Regularization and normalization have become indispensable components in training deep neural networks, resulting in faster training and improved generalization performance. We propose the projected error function regularization loss (PER) that encourages activations to follow the standard normal distribution. PER randomly projects activations onto one-dimensional space and computes the regularization loss in the projected space. PER is similar to the Pseudo-Huber loss in the projected space, thus taking advantage of both $L^1$ and $L^2$ regularization losses. Besides, PER can capture the interaction between hidden units by projection vector drawn from a unit sphere. By doing so, PER minimizes the upper bound of the Wasserstein distance of order one between an empirical distribution of activations and the standard normal distribution. To the best of the authors' knowledge, this is the first work to regularize activations via distribution matching in the probability distribution space. We evaluate the proposed method on the image classification task and the word-level language modeling task.
Tel Aviv University（特拉维夫大学）；Facebook AI Research（脸书人工智能研究院）
Normalization techniques play an important role in supporting efficient and often more effective training of deep neural networks. While conventional methods explicitly normalize the activations, we suggest to add a loss term instead. This new loss term encourages the variance of the activations to be stable and not vary from one random mini-batch to the next. As we prove, this encourages the activations to be distributed around a few distinct modes. We also show that if the inputs are from a mixture of two Gaussians, the new loss would either join the two together, or separate between them op…
We stabilize the activations of Recurrent Neural Networks (RNNs) by penalizing the squared distance between successive hidden states' norms. This penalty term is an effective regularizer for RNNs including LSTMs and IRNNs, improving performance on character-level language modeling and phoneme recognition, and outperforming weight noise and dropout. We achieve competitive performance (18.6\% PER) on the TIMIT phoneme recognition task for RNNs evaluated without beam search or an RNN transducer. With this penalty term, IRNN can achieve similar performance to LSTM on language modeling, although ad…
Entropy Regularizing Activation: Boosting Continuous Control, Large Language Models, and Image Classification with Activation as Entropy Constraints
Shanghai Qi Zhi Institute（上海启智研究所）；Department of Computer Science and Technology, Tsinghua University（清华大学计算机科学与技术系）；Institute for Interdisciplinary Information Sciences, Tsinghua University（清华大学交叉信息研究院）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）
MILA, Université de Montréal（蒙特利尔大学 MILA）；École Polytechnique de Montréal（蒙特利尔理工学院）
We propose zoneout, a novel method for regularizing RNNs. At each timestep, zoneout stochastically forces some hidden units to maintain their previous values. Like dropout, zoneout uses random noise to train a pseudo-ensemble, improving generalization. But by preserving instead of dropping hidden units, gradient information and state information are more readily propagated through time, as in feedforward stochastic depth networks. We perform an empirical investigation of various RNN regularizers, and find that zoneout gives significant performance improvements across tasks. We achieve competit…
Wasserstein GAN(WGAN) is a model that minimizes the Wasserstein distance between a data distribution and sample distribution. Recent studies have proposed stabilizing the training process for the WGAN and implementing the Lipschitz constraint. In this study, we prove the local stability of optimizing the simple gradient penalty $μ$-WGAN(SGP $μ$-WGAN) under suitable assumptions regarding the equilibrium and penalty measure $μ$. The measure valued differentiation concept is employed to deal with the derivative of the penalty terms, which is helpful for handling abstract singular measures with lo…
University of Maryland（马里兰大学）；GE Global Research（通用电气全球研究中心）；Avitas Systems（阿维塔斯系统公司）
Adversarial training has been shown to regularize deep neural networks in addition to increasing their robustness to adversarial examples. However, its impact on very deep state of the art networks has not been fully investigated. In this paper, we present an efficient approach to perform adversarial training by perturbing intermediate layer activations and study the use of such perturbations as a regularizer during training. We use these perturbations to train very deep models such as ResNets and show improvement in performance both on adversarial and original test data. Our experiments highl…
Stanford University（斯坦福大学）；The University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of South Carolina（南卡罗来纳大学）
The computation of Wasserstein gradient direction is essential for posterior sampling problems and scientific computing. The approximation of the Wasserstein gradient with finite samples requires solving a variational problem. We study the variational problem in the family of two-layer networks with squared-ReLU activations, towards which we derive a semi-definite programming (SDP) relaxation. This SDP can be viewed as an approximation of the Wasserstein gradient in a broader function family including two-layer networks. By solving the convex SDP, we obtain the optimal approximation of the Was…
