The incredible effectiveness of adversarial attacks on fooling deep neural networks poses a tremendous hurdle in the widespread adoption of deep learning in safety and security-critical domains. While adversarial defense mechanisms have been proposed since the discovery of the adversarial vulnerability issue of deep neural networks, there is a long path to fully understand and address this issue. In this study, we hypothesize that part of the reason for the incredible effectiveness of adversarial attacks is their ability to implicitly tap into and exploit the gradient flow of a deep neural network. This innate ability to exploit gradient flow makes defending against such attacks quite challenging. Motivated by this hypothesis we argue that if a deep neural network architecture can explicitly tap into its own gradient flow during the training, it can boost its defense capability significantly. Inspired by this fact, we introduce the concept of self-gradient networks, a novel deep neural network architecture designed to be more robust against adversarial perturbations. Gradient flow information is leveraged within self-gradient networks to achieve greater perturbation stability beyond what can be achieved in the standard training process. We conduct a theoretical analysis to gain better insights into the behaviour of the proposed self-gradient networks to illustrate the efficacy of leverage this additional gradient flow information. The proposed self-gradient network architecture enables much more efficient and effective adversarial training, leading to faster convergence towards an adversarially robust solution by at least 10X. Experimental results demonstrate the effectiveness of self-gradient networks when compared with state-of-the-art adversarial learning strategies, with 10% improvement on the CIFAR10 dataset under PGD and CW adversarial perturbations.
Australian National University（澳大利亚国立大学）；Amazon Science（亚马逊科学）；DATA61, CSIRO（联邦科学与工业研究组织数据61）
Neural network quantization has become increasingly popular due to efficient memory consumption and faster computation resulting from bitwise operations on the quantized networks. Even though they exhibit excellent generalization capabilities, their robustness properties are not well-understood. In this work, we systematically study the robustness of quantized networks against gradient based adversarial attacks and demonstrate that these quantized models suffer from gradient vanishing issues and show a fake sense of robustness. By attributing gradient vanishing to poor forward-backward signal …
We propose gradient adversarial training, an auxiliary deep learning framework applicable to different machine learning problems. In gradient adversarial training, we leverage a prior belief that in many contexts, simultaneous gradient updates should be statistically indistinguishable from each other. We enforce this consistency using an auxiliary network that classifies the origin of the gradient tensor, and the main network serves as an adversary to the auxiliary network in addition to performing standard task-based training. We demonstrate gradient adversarial training for three different s…
Arizona State University（亚利桑那州立大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Pacific Northwest National Laboratory（太平洋西北国家实验室）
Novelty detection aims to automatically identify out-of-distribution (OOD) data, without any prior knowledge of them. It is a critical step in data monitoring, behavior analysis and other applications, helping enable continual learning in the field. Conventional methods of OOD detection perform multi-variate analysis on an ensemble of data or features, and usually resort to the supervision with OOD data to improve the accuracy. In reality, such supervision is impractical as one cannot anticipate the anomalous data. In this paper, we propose a novel, self-supervised approach that does not rely …
Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation over Transformation (EOT) attack. We investigate the effect of the adversarial attacks using proxy gradients on randomized neural networks and demonstrate that it highly relies on the directional distribution of the loss gradients of the randomized neural network. We show in particular that proxy gradients are less effective when the gradients are more scattere…
Lomonosov Moscow State University（罗蒙诺索夫莫斯科国立大学）；Huawei Technologies Co., Ltd.（华为技术有限公司）；China Nanhu Academy of Electronics and Information Technology（中国南湖电子信息技术研究院）
Lateral inhibitory connections have been observed in the cortex of the biological brain, and has been extensively studied in terms of its role in cognitive functions. However, in the vanilla version of backpropagation in deep learning, all gradients (which can be understood to comprise of both signal and noise gradients) flow through the network during weight updates. This may lead to overfitting. In this work, inspired by biological lateral inhibition, we propose Gradient Mask, which effectively filters out noise gradients in the process of backpropagation. This allows the learned feature inf…
Institute of Computational Mathematics and Scientific/Engineering Computing（科学与工程计算研究所）
We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated gradient information to yield enhanced approximation accuracy. In particular, the gradient information is included as a regularization term in the gradient-enhanced DNNs approach, for which we present similar posterior estimates (by the two-layer neural networks) as those in the path-norm regularized DNNs approximations. We also discuss the application of this …
The Open University（开放大学）；IDC Herzeliya（赫兹利亚跨学科研究中心）；Bar-Ilan University（巴伊兰大学）；Microsoft（微软）；Technion（以色列理工学院）；Tel Aviv University（特拉维夫大学）
Transformer-based language models significantly advanced the state-of-the-art in many linguistic tasks. As this revolution continues, the ability to explain model predictions has become a major area of interest for the NLP community. In this work, we present Gradient Self-Attention Maps (Grad-SAM) - a novel gradient-based method that analyzes self-attention units and identifies the input elements that explain the model's prediction the best. Extensive evaluations on various benchmarks show that Grad-SAM obtains significant improvements over state-of-the-art alternatives.
