Overparameterized Neural Networks (NN) display state-of-the-art performance. However, there is a growing need for smaller, energy-efficient, neural networks tobe able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained NN (LeCun et al.,1990; Hassibi et al., 1993), recent work by Lee et al. (2018) has shown promising results when pruning at initialization. However, for Deep NNs, such procedures remain unsatisfactory as the resulting pruned networks can be difficult to train and, for instance, they do not prevent one layer from being fully pruned. In this paper, we provide a comprehensive theoretical analysis of Magnitude and Gradient based pruning at initialization and training of sparse architectures. This allows us to propose novel principled approaches which we validate experimentally on a variety of NN architectures.
University of Oxford（牛津大学）；Australian National University（澳大利亚国立大学）
Network pruning is a promising avenue for compressing deep neural networks. A typical approach to pruning starts by training a model and then removing redundant parameters while minimizing the impact on what is learned. Alternatively, a recent approach shows that pruning can be done at initialization prior to training, based on a saliency criterion called connection sensitivity. However, it remains unclear exactly why pruning an untrained, randomly initialized neural network is effective. In this work, by noting connection sensitivity as a form of gradient, we formally characterize initializat…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Element AI（Element AI公司）；University of Toronto（多伦多大学）；Vector Institute（矢量研究院）
Recent work has explored the possibility of pruning neural networks at initialization. We assess proposals for doing so: SNIP (Lee et al., 2019), GraSP (Wang et al., 2020), SynFlow (Tanaka et al., 2020), and magnitude pruning. Although these methods surpass the trivial baseline of random pruning, they remain below the accuracy of magnitude pruning after training, and we endeavor to understand why. We show that, unlike pruning after training, randomly shuffling the weights these methods prune within each layer or sampling new initial values preserves or improves accuracy. As such, the per-weigh…
Ritsumeikan University（立命馆大学）；Hitotsubashi University（一桥大学）；Nagoya University（名古屋大学）；Dalian University of Technology（大连理工大学）
One-shot Network Pruning at Initialization (OPaI) is an effective method to decrease network pruning costs. Recently, there is a growing belief that data is unnecessary in OPaI. However, we obtain an opposite conclusion by ablation experiments in two representative OPaI methods, SNIP and GraSP. Specifically, we find that informative data is crucial to enhancing pruning performance. In this paper, we propose two novel methods, Discriminative One-shot Network Pruning (DOP) and Super Stitching, to prune the network by high-level visual discriminative image patches. Our contributions are as follow…
Neural network pruning typically removes connections or neurons from a pretrained converged model; while a new pruning paradigm, pruning at initialization (PaI), attempts to prune a randomly initialized network. This paper offers the first survey concentrated on this emerging pruning fashion. We first introduce a generic formulation of neural network pruning, followed by the major classic pruning topics. Then, as the main body of this paper, a thorough and structured literature review of PaI methods is presented, consisting of two major tracks (sparse training and sparse selection). Finally, w…
Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven …
Pruning is a popular technique for reducing the model size and computational cost of convolutional neural networks (CNNs). However, a slow retraining or fine-tuning procedure is often required to recover the accuracy loss caused by pruning. Recently, a new research direction on weight pruning, pruning-at-initialization (PAI), is proposed to directly prune CNNs before training so that fine-tuning or retraining can be avoided. While PAI has shown promising results in reducing the model size, existing approaches rely on fine-grained weight pruning which requires unstructured sparse matrix computa…
Learning effective pruning at initialization from iterative pruning
State Key Laboratory of Robotics and Systems（机器人系统国家重点实验室）；Harbin Institute of Technology（哈尔滨工业大学）；Technical University of Munich（慕尼黑技术大学）；University of Liverpool（利物浦大学）
Australian National University（澳大利亚国立大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Data61, CSIRO（澳大利亚联邦科学与工业研究组织Data61）；Microsoft Research（微软研究院）
Although 3D Convolutional Neural Networks (CNNs) are essential for most learning based applications involving dense 3D data, their applicability is limited due to excessive memory and computational requirements. Compressing such networks by pruning therefore becomes highly desirable. However, pruning 3D CNNs is largely unexplored possibly because of the complex nature of typical pruning algorithms that embeds pruning into an iterative optimization paradigm. In this work, we introduce a Resource Aware Neuron Pruning (RANP) algorithm that prunes 3D CNNs at initialization to high sparsity levels.…