Generative Adversarial Networks (GANs) are commonly used for modeling complex distributions of data. Both the generators and discriminators of GANs are often modeled by neural networks, posing a non-transparent optimization problem which is non-convex and non-concave over the generator and discriminator, respectively. Such networks are often heuristically optimized with gradient descent-ascent (GDA), but it is unclear whether the optimization problem contains any saddle points, or whether heuristic methods can find them in practice. In this work, we analyze the training of Wasserstein GANs wit…
University of Cambridge（剑桥大学）；University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；Alan Turing Institute（艾伦·图灵研究所）
Despite their success with unstructured data, deep neural networks are not yet a panacea for structured tabular data. In the tabular domain, their efficiency crucially relies on various forms of regularization to prevent overfitting and provide strong generalization performance. Existing regularization techniques include broad modelling decisions such as choice of architecture, loss functions, and optimization methods. In this work, we introduce Tabular Neural Gradient Orthogonalization and Specialization (TANGOS), a novel framework for regularization in the tabular setting built on latent uni…
Sapienza University of Rome（罗马第一大学）；University of Bologna（博洛尼亚大学）
Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered either the progressive increase in the size of the networks, or have tried to regularize the network behavior to equalize it with respect to previously observed tasks. In the latter case, it is essential to understand what type of information best represents this past behavior. Common techniques include regularizing the past outputs, gradients, or individual w…
University of Technology Sydney（悉尼科技大学）；NTT Media Intelligence Laboratories, NTT Corporation（日本电报电话公司NTT媒体情报实验室）
Graph convolutional networks have been successfully applied in various graph-based tasks. In a typical graph convolutional layer, node features are updated by aggregating neighborhood information. Repeatedly applying graph convolutions can cause the oversmoothing issue, i.e., node features at deep layers converge to similar values. Previous studies have suggested that oversmoothing is one of the major issues that restrict the performance of graph convolutional networks. In this paper, we propose a stochastic regularization method to tackle the oversmoothing problem. In the proposed method, we …
Learning with Differentially Private (Sliced) Wasserstein Gradients
Universidad de Valladolid and IMUVA（巴利亚多利德大学和IMUVA）；Institut de Mathématiques de Toulouse（图卢兹数学研究所）；Université de Toulouse（图卢兹大学）；ANITI & Regalia INRIA（ANITI与INRIA Regalia团队）
We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentati…
École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
Training certifiable neural networks enables one to obtain models with robustness guarantees against adversarial attacks. In this work, we introduce a framework to bound the adversary-free region in the neighborhood of the input data by a polyhedral envelope, which yields finer-grained certified robustness. We further introduce polyhedral envelope regularization (PER) to encourage larger polyhedral envelopes and thus improve the provable robustness of the models. We demonstrate the flexibility and effectiveness of our framework on standard benchmarks; it applies to networks of different archit…
Several regularization methods have recently been introduced which force the latent activations of an autoencoder or deep neural network to conform to either a Gaussian or hyperspherical distribution, or to minimize the implicit rank of the distribution in latent space. In the present work, we introduce a novel regularizing loss function which simulates a pairwise repulsive force between items and an attractive force of each item toward the origin. We show that minimizing this loss function in isolation achieves a hyperspherical distribution. Moreover, when used as a regularizing term, the sca…
We examine one-hidden-layer neural networks with random weights. It is well-known that in the limit of infinitely many neurons they simplify to Gaussian processes. For networks with a polynomial activation, we demonstrate that the rate of this convergence in 2-Wasserstein metric is $O(n^{-\frac{1}{2}})$, where $n$ is the number of hidden neurons. We suspect this rate is asymptotically sharp. We improve the known convergence rate for other activations, to power-law in $n$ for ReLU and inverse-square-root up to logarithmic factors for erf. We explore the interplay between spherical harmonics, St…
Mitigating the Impact of Outlier Channels for Language Model Quantization with Activation Regularization
Massachusetts Institute of Technology（麻省理工学院）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）；IST Austria（奥地利科学技术研究所）；Neural Magic, Inc.（Neural Magic公司）
In this paper, we study a physics-informed algorithm for Wasserstein Generative Adversarial Networks (WGANs) for uncertainty quantification in solutions of partial differential equations. By using groupsort activation functions in adversarial network discriminators, network generators are utilized to learn the uncertainty in solutions of partial differential equations observed from the initial/boundary data. Under mild assumptions, we show that the generalization error of the computed generator converges to the approximation error of the network with high probability, when the number of sample…
Non-asymptotic convergence analysis of the stochastic gradient Hamiltonian Monte Carlo algorithm with discontinuous stochastic gradient with applications to training of ReLU neural networks
