Learning Low-rank Deep Neural Networks via Singular Vector Orthogonality Regularization and Singular Value Sparsification
Duke University（杜克大学）；Tsinghua University（清华大学）；University of Nevada, Reno（内华达大学里诺分校）；Newport High School（纽波特高中）
Huanrui Yang, Minxue Tang, Wei Wen, Feng Yan, Daniel Hu, Ang Li, Hai Li, Yiran Chen
备注：
In proceeding of 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW). To be presented at EDLCV 2020 workshop co-located with CVPR 2020
Modern deep neural networks (DNNs) often require high memory consumption and large computational loads. In order to deploy DNN algorithms efficiently on edge or mobile devices, a series of DNN compression algorithms have been explored, including factorization methods. Factorization methods approximate the weight matrix of a DNN layer with the multiplication of two or multiple low-rank matrices. However, it is hard to measure the ranks of DNN layers during the training process. Previous works mainly induce low-rank through implicit approximations or via costly singular value decomposition (SVD) process on every training step. The former approach usually induces a high accuracy loss while the latter has a low efficiency. In this work, we propose SVD training, the first method to explicitly achieve low-rank DNNs during training without applying SVD on every step. SVD training first decomposes each layer into the form of its full-rank SVD, then performs training directly on the decomposed weights. We add orthogonality regularization to the singular vectors, which ensure the valid form of SVD and avoid gradient vanishing/exploding. Low-rank is encouraged by applying sparsity-inducing regularizers on the singular values of each layer. Singular value pruning is applied at the end to explicitly reach a low-rank model. We empirically show that SVD training can significantly reduce the rank of DNN layers and achieve higher reduction on computation load under the same accuracy, comparing to not only previous factorization methods but also state-of-the-art filter pruning methods.
We propose a hierarchical learning strategy aimed at generating sparse representations and associated models for large noisy datasets. The hierarchy follows from approximation spaces identified at successively finer scales. For promoting model generalization at each scale, we also introduce a novel, projection based penalty operator across multiple dimension, using permutation operators for incorporating proximity and ordering information. The paper presents a detailed analysis of approximation properties in the reconstruction Reproducing Kernel Hilbert Spaces (RKHS) with emphasis on optimalit…
This paper seeks to answer the question: as the (near-) orthogonality of weights is found to be a favorable property for training deep convolutional neural networks, how can we enforce it in more effective and easy-to-use ways? We develop novel orthogonality regularizations on training deep CNNs, utilizing various advanced analytical tools such as mutual coherence and restricted isometry property. These plug-and-play regularizations can be conveniently incorporated into training almost any CNN without extra hassle. We then benchmark their effects on state-of-the-art models: ResNet, WideResNet,…
Among the most successful methods for sparsifying deep (neural) networks are those that adaptively mask the network weights throughout training. By examining this masking, or dropout, in the linear case, we uncover a duality between such adaptive methods and regularization through the so-called "$η$-trick" that casts both as iteratively reweighted optimizations. We show that any dropout strategy that adapts to the weights in a monotonic way corresponds to an effective subquadratic regularization penalty, and therefore leads to sparse solutions. We obtain the effective penalties for several pop…
Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；School of Artificial Intelligence, University of Chinese Academy of Sciences（中国科学院大学人工智能学院）
User-level differential privacy (DP) provides certifiable privacy guarantees to the information that is specific to any user's data in federated learning. Existing methods that ensure user-level DP come at the cost of severe accuracy decrease. In this paper, we study the cause of model performance degradation in federated learning under user-level DP guarantee. We find the key to solving this issue is to naturally restrict the norm of local updates before executing operations that guarantee DP. To this end, we propose two techniques, Bounded Local Update Regularization and Local Update Sparsif…
Likelihood-guided Regularization in Attention Based Models
Department of Statistics, Virginia Polytechnic Institute and State University（统计学系，弗吉尼亚理工大学和州立大学）；Department of Statistics, Virginia Tech.（统计学系，弗吉尼亚理工大学）
Qualcomm AI Research, Qualcomm Korea YH（高通人工智能研究院，高通韩国YH）
Multi-head attention mechanism is capable of learning various representations from sequential data while paying attention to different subsequences, e.g., word-pieces or syllables in a spoken word. From the subsequences, it retrieves richer information than a single-head attention which only summarizes the whole sequence into one context vector. However, a naive use of the multi-head attention does not guarantee such richness as the attention heads may have positional and representational redundancy. In this paper, we propose a regularization technique for multi-head attention mechanism in an …
TTI-Chicago（芝加哥丰田技术研究院）；University of Alberta（阿尔伯塔大学）；University of Chicago（芝加哥大学）