Australian National University（澳大利亚国立大学）；Australian Centre for Robotic Vision（澳大利亚机器人视觉中心）；Microsoft Research（微软研究院）；Data61, CSIRO（联邦科学与工业研究组织Data61）；Amazon（亚马逊）
Although 3D Convolutional Neural Networks are essential for most learning based applications involving dense 3D data, their applicability is limited due to excessive memory and computational requirements. Compressing such networks by pruning therefore becomes highly desirable. However, pruning 3D CNNs is largely unexplored possibly because of the complex nature of typical pruning algorithms that embeds pruning into an iterative optimization paradigm. In this work, we introduce a Resource Aware Neuron Pruning (RANP) algorithm that prunes 3D CNNs at initialization to high sparsity levels. Specif…
University of California, Berkeley（加利福尼亚大学伯克利分校）；Tsinghua University（清华大学）
Network pruning is widely used for reducing the heavy inference cost of deep models in low-resource settings. A typical pruning algorithm is a three-stage pipeline, i.e., training (a large model), pruning and fine-tuning. During pruning, according to a certain criterion, redundant weights are pruned and important weights are kept to best preserve the accuracy. In this work, we make several surprising observations which contradict common beliefs. For all state-of-the-art structured pruning algorithms we examined, fine-tuning a pruned model only gives comparable or worse performance than trainin…
Pruning enables appealing reductions in network memory footprint and time complexity. Conventional post-training pruning techniques lean towards efficient inference while overlooking the heavy computation for training. Recent exploration of pre-training pruning at initialization hints on training cost reduction via pruning, but suffers noticeable performance degradation. We attempt to combine the benefits of both directions and propose a policy that prunes as early as possible during training without hurting performance. Instead of pruning at initialization, our method exploits initial dense t…
Several recent works [40, 24] observed an interesting phenomenon in neural network pruning: A larger finetuning learning rate can improve the final performance significantly. Unfortunately, the reason behind it remains elusive up to date. This paper is meant to explain it through the lens of dynamical isometry [42]. Specifically, we examine neural network pruning from an unusual perspective: pruning as initialization for finetuning, and ask whether the inherited weights serve as a good initialization for the finetuning? The insights from dynamical isometry suggest a negative answer. Despite it…
Despite the popularization of deep neural networks (DNNs) in many fields, it is still challenging to deploy state-of-the-art models to resource-constrained devices due to high computational overhead. Model pruning provides a feasible solution to the aforementioned challenges. However, the interpretation of existing pruning criteria is always overlooked. To counter this issue, we propose a novel layer pruning method by exploring the Stochastic Re-initialization. Our SR-init method is inspired by the discovery that the accuracy drop due to stochastic re-initialization of layer parameters differs…
Robert Bosch GmbH（罗伯特·博世公司）；University of Freiburg（弗莱堡大学）；Institute for Autonomous Intelligent Systems（自主智能系统研究所）
Deep neural networks (DNNs) are usually over-parameterized to increase the likelihood of getting adequate initial weights by random initialization. Consequently, trained DNNs have many redundancies which can be pruned from the model to reduce complexity and improve the ability to generalize. Structural sparsity, as achieved by filter pruning, directly reduces the tensor sizes of weights and activations and is thus particularly effective for reducing complexity. We propose "Holistic Filter Pruning" (HFP), a novel approach for common DNN training that is easy to implement and enables to specify …
Finding Sparse Subnetworks in One Training Cycle via Progressive Magnitude-Based Pruning
King Abdullah University of Science and Technology（阿卜杜拉国王科技大学）；University of Jeddah（吉达大学）；King Fahd University of Petroleum and Minerals（法赫德国王石油矿产大学）；King Saud University（沙特国王大学）
In safety-critical but computationally resource-constrained applications, deep learning faces two key challenges: lack of robustness against adversarial attacks and large neural network size (often millions of parameters). While the research community has extensively explored the use of robust training and network pruning independently to address one of these challenges, only a few recent works have studied them jointly. However, these works inherit a heuristic pruning strategy that was developed for benign training, which performs poorly when integrated with robust training techniques, includ…
MIT EECS（麻省理工学院电气工程与计算机科学系）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）