University of Toronto（多伦多大学）；Vector Institute（向量学院）；Max Planck Institute for Intelligent Systems（马克斯·普朗克智能系统研究所）
Standard first-order stochastic optimization algorithms base their updates solely on the average mini-batch gradient, and it has been shown that tracking additional quantities such as the curvature can help de-sensitize common hyperparameters. Based on this intuition, we explore the use of exact per-sample Hessian-vector products and gradients to construct optimizers that are self-tuning and hyperparameter-free. Based on a dynamics model of the gradient, we derive a process which leads to a curvature-corrected, noise-adaptive online gradient estimate. The smoothness of our updates makes it mor…
Department of Computer Science, University of California, Los Angeles, CA, USA（加州大学洛杉矶分校计算机科学系）；Princeton AI Laboratory, Princeton University, Princeton, NJ, USA（普林斯顿大学普林斯顿AI实验室）
University of the Witwatersrand（金山大学）；InstaDeep；Google Brain（谷歌大脑）
Training sparse networks to converge to the same performance as dense neural architectures has proven to be elusive. Recent work suggests that initialization is the key. However, while this direction of research has had some success, focusing on initialization alone appears to be inadequate. In this paper, we take a broader view of training sparse networks and consider the role of regularization, optimization, and architecture choices on sparse models. We propose a simple experimental framework, Same Capacity Sparse vs Dense Comparison (SC-SDC), that allows for a fair comparison of sparse and …
As gradient descent method in deep learning causes a series of questions, this paper proposes a novel gradient-free deep learning structure. By adding a new module into traditional Self-Organizing Map and introducing residual into the map, a Deep Valued Self-Organizing Map network is constructed. And analysis about the convergence performance of such a deep Valued Self-Organizing Map network is proved in this paper, which gives an inequality about the designed parameters with the dimension of inputs and the loss of prediction.
Much of the focus in machine learning research is placed in creating new architectures and optimization methods, but the overall loss function is seldom questioned. This paper interprets machine learning from a multi-objective optimization perspective, showing the limitations of the default linear combination of loss functions over a data set and introducing the hypervolume indicator as an alternative. It is shown that the gradient of the hypervolume is defined by a self-adjusting weighted mean of the individual loss gradients, making it similar to the gradient of a weighted mean loss but with…
We study convergence rates of AdaGrad-Norm as an exemplar of adaptive stochastic gradient methods (SGD), where the step sizes change based on observed stochastic gradients, for minimizing non-convex, smooth objectives. Despite their popularity, the analysis of adaptive SGD lags behind that of non adaptive methods in this setting. Specifically, all prior works rely on some subset of the following assumptions: (i) uniformly-bounded gradient norms, (ii) uniformly-bounded stochastic gradient variance (or even noise support), (iii) conditional independence between the step size and stochastic gradi…
Zhejiang University/University of Illinois at Urbana-Champaign Institute（浙江大学-伊利诺伊大学厄巴纳香槟校区联合学院）；Hong Kong Metropolitan University（香港都会大学）；Singapore University of Technology and Design（新加坡科技设计大学）；Princeton University（普林斯顿大学）
Federated learning (FL) is an emerging machine learning method that can be applied in mobile edge systems, in which a server and a host of clients collaboratively train a statistical model utilizing the data and computation resources of the clients without directly exposing their privacy-sensitive data. We show that running stochastic gradient descent (SGD) in such a setting can be viewed as adding a momentum-like term to the global aggregation process. Based on this finding, we further analyze the convergence rate of a federated learning system by accounting for the effects of parameter stale…
Texas A&M University（德州农工大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Semantic hashing has become a crucial component of fast similarity search in many large-scale information retrieval systems, in particular, for text data. Variational auto-encoders (VAEs) with binary latent variables as hashing codes provide state-of-the-art performance in terms of precision for document retrieval. We propose a pairwise loss function with discrete latent VAE to reward within-class similarity and between-class dissimilarity for supervised hashing. Instead of solving the optimization relying on existing biased gradient estimators, an unbiased low-variance gradient estimator is a…
Imbalanced image datasets are commonly available in the domain of biomedical image analysis. Biomedical images contain diversified features that are significant in predicting targeted diseases. Generative Adversarial Networks (GANs) are utilized to address the data limitation problem via the generation of synthetic images. Training challenges such as mode collapse, non-convergence, and instability degrade a GAN's performance in synthesizing diversified and high-quality images. In this work, MSG-SAGAN, an attention-guided multi-scale gradient GAN architecture is proposed to model the relationsh…
We present a derivation of the gradients of feedforward neural networks using Fréchet calculus which is arguably more compact than the ones usually presented in the literature. We first derive the gradients for ordinary neural networks working on vectorial data and show how these derived formulas can be used to derive a simple and efficient algorithm for calculating a neural networks gradients. Subsequently we show how our analysis generalizes to more general neural network architectures including, but not limited to, convolutional networks.