The search for efficient, sparse deep neural network models is most prominently performed by pruning: training a dense, overparameterized network and removing parameters, usually via following a manually-crafted heuristic. Additionally, the recent Lottery Ticket Hypothesis conjectures that, for a typically-sized neural network, it is possible to find small sub-networks which, when trained from scratch on a comparable budget, match the performance of the original dense counterpart. We revisit fundamental aspects of pruning algorithms, pointing out missing ingredients in previous approaches, and…
Max Planck Institute For Informatics（马克斯·普朗克信息学研究所）；Saarland Informatics Campus（萨尔兰信息学园区）；Ulsan National Institute of Science and Technology（蔚山科学技术院）
We show implicit filter level sparsity manifests in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. Through an extensive empirical study (Mehta et al., 2019) we hypothesize the mechanism behind the sparsification process, and find surprising links to certain filter sparsification heuristics proposed in literature. Emergence of, and the subsequent pruning of selective features is observed to be one of the contributing mechanisms, leading to feature sparsity…
Regularization techniques are widely used to improve the generality, robustness, and efficiency of deep convolutional neural networks (DCNNs). In this paper, we propose a novel approach of regulating DCNN convolutional kernels by a structured filter bank. Comparing with the existing regularization methods, such as $\ell_1$ or $\ell_2$ minimization of DCNN kernel weights and the kernel orthogonality, which ignore sample correlations within a kernel, the use of filter bank in regularization of DCNNs can mold the DCNN kernels to common spatial structures and features (e.g., edges or textures of v…
$\boldsymbolλ$-Orthogonality Regularization for Compatible Representation Learning
DINFO (Department of Information Engineering), University of Florence, Italy（意大利佛罗伦萨大学信息工程系）；MICC (Media Integration and Communication Center)（媒体整合与通信中心）；Queen Mary University of London, UK（英国伦敦女王学院）
Training deep neural networks with an $L_0$ regularization is one of the prominent approaches for network pruning or sparsification. The method prunes the network during training by encouraging weights to become exactly zero. However, recent work of Gale et al. reveals that although this method yields high compression rates on smaller datasets, it performs inconsistently on large-scale learning tasks, such as ResNet50 on ImageNet. We analyze this phenomenon through the lens of variational inference and find that it is likely due to the independent modeling of binary gates, the mean-field appro…
University of Illinois Chicago（伊利诺伊大学芝加哥分校）；Amazon Web Services（亚马逊云科技）；Carnegie Mellon University（卡内基梅隆大学）
Graph Neural Networks (GNNs) are currently dominating in modeling graph-structure data, while their high reliance on graph structure for inference significantly impedes them from widespread applications. By contrast, Graph-regularized MLPs (GR-MLPs) implicitly inject the graph structure information into model weights, while their performance can hardly match that of GNNs in most tasks. This motivates us to study the causes of the limited performance of GR-MLPs. In this paper, we first demonstrate that node embeddings learned from conventional GR-MLPs suffer from dimensional collapse, a phenome…
Graph Neural Networks (GNNs) have attracted increasing attention due to its successful applications on various graph-structure data. However, recent studies have shown that adversarial attacks are threatening the functionality of GNNs. Although numerous works have been proposed to defend adversarial attacks from various perspectives, most of them can be robust against the attacks only on specific scenarios. To address this shortage of robust generalization, we propose to defend the adversarial attacks on GNN through applying the Spatio-Temporal sparsification (called ST-Sparse) on the GNN hidd…
Duke University（杜克大学）；Black Sesame Technologies（黑芝麻科技）
With the rapid scaling up of deep neural networks (DNNs), extensive research studies on network model compression such as weight pruning have been performed for improving deployment efficiency. This work aims to advance the compression beyond the weights to neuron activations. We propose the joint regularization technique which simultaneously regulates the distribution of weights and activations. By distinguishing and leveraging the significance difference among neuron responses and connections during learning, the jointly pruned network, namely \textit{JPnet}, optimizes the sparsity of activa…
Pennsylvania State University（宾夕法尼亚州立大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
Compressed Sensing using $\ell_1$ regularization is among the most powerful and popular sparsification technique in many applications, but why has it not been used to obtain sparse deep learning model such as convolutional neural network (CNN)? This paper is aimed to provide an answer to this question and to show how to make it work. We first demonstrate that the commonly used stochastic gradient decent (SGD) and variants training algorithm is not an appropriate match with $\ell_1$ regularization and then replace it with a different training algorithm based on a regularized dual averaging (RDA…