Magnitude pruning is a common, effective technique to identify sparse subnetworks at little cost to accuracy. In this work, we ask whether a particular architecture's accuracy-sparsity tradeoff can be improved by combining pruning information across multiple runs of training. From a shared ResNet-20 initialization, we train several network copies (\emph{siblings}) to completion using different SGD data orders on CIFAR-10. While the siblings' pruning masks are naively not much more similar than chance, starting sibling training after a few epochs of shared pretraining significantly increases pr…
Pruning large neural networks while maintaining their performance is often desirable due to the reduced space and time complexity. In existing methods, pruning is done within an iterative optimization procedure with either heuristically designed pruning schedules or additional hyperparameters, undermining their utility. In this work, we present a new approach that prunes a given network once at initialization prior to training. To achieve this, we introduce a saliency criterion based on connection sensitivity that identifies structurally important connections in the network for the given task.…
When large scale training data is available, one can obtain compact and accurate networks to be deployed in resource-constrained environments effectively through quantization and pruning. However, training data are often protected due to privacy concerns and it is challenging to obtain compact networks without data. We study data-free quantization and pruning by transferring knowledge from trained large networks to compact networks. Auxiliary generators are simultaneously and adversarially trained with the targeted compact networks to generate synthetic inputs that maximize the discrepancy bet…
Beijing National Research Center for Information Science and Technology (BNRist)（北京信息科学与技术国家研究中心（BNRist））；School of Software, Tsinghua University（清华大学软件学院）；Department of Electronic Engineering, Tsinghua University（清华大学电子工程系）；Department of Automation, Tsinghua University（清华大学自动化系）；Institute for Brain and Cognitive Sciences, Tsinghua University（清华大学脑与认知科学研究院）；WMG Data Science, University of Warwick（华威大学制造工程学院数据科学系）；Kwai Seattle AI Lab, Kwai FeDA Lab, Kwai AI platform（快手西雅图人工智能实验室、快手联邦与分布式人工智能实验室、快手人工智能平台）
Deep Neural Network (DNN) is powerful but computationally expensive and memory intensive, thus impeding its practical usage on resource-constrained front-end devices. DNN pruning is an approach for deep model compression, which aims at eliminating some parameters with tolerable performance degradation. In this paper, we propose a novel momentum-SGD-based optimization method to reduce the network complexity by on-the-fly pruning. Concretely, given a global compression ratio, we categorize all the parameters into two parts at each training iteration which are updated using different rules. In th…
Eindhoven University of Technology（埃因霍温理工大学）；University of Texas at Austin（得克萨斯大学奥斯汀分校）；University of Twente（特文特大学）；University of Leeds（利兹大学）；JD Explore Academy（京东探索研究院）；University of Jyväskylä（于韦斯屈莱大学）
Works on lottery ticket hypothesis (LTH) and single-shot network pruning (SNIP) have raised a lot of attention currently on post-training pruning (iterative magnitude pruning), and before-training pruning (pruning at initialization). The former method suffers from an extremely large computation cost and the latter usually struggles with insufficient performance. In comparison, during-training pruning, a class of pruning methods that simultaneously enjoys the training/inference efficiency and the comparable performance, temporarily, has been less explored. To better understand during-training p…
Chengdu Union Big Data Technology Co. Ltd.（成都联合大数据科技有限公司）；University of Electronic Science and Technology of China（电子科技大学）
Channel pruning is a promising technique to compress the parameters of deep convolutional neural networks(DCNN) and to speed up the inference. This paper aims to address the long-standing inefficiency of channel pruning. Most channel pruning methods recover the prediction accuracy by re-training the pruned model from the remaining parameters or random initialization. This re-training process is heavily dependent on the sufficiency of computational resources, training data, and human interference(tuning the training strategy). In this paper, a highly efficient pruning method is proposed to sign…
One-Cycle Structured Pruning via Stability-Driven Subnetwork Search
IT Application Research Center, Korea Electronics Technology Institute（韩国电子技术研究所应用信息技术中心）；Department of Intelligent Semiconductors, Soongsil University（顺慈大学智能半导体系）；Department of Computer Science & Engineering, Seoul National University（首尔国立大学计算机科学与工程系）
State-of-the-art neural networks are getting deeper and wider. While their performance increases with the increasing number of layers and neurons, it is crucial to design an efficient deep architecture in order to reduce computational and memory costs. Designing an efficient neural network, however, is labor intensive requiring many experiments, and fine-tunings. In this paper, we introduce network trimming which iteratively optimizes the network by pruning unimportant neurons based on analysis of their outputs on a large dataset. Our algorithm is inspired by an observation that the outputs of…
