel-Max Trick for sampling elements from a categorical distribution (or more generally a non-negative vector) and its variants have been widely used in areas such as machine learning and information retrieval. To sample a random element $i$ in proportion to its positive weight $v_i$, the Gumbel-Max Trick first computes a Gumbel random variable $g_i$ for each positive weight element $i$, and then samples the element $i$ with the largest value of $g_i+\ln v_i$. Recently, applications including similarity estimation and weighted cardinality estimation require to generate $k$ ind…
Kernel methods form a powerful, versatile, and theoretically-grounded unifying framework to solve nonlinear problems in signal processing and machine learning. The standard approach relies on the kernel trick to perform pairwise evaluations of a kernel function, which leads to scalability issues for large datasets due to its linear and superlinear growth with respect to the training data. A popular approach to tackle this problem, known as random Fourier features (RFFs), samples from a distribution to obtain the data-independent basis of a higher finite-dimensional feature space, where its dot…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Rice University（莱斯大学）
Training deep graph neural networks (GNNs) is notoriously hard. Besides the standard plights in training deep architectures such as vanishing gradients and overfitting, it also uniquely suffers from over-smoothing, information squashing, and so on, which limits their potential power for encoding the high-order neighbor structure in large-scale graphs. Although numerous efforts are proposed to address these limitations, such as various forms of skip connections, graph normalization, and random dropping, it is difficult to disentangle the advantages brought by a deep GNN architecture from those …
University of British Columbia（不列颠哥伦比亚大学）；RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend their application to estimate \emph{structured} approximations such as mixtures of EF distributions. Such approximations can fit complex, multimodal posterior distributions and are generally more accurate than unimodal EF approximations. By using a \emph{minimal conditional-EF} representation of such approximations, we derive simple natural-gradient updates. Our…
Guangdong University of Finance and Economics（广东财经大学）
-The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms. The work in this paper remedy this issue by introducing a novel unbiased stratified statistic \ $\bar{G}_{mst}$\ , a sufficient condition of fast convergence for \ $\bar{G}_{mst}$\ also is established. A novel algorithm named MSSG designed based on \ $\bar{G}_{mst}$\ outperforms other sgd-like algorithms. Theoretical conclusions and experimental evidence strongly suggest to employ MSSG when train…
As an adaptive, interpretable, robust, and accurate meta-algorithm for arbitrary differentiable loss functions, gradient tree boosting is one of the most popular machine learning techniques, though the computational expensiveness severely limits its usage. Stochastic gradient boosting could be adopted to accelerates gradient boosting by uniformly sampling training instances, but its estimator could introduce a high variance. This situation arises motivation for us to optimize gradient tree boosting. We combine gradient tree boosting with importance sampling, which achieves better performance b…
Tsinghua University（清华大学）；Institute for Interdisciplinary Information Sciences（交叉信息研究院）
Gradient Boosted Decision Trees (GBDT) is a very successful ensemble learning algorithm widely used across a variety of applications. Recently, several variants of GBDT training algorithms and implementations have been designed and heavily optimized in some very popular open sourced toolkits including XGBoost, LightGBM and CatBoost. In this paper, we show that both the accuracy and efficiency of GBDT can be further enhanced by using more complex base learners. Specifically, we extend gradient boosting to use piecewise linear regression trees (PL Trees), instead of piecewise constant regression…
UCSF（加州大学旧金山分校）；INRIA-CNRS-UPSud-UPSay（法国国家信息与自动化研究所-法国国家科学研究中心-巴黎南大学-巴黎萨克雷大学）；TAU, U. Paris-Sud（计算机科学研究实验室，巴黎南大学）；CNRS-UPSud-INRIA-UPSay（法国国家科学研究中心-巴黎南大学-法国国家信息与自动化研究所-巴黎萨克雷大学）
When applied to training deep neural networks, stochastic gradient descent (SGD) often incurs steady progression phases, interrupted by catastrophic episodes in which loss and gradient norm explode. A possible mitigation of such events is to slow down the learning process. This paper presents a novel approach to control the SGD learning rate, that uses two statistical tests. The first one, aimed at fast learning, compares the momentum of the normalized gradient vectors to that of random unit vectors and accordingly gracefully increases or decreases the learning rate. The second one is a change…
Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and time consuming. Recently, researchers have tried to use deep learning algorithms to exploit the landscape of the loss function of the training problem of interest, and learn how to optimize over it in an automatic way. In this paper, we propose a new learning-to-learn model and some useful and practical tricks. Our optimizer outperforms generic, hand-crafte…
Rochester Institute of Technology（罗切斯特理工学院）；The Pennsylvania State University（宾夕法尼亚州立大学）
Training deep neural networks on large-scale datasets requires significant hardware resources whose costs (even on cloud platforms) put them out of reach of smaller organizations, groups, and individuals. Backpropagation, the workhorse for training these networks, is an inherently sequential process that is difficult to parallelize. Furthermore, it requires researchers to continually develop various tricks, such as specialized weight initializations and activation functions, in order to ensure a stable parameter optimization. Our goal is to seek an effective, neuro-biologically-plausible alter…
Carnegie Mellon University（卡内基梅隆大学）；University of California, Berkeley（加利福尼亚大学伯克利分校）
Whereas it is believed that techniques such as Adam, batch normalization and, more recently, SeLU nonlinearities "solve" the exploding gradient problem, we show that this is not the case in general and that in a range of popular MLP architectures, exploding gradients exist and that they limit the depth to which networks can be effectively trained, both in theory and in practice. We explain why exploding gradients occur and highlight the *collapsing domain problem*, which can arise in architectures that avoid exploding gradients. ResNets have significantly lower gradients and thus can circumven…
University of California, Irvine（加州大学欧文分校）；University at Albany, State University of New York（纽约州立大学奥尔巴尼分校）
Quantized or low-bit neural networks are attractive due to their inference efficiency. However, training deep neural networks with quantized activations involves minimizing a discontinuous and piecewise constant loss function. Such a loss function has zero gradients almost everywhere (a.e.), which makes the conventional gradient-based algorithms inapplicable. To this end, we study a novel class of \emph{biased} first-order oracle, termed coarse gradient, for overcoming the vanished gradient issue. A coarse gradient is generated by replacing the a.e. zero derivatives of quantized (i.e., stair-c…
Despite the fundamental distinction between adversarial and natural training (AT and NT), AT methods generally adopt momentum SGD (MSGD) for the outer optimization. This paper aims to analyze this choice by investigating the overlooked role of outer optimization in AT. Our exploratory evaluations reveal that AT induces higher gradient norm and variance compared to NT. This phenomenon hinders the outer optimization in AT since the convergence rate of MSGD is highly dependent on the variance of the gradients. To this end, we propose an optimization method called ENGM which regularizes the contri…
College of Computer Science, Zhejiang University（浙江大学计算机科学与技术学院）；School of Software Technology, Zhejiang University（浙江大学软件学院）
With the rapid increase of big data, distributed Machine Learning (ML) has been widely applied in training large-scale models. Stochastic Gradient Descent (SGD) is arguably the workhorse algorithm of ML. Distributed ML models trained by SGD involve large amounts of gradient communication, which limits the scalability of distributed ML. Thus, it is important to compress the gradients for reducing communication. In this paper, we propose FastSGD, a Fast compressed SGD framework for distributed ML. To achieve a high compression ratio at a low cost, FastSGD represents the gradients as key-value pa…
RIKEN Center for Advanced Intelligence Project（理化学研究所先进智能项目中心）
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating Bayesian inference as an optimization problem and solving it using gradient-based optimization. In this paper, we argue in favor of natural-gradient approaches which, unlike their gradient-based counterparts, can improve convergence by exploiting the information geometry of the solutions. We show how to derive fast yet simple natural-gradient updates by using a …