We apply concepts from manifold regularization to develop new regularization techniques for training locally stable deep neural networks. Our regularizers are based on a sparsification of the graph Laplacian which holds with high probability when the data is sparse in high dimensions, as is common in deep learning. Empirically, our networks exhibit stability in a diverse set of perturbation models, including $\ell_2$, $\ell_\infty$, and Wasserstein-based perturbations; in particular, we achieve 40% adversarial accuracy on CIFAR-10 against an adaptive PGD attack using $\ell_\infty$ perturbation…
This paper is concerned with the sparsification of the input-hidden weights of ELM (Extreme Learning Machine). For ordinary feedforward neural networks, the sparsification is usually done by introducing certain regularization technique into the learning process of the network. But this strategy can not be applied for ELM, since the input-hidden weights of ELM are supposed to be randomly chosen rather than to be learned. To this end, we propose a modified ELM, called ELM-LC (ELM with local connections), which is designed for the sparsification of the input-hidden weights as follows: The hidden …
Standard deep learning models that employ the categorical cross-entropy loss are known to perform well at image classification tasks. However, many standard models thus obtained often exhibit issues like feature redundancy, low interpretability, and poor calibration. A body of recent work has emerged that has tried addressing some of these challenges by proposing the use of new regularization functions in addition to the cross-entropy loss. In this paper, we present some surprising findings that emerge from exploring the role of simple orthogonality constraints as a means of imposing physics-m…
We propose a method for efficiently incorporating constraints into a stochastic gradient Langevin framework for the training of deep neural networks. Constraints allow direct control of the parameter space of the model. Appropriately designed, they reduce the vanishing/exploding gradient problem, control weight magnitudes and stabilize deep neural networks and thus improve the robustness of training algorithms and the generalization capabilities of the trained neural network. We present examples of constrained training methods motivated by orthogonality preservation for weight matrices and exp…
MSQ: Memory-Efficient Bit Sparsification Quantization
Department of Electrical and Computer Engineering, Sungkyunkwan University（全州大学电子与计算机工程系）；Department of Electrical and Computer Engineering, University of Arizona（亚利桑那大学电子与计算机工程系）
University of California, Berkeley（加州大学伯克利分校）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Tel-Aviv University（特拉维夫大学）；École Polytechnique Fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The Hong Kong University of Science and Technology（香港科技大学）
In this paper, the estimation problem for sparse reduced rank regression (SRRR) model is considered. The SRRR model is widely used for dimension reduction and variable selection with applications in signal processing, econometrics, etc. The problem is formulated to minimize the least squares loss with a sparsity-inducing penalty considering an orthogonality constraint. Convex sparsity-inducing functions have been used for SRRR in literature. In this work, a nonconvex function is proposed for better sparsity inducing. An efficient algorithm is developed based on the alternating minimization (or…
To put a state-of-the-art neural network to practical use, it is necessary to design a model that has a good trade-off between the resource consumption and performance on the test set. Many researchers and engineers are developing methods that enable training or designing a model more efficiently. Developing an efficient model includes several strategies such as network architecture search, pruning, quantization, knowledge distillation, utilizing cheap convolution, regularization, and also includes any craft that leads to a better performance-resource trade-off. When combining these technologi…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Technion - Israel Institute of Technology（以色列理工学院）
We study the implicit bias of ReLU neural networks trained by a variant of SGD where at each step, the label is changed with probability $p$ to a random label (label smoothing being a close variant of this procedure). Our experiments demonstrate that label noise propels the network to a sparse solution in the following sense: for a typical input, a small fraction of neurons are active, and the firing pattern of the hidden layers is sparser. In fact, for some instances, an appropriate amount of label noise does not only sparsify the network but further reduces the test error. We then turn to th…
FasterAI is a PyTorch-based library, aiming to facilitate the utilization of deep neural networks compression techniques such as sparsification, pruning, knowledge distillation, or regularization. The library is built with the purpose of enabling quick implementation and experimentation. More particularly, compression techniques are leveraging Callback systems of libraries such as fastai and Pytorch Lightning to bring a user-friendly and high-level API. The main asset of FasterAI is its lightweight, yet powerful, simplicity of use. Indeed, because it was developed in a very granular way, users…
GRIP2: A Robust and Powerful Deep Knockoff Method for Feature Selection
Institute for Computational and Mathematical Engineering, Stanford University, Stanford, California, USA（计算与数学工程研究所，斯坦福大学）；Department of Biomedical Data Science, Stanford University, Stanford, California, USA（生物医学数据科学系，斯坦福大学）
Incheon National University（仁川大学）；Dain Technology, Inc.