Unsupervised neural nets such as Restricted Boltzmann Machines(RBMs) and Deep Belif Networks(DBNs), are powerful in automatic feature extraction,unsupervised weight initialization and density estimation. In this paper,we demonstrate that the parameters of these neural nets can be dramatically reduced without affecting their performance. We describe a method to reduce the parameters required by RBM which is the basic building block for deep architectures. Further we propose an unsupervised sparse deep architectures selection algorithm to form sparse deep neural networks.Experimental results sho…
Adversarial pruning compresses models while preserving robustness. Current methods require access to adversarial examples during pruning. This significantly hampers training efficiency. Moreover, as new adversarial attacks and training methods develop at a rapid rate, adversarial pruning methods need to be modified accordingly to keep up. In this work, we propose a novel framework to prune a previously trained robust neural network while maintaining adversarial robustness, without further generating adversarial examples. We leverage concurrent self-distillation and pruning to preserve knowledg…
Multimodal-Guided Dynamic Dataset Pruning for Robust and Efficient Data-Centric Learning
National Key Laboratory for Novel Software Technology, Nanjing University（新型软件技术国家重点实验室，南京大学）；Shanghai Artificial Intelligence Laboratory（上海人工智能实验室）；The Chinese University of Hong Kong（香港中文大学）
Network pruning in Convolutional Neural Networks (CNNs) has been extensively investigated in recent years. To determine the impact of pruning a group of filters on a network's accuracy, state-of-the-art pruning methods consistently assume filters of a CNN are independent. This allows the importance of a group of filters to be estimated as the sum of importances of individual filters. However, overparameterization in modern networks results in highly correlated filters that invalidate this assumption, thereby resulting in incorrect importance estimates. To address this issue, we propose OrthoRe…
Peking University（北京大学）；National Engineering Research Center of Visual Technology（视觉技术国家工程研究中心）；Peng Cheng Laboratory（鹏城实验室）
Soft threshold pruning is among the cutting-edge pruning methods with state-of-the-art performance. However, previous methods either perform aimless searching on the threshold scheduler or simply set the threshold trainable, lacking theoretical explanation from a unified perspective. In this work, we reformulate soft threshold pruning as an implicit optimization problem solved using the Iterative Shrinkage-Thresholding Algorithm (ISTA), a classic method from the fields of sparse recovery and compressed sensing. Under this theoretical framework, all threshold tuning strategies proposed in previ…
Channel pruning is one of the major compression approaches for deep neural networks. While previous pruning methods have mostly focused on identifying unimportant channels, channel pruning is considered as a special case of neural architecture search in recent years. However, existing methods are either complicated or prone to sub-optimal pruning. In this paper, we propose a pruning framework that adaptively determines the number of each layer's channels as well as the wights inheritance criteria for sub-network. Firstly, evaluate the importance of each block in the network based on the mean o…
Factorized layers--operations parameterized by products of two or more matrices--occur in a variety of deep learning contexts, including compressed model training, certain types of knowledge distillation, and multi-head self-attention architectures. We study how to initialize and regularize deep nets containing such layers, examining two simple, understudied schemes, spectral initialization and Frobenius decay, for improving their performance. The guiding insight is to design optimization routines for these networks that are as close as possible to that of their well-tuned, non-decomposed coun…
Institute of Information Engineering, Chinese Academy of Sciences（中国科学院信息工程研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Tencent Inc.（腾讯公司）；The Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）；Sun Yat-sen University（中山大学）
Adversarial training (AT) has been demonstrated to be effective in improving model robustness by leveraging adversarial examples for training. However, most AT methods are in face of expensive time and computational cost for calculating gradients at multiple steps in generating adversarial examples. To boost training efficiency, fast gradient sign method (FGSM) is adopted in fast AT methods by calculating gradient only once. Unfortunately, the robustness is far from satisfactory. One reason may arise from the initialization fashion. Existing fast AT generally uses a random sample-agnostic init…