We introduce a new technique for gradient normalization during neural network training. The gradients are rescaled during the backward pass using normalization layers introduced at certain points within the network architecture. These normalization nodes do not affect forward activity propagation, but modify backpropagation equations to permit a well-scaled gradient flow that reaches the deepest network layers without experimenting vanishing or explosion. Results on tests with very deep neural networks show that the new technique can do an effective control of the gradient norm, allowing the u…
University of Connecticut（康涅狄格大学）；Northeastern University（东北大学）；Duke University（杜克大学）；Amazon Web Services, Inc.（亚马逊云科技公司）；Stevens Institute of Technology（史蒂文斯理工学院）
Distributed learning such as federated learning or collaborative learning enables model training on decentralized data from users and only collects local gradients, where data is processed close to its sources for data privacy. The nature of not centralizing the training data addresses the privacy issue of privacy-sensitive data. Recent studies show that a third party can reconstruct the true training data in the distributed machine learning system through the publicly-shared gradients. However, existing reconstruction attack frameworks lack generalizability on different Deep Neural Network (D…
Department of Computer Science, University College London（伦敦大学学院计算机科学系）；Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；Huawei R&D U.K.（华为英国研发中心）；Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所）
The Schrödinger equation is at the heart of modern quantum mechanics. Since exact solutions of the ground state are typically intractable, standard approaches approximate Schrödinger equation as forms of nonlinear generalized eigenvalue problems $F(V)V = SVΛ$ in which $F(V)$, the matrix to be decomposed, is a function of its own top-$k$ smallest eigenvectors $V$, leading to a "self-consistency problem". Traditional iterative methods heavily rely on high-quality initial guesses of $V$ generated via domain-specific heuristics methods based on quantum mechanics. In this work, we eliminate such a …
Mila - Quebec AI Institute（Mila-魁北克人工智能研究所）；Université de Montréal（蒙特利尔大学）
Attention and self-attention mechanisms, are now central to state-of-the-art deep learning on sequential tasks. However, most recent progress hinges on heuristic approaches with limited understanding of attention's role in model optimization and computation, and rely on considerable memory and computational resources that scale poorly. In this work, we present a formal analysis of how self-attention affects gradient propagation in recurrent networks, and prove that it mitigates the problem of vanishing gradients when trying to capture long-term dependencies by establishing concrete bounds for …
Facebook（脸书）；University of Maryland, College Park（马里兰大学学院市分校）；DeepMind（深度思维）
This paper studies how neural network architecture affects the speed of training. We introduce a simple concept called gradient confusion to help formally analyze this. When gradient confusion is high, stochastic gradients produced by different data samples may be negatively correlated, slowing down convergence. But when gradient confusion is low, data samples interact harmoniously, and training proceeds quickly. Through theoretical and experimental results, we demonstrate how the neural network architecture affects gradient confusion, and thus the efficiency of training. Our results show that…
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）
We introduce optimization methods for convolutional neural networks that can be used to improve existing gradient-based optimization in terms of generalization error. The method requires only simple processing of existing stochastic gradients, can be used in conjunction with any optimizer, and has only a linear overhead (in the number of parameters) compared to computation of the stochastic gradient. The method works by computing the gradient of the loss function with respect to output-channel directed re-weighted L2 or Sobolev metrics, which has the effect of smoothing components of the gradi…
In this paper, we propose a novel normalization method called gradient normalization (GN) to tackle the training instability of Generative Adversarial Networks (GANs) caused by the sharp gradient space. Unlike existing work such as gradient penalty and spectral normalization, the proposed GN only imposes a hard 1-Lipschitz constraint on the discriminator function, which increases the capacity of the discriminator. Moreover, the proposed gradient normalization can be applied to different GAN architectures with little modification. Extensive experiments on four datasets show that GANs trained wi…
Self-Evidencing Through Hierarchical Gradient Decomposition: A Dissipative System That Maintains Non-Equilibrium Steady-State by Minimizing Variational Free Energy
While much effort has been devoted to deriving and analyzing effective convex formulations of signal processing problems, the gradients of convex functions also have critical applications ranging from gradient-based optimization to optimal transport. Recent works have explored data-driven methods for learning convex objective functions, but learning their monotone gradients is seldom studied. In this work, we propose C-MGN and M-MGN, two monotone gradient neural network architectures for directly learning the gradients of convex functions. We show that, compared to state of the art methods, ou…
In recent years, state-of-the-art game-playing agents often involve policies that are trained in self-playing processes where Monte Carlo tree search (MCTS) algorithms and trained policies iteratively improve each other. The strongest results have been obtained when policies are trained to mimic the search behaviour of MCTS by minimising a cross-entropy loss. Because MCTS, by design, includes an element of exploration, policies trained in this manner are also likely to exhibit a similar extent of exploration. In this paper, we are interested in learning policies for a project with future goals…
TTI at Chicago（芝加哥丰田理工学院）；USC（南加利福尼亚大学）；Technion（以色列理工学院）
We show that gradient descent on full-width linear convolutional networks of depth $L$ converges to a linear predictor related to the $\ell_{2/L}$ bridge penalty in the frequency domain. This is in contrast to linearly fully connected networks, where gradient descent converges to the hard margin linear support vector machine solution, regardless of depth.