Modern convolutional neural networks (CNNs) have massive identical convolution blocks, and, hence, recursive sharing of parameters across these blocks has been proposed to reduce the amount of parameters. However, naive sharing of parameters poses many challenges such as limited representational power and the vanishing/exploding gradients problem of recursively shared parameters. In this paper, we present a recursive convolution block design and training method, in which a recursively shareable part, or a filter basis, is separated and learned while effectively avoiding the vanishing/exploding…
The de-facto standard approach of promoting sparsity by means of $\ell_1$-regularization becomes ineffective in the presence of simplex constraints, i.e.,~the target is known to have non-negative entries summing up to a given constant. The situation is analogous for the use of nuclear norm regularization for low-rank recovery of Hermitian positive semidefinite matrices with given trace. In the present paper, we discuss several strategies to deal with this situation, from simple to more complex. As a starting point, we consider empirical risk minimization (ERM). It follows from existing theory …
Synaptic Pruning: A Biological Inspiration for Deep Learning Regularization
College of Science and Engineering, James Cook University（詹姆斯库克大学科学与工程学院）；College of Health Care Sciences, James Cook University（詹姆斯库克大学健康护理科学学院）；College of Public Health, Medical, and Vet Sciences, James Cook University（詹姆斯库克大学公共卫生、医学与兽医学科学学院）
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）
Catastrophic overfitting is a phenomenon observed during Adversarial Training (AT) with the Fast Gradient Sign Method (FGSM) where the test robustness steeply declines over just one epoch in the training stage. Prior work has attributed this loss in robustness to a sharp decrease in $\textit{local linearity}$ of the neural network with respect to the input space, and has demonstrated that introducing a local linearity measure as a regularization term prevents catastrophic overfitting. Using a simple neural network architecture, we experimentally demonstrate that maintaining high local linearit…
Parameter-Efficient Fine-Tuning for Continual Learning: A Neural Tangent Kernel Perspective
School of Electrical and Information Engineering, Tianjin Key Laboratory of Brain-Inspired Intelligence Technology, Tianjin University（电子信息工程学院，天津脑启发智能技术重点实验室，天津大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；College of Information Science and Electronic Engineering, Zhejiang University（信息科学与电子工程学院，浙江大学）；Department of Computer Science, the University of Sheffield（计算机科学系，谢菲尔德大学）；Institute of Artificial Intelligence (TeleAI) of China Telecom（中国电信人工智能研究院（TeleAI））
MPI For Informatics（马克斯·普朗克信息学研究所）；UNIST（蔚山科学技术院）；Saarland Informatics Campus（萨尔兰信息学园区）
We investigate filter level sparsity that emerges in convolutional neural networks (CNNs) which employ Batch Normalization and ReLU activation, and are trained with adaptive gradient descent techniques and L2 regularization or weight decay. We conduct an extensive experimental study casting our initial findings into hypotheses and conclusions about the mechanisms underlying the emergent filter level sparsity. This study allows new insight into the performance gap obeserved between adapative and non-adaptive gradient descent methods in practice. Further, analysis of the effect of training strat…
We employ constraints to control the parameter space of deep neural networks throughout training. The use of customized, appropriately designed constraints can reduce the vanishing/exploding gradients problem, improve smoothness of classification boundaries, control weight magnitudes and stabilize deep neural networks, and thus enhance the robustness of training algorithms and the generalization capabilities of neural networks. We provide a general approach to efficiently incorporate constraints into a stochastic gradient Langevin framework, allowing enhanced exploration of the loss landscape.…
Feature Map Similarity Reduction in Convolutional Neural Networks
Cranfield University（克兰菲尔德大学）；Centre for Computational Engineering Sciences（计算工程科学中心）；Inria（法国国家信息与自动化技术研究院）；Univ. Bordeaux（波尔多大学）；ESTIA-Institute of Technology（ESTIA技术研究所）
TCS Research and Innovation（TCS研究与创新中心）；University of Applied Sciences（应用科学大学）；University of Murcia（穆尔西亚大学）；Tata Consultancy Services（塔塔咨询服务公司）；Western Switzerland (HES-SO)（瑞士西部高等专业学院）
Deep Neural Networks (DNN) have been successfully used to perform classification and regression tasks, particularly in computer vision based applications. Recently, owing to the widespread deployment of Internet of Things (IoT), we identify that the classification tasks for time series data, specifically from different sensors are of utmost importance. In this paper, we present SRDCNN: Strongly Regularized Deep Convolution Neural Network (DCNN) based deep architecture to perform time series classification tasks. The novelty of the proposed approach is that the network weights are regularized b…