This paper presents a dynamic network rewiring (DNR) method to generate pruned deep neural network (DNN) models that are robust against adversarial attacks yet maintain high accuracy on clean images. In particular, the disclosed DNR method is based on a unified constrained optimization formulation using a hybrid loss function that merges ultra-high model compression with robust adversarial training. This training strategy dynamically adjusts inter-layer connectivity based on per-layer normalized momentum computed from the hybrid loss function. In contrast to existing robust pruning frameworks …
Hefei University of Technology（合肥工业大学）；Engineering Research Center of Safety Critical Industrial Measurement and Control Technology, Ministry of Education（教育部安全关键工业测控技术工程研究中心）
As the convolutional neural network (CNN) gets deeper and wider in recent years, the requirements for the amount of data and hardware resources have gradually increased. Meanwhile, CNN also reveals salient redundancy in several tasks. The existing magnitude-based pruning methods are efficient, but the performance of the compressed network is unpredictable. While the accuracy loss after pruning based on the structure sensitivity is relatively slight, the process is time-consuming and the algorithm complexity is notable. In this article, we propose a novel automatic channel pruning method (ACP).…
Simon Fraser University（西蒙弗雷泽大学）；Adobe Research（Adobe 研究院）
Many monocular visual SLAM algorithms are derived from incremental structure-from-motion (SfM) methods. This work proposes a novel monocular SLAM method which integrates recent advances made in global SfM. In particular, we present two main contributions to visual SLAM. First, we solve the visual odometry problem by a novel rank-1 matrix factorization technique which is more robust to the errors in map initialization. Second, we adopt a recent global SfM method for the pose-graph optimization, which leads to a multi-stage linear formulation and enables L1 optimization for better robustness to …
Duke University（杜克大学）；Shanghai International Studies University（上海外国语大学）；KAUST（阿卜杜拉国王科技大学）
Weight pruning is among the most popular approaches for compressing deep convolutional neural networks. Recent work suggests that in a randomly initialized deep neural network, there exist sparse subnetworks that achieve performance comparable to the original network. Unfortunately, finding these subnetworks involves iterative stages of training and pruning, which can be computationally expensive. We propose Structured Sparse Convolution (SSC), which leverages the inherent structure in images to reduce the parameters in the convolutional filter. This leads to improved efficiency of convolution…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；University of Cambridge（剑桥大学）；Element AI；University of Toronto（多伦多大学）；Vector Institute
Pruning is a well-established technique for removing unnecessary structure from neural networks after training to improve the performance of inference. Several recent results have explored the possibility of pruning at initialization time to provide similar benefits during training. In particular, the "lottery ticket hypothesis" conjectures that typical neural networks contain small subnetworks that can train to similar accuracy in a commensurate number of steps. The evidence for this claim is that a procedure based on iterative magnitude pruning (IMP) reliably finds such subnetworks retroacti…
Deep neural networks have achieved impressive performance in many applications but their large number of parameters lead to significant computational and storage overheads. Several recent works attempt to mitigate these overheads by designing compact networks using pruning of connections. However, we observe that most of the existing strategies to design compact networks fail to preserve network robustness against adversarial examples. In this work, we rigorously study the extension of network pruning strategies to preserve both benign accuracy and robustness of a network. Starting with a form…
University of California, Riverside（加州大学河滨分校）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
Model pruning is an essential procedure for building compact and computationally-efficient machine learning models. A key feature of a good pruning algorithm is that it accurately quantifies the relative importance of the model weights. While model pruning has a rich history, we still don't have a full grasp of the pruning mechanics even for relatively simple problems involving linear models or shallow neural nets. In this work, we provide a principled exploration of pruning by building on a natural notion of importance. For linear models, we show that this notion of importance is captured by …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Overparameterization has been shown to benefit both the optimization and generalization of neural networks, but large networks are resource hungry at both training and test time. Network pruning can reduce test-time resource requirements, but is typically applied to trained networks and therefore cannot avoid the expensive training process. We aim to prune networks at initialization, thereby saving resources at training time as well. Specifically, we argue that efficient training requires preserving the gradient flow through the network. This leads to a simple but effective pruning criterion w…