School of Mathematics, Renmin University of China, Beijing, China（中国人民大学数学学院）；Division of Mathematical Sciences, Nanyang Technological University, 21 Nanyang Link, 637371 Singapore（南洋理工大学数学科学学院）；Financial Technology Thrust, Society Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, China（香港科技大学（广州）金融科技中心）
Sliced-Wasserstein Distribution Alignment Loss Improves the Ultra-Low-Bit Quantization of Large Language Models
Department of Information and Communication Engineering, The University of Tokyo（信息与通信工程系，东京大学）；Department of Computer Science, University of Toronto（计算机科学系，多伦多大学）；Department of Mechanical and Industrial Engineering, University of Toronto（机械与工业工程系，多伦多大学）
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；Duke University（杜克大学）
This paper studies the universal approximation property of deep neural networks for representing probability distributions. Given a target distribution $π$ and a source distribution $p_z$ both defined on $\mathbb{R}^d$, we prove under some assumptions that there exists a deep neural network $g:\mathbb{R}^d\rightarrow \mathbb{R}$ with ReLU activation such that the push-forward measure $(\nabla g)_\# p_z$ of $p_z$ under the map $\nabla g$ is arbitrarily close to the target measure $π$. The closeness are measured by three classes of integral probability metrics between probability distributions: …
The Robotics Institute, School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院机器人研究所）；Facebook；Michigan State University（密歇根州立大学）
Feature representations from pre-trained deep neural networks have been known to exhibit excellent generalization and utility across a variety of related tasks. Fine-tuning is by far the simplest and most widely used approach that seeks to exploit and adapt these feature representations to novel tasks with limited data. Despite the effectiveness of fine-tuning, itis often sub-optimal and requires very careful optimization to prevent severe over-fitting to small datasets. The problem of sub-optimality and over-fitting, is due in part to the large number of parameters used in a typical deep conv…
University of California, Santa Cruz（加州大学圣克鲁兹分校）；University of California at Berkeley（加州大学伯克利分校）
We provide gradient flow interpretations for the continuous-time continuous-state Hopfield neural network (HNN). The ordinary and stochastic differential equations associated with the HNN were introduced in the literature as analog optimizers, and were reported to exhibit good performance in numerical experiments. In this work, we point out that the deterministic HNN can be transcribed into Amari's natural gradient descent, and thereby uncover the explicit relation between the underlying Riemannian metric and the activation functions. By exploiting an equivalence between the natural gradient d…
Signal Processing and Speech Communication Laboratory（信号处理与语音通信实验室）；Graz University of Technology（格拉茨技术大学）
Deep neural networks rely heavily on normalization methods to improve their performance and learning behavior. Although normalization methods spurred the development of increasingly deep and efficient architectures, they also increase the vulnerability with respect to noise and input corruptions. In most applications, however, noise is ubiquitous and diverse; this can often lead to complete failure of machine learning systems as they fail to cope with mismatches between the input distribution during training- and test-time. The most common normalization method, batch normalization, reduces the…
Soft Matching Distance: A metric on neural representations that captures single-neuron tuning
McGovern Institute for Brain Research（麦戈文脑研究所）；Massachusetts Institute for Technology（麻省理工学院）；Center for Neural Science, New York University（纽约大学神经科学中心）；Center for Computational Neuroscience（计算神经科学中心）；Flatiron Institute（熨斗研究所）
We consider learning two layer neural networks using stochastic gradient descent. The mean-field description of this learning dynamics approximates the evolution of the network weights by an evolution in the space of probability distributions in $R^D$ (where $D$ is the number of parameters associated to each neuron). This evolution can be defined through a partial differential equation or, equivalently, as the gradient flow in the Wasserstein space of probability distributions. Earlier work shows that (under some regularity assumptions), the mean field description is accurate as soon as the nu…
We address the problem of detecting speech directed to a device that does not contain a specific wake-word. Specifically, we focus on audio coming from a touch-based invocation. Mitigating virtual assistants (VAs) activation due to accidental button presses is critical for user experience. While the majority of approaches to false trigger mitigation (FTM) are designed to detect the presence of a target keyword, inferring user intent in absence of keyword is difficult. This also poses a challenge when creating the training/evaluation data for such systems due to inherent ambiguity in the user's…
Despite the promise of Convolutional neural network (CNN) based classification models for histopathological images, it is infeasible to quantify its uncertainties. Moreover, CNNs may suffer from overfitting when the data is biased. We show that Bayesian-CNN can overcome these limitations by regularizing automatically and by quantifying the uncertainty. We have developed a novel technique to utilize the uncertainties provided by the Bayesian-CNN that significantly improves the performance on a large fraction of the test data (about 6% improvement in accuracy on 77% of test data). Further, we pr…