Rice University（莱斯大学）；Technical University of Munich（慕尼黑工业大学）
Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem arises in recent approaches for solving inverse problems such as the deep image prior or the deep decoder. We show that for this setup, channel normalization, which centers and normalizes each channel individually, avoids vanishing gradients, whereas, without normalization, gradients vanish which prevents efficient optimization. This effect prevails in deep singl…
Ultra-Strong Gradient Diffusion MRI with Self-Supervised Learning for Prostate Cancer Characterization
University College London（伦敦大学学院）；Cardiff University（卡迪夫大学）；Siemens Healthcare Ltd（西门子医疗有限公司）；Siemens Healthcare GmbH（西门子医疗股份公司）；University Medical Center Utrecht（乌得勒支大学医学中心）
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient in the forward and backward passes through the BN and residual branches, respectively, we show that they work together to confine the gradient variance to a certain range across residual blocks in backpropagation. As a result, the gradient vanishing/explosion problem is avoided. W…
Learn to Evolve: Self-supervised Neural JKO Operator for Wasserstein Gradient Flow
Department of Mathematics, University of California, Los Angeles, CA（加州大学洛杉矶分校数学系）；School of Mathematics, University of Minnesota, Minneapolis, MN（明尼苏达大学数学学院）；Purdue University（普渡大学）
Natural gradient descent (NGD) provided deep insights and powerful tools to deep neural networks. However the computation of Fisher information matrix becomes more and more difficult as the network structure turns large and complex. This paper proposes a new optimization method whose main idea is to accurately replace the natural gradient optimization by reconstructing the network. More specifically, we reconstruct the structure of the deep neural network, and optimize the new network using traditional gradient descent (GD). The reconstructed network achieves the effect of the optimization way…
McGill University（麦吉尔大学）；University of Toronto（多伦多大学）；Facebook AI Research（Facebook AI研究院）
The gradients of convex functions are expressive models of non-trivial vector fields. For example, Brenier's theorem yields that the optimal transport map between any two measures on Euclidean space under the squared distance is realized as a convex gradient, which is a key insight used in recent generative flow models. In this paper, we study how to model convex gradients by integrating a Jacobian-vector product parameterized by a neural network, which we call the Input Convex Gradient Network (ICGN). We theoretically study ICGNs and compare them to taking the gradient of an Input-Convex Neur…
It has been observed that design choices of neural networks are often crucial for their successful optimization. In this article, we therefore discuss the question if it is always possible to redesign a neural network so that it trains well with gradient descent. This yields the following universality result: If, for a given network, there is any algorithm that can find good network weights for a classification task, then there exists an extension of this network that reproduces these weights and the corresponding forward output by mere gradient descent training. The construction is not intend…
We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow ReLU networks with one-dimensional input, solving least-squares interpolation. We show that the gradient dynamics of such networks are determined by the gradient flow in a non-redundant parameterization of the network function. We examine the principal qualitative features of this gradient flow. In particular, we determine conditions for two learning regimes:kernel and adaptive, which depend both on the relative magnitude of initialization of weights in different layers and the asymptotic behavio…
We prove that a single step of gradient decent over depth two network, with $q$ hidden neurons, starting from orthogonal initialization, can memorize $Ω\left(\frac{dq}{\log^4(d)}\right)$ independent and randomly labeled Gaussians in $\mathbb{R}^d$. The result is valid for a large class of activation functions, which includes the absolute value.
We present RNNbow, an interactive tool for visualizing the gradient flow during backpropagation training in recurrent neural networks. RNNbow is a web application that displays the relative gradient contributions from Recurrent Neural Network (RNN) cells in a neighborhood of an element of a sequence. We describe the calculation of backpropagation through time (BPTT) that keeps track of itemized gradients, or gradient contributions from one element of a sequence to previous elements of a sequence. By visualizing the gradient, as opposed to activations, RNNbow offers insight into how the network…
