Global Sparse Momentum SGD for Pruning Very Deep Neural Networks
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）
Xiaohan Ding, Guiguang Ding, Xiangxin Zhou, Yuchen Guo, Jungong Han, Ji Liu
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 this way, we gradually zero out the redundant parameters, as we update them using only the ordinary weight decay but no gradients derived from the objective function. As a departure from prior methods that require heavy human works to tune the layer-wise sparsity ratios, prune by solving complicated non-differentiable problems or finetune the model after pruning, our method is characterized by 1) global compression that automatically finds the appropriate per-layer sparsity ratios; 2) end-to-end training; 3) no need for a time-consuming re-training process after pruning; and 4) superior capability to find better winning tickets which have won the initialization lottery.
The redundancy is widely recognized in Convolutional Neural Networks (CNNs), which enables to remove unimportant filters from convolutional layers so as to slim the network with acceptable performance drop. Inspired by the linear and combinational properties of convolution, we seek to make some filters increasingly close and eventually identical for network slimming. To this end, we propose Centripetal SGD (C-SGD), a novel optimization method, which can train several filters to collapse into a single point in the parameter hyperspace. When the training is completed, the removal of the identica…
University of Missouri（密苏里大学）；Purdue University（普渡大学）
In the light of the fact that the stochastic gradient descent (SGD) often finds a flat minimum valley in the training loss, we propose a novel directional pruning method which searches for a sparse minimizer in or close to that flat region. The proposed pruning method does not require retraining or the expert knowledge on the sparsity level. To overcome the computational formidability of estimating the flat directions, we propose to use a carefully tuned $\ell_1$ proximal gradient algorithm which can provably achieve the directional pruning with a small learning rate after sufficient training.…
The existence of redundancy in Convolutional Neural Networks (CNNs) enables us to remove some filters/channels with acceptable performance drops. However, the training objective of CNNs usually tends to minimize an accuracy-related loss function without any attention paid to the redundancy, making the redundancy distribute randomly on all the filters, such that removing any of them may trigger information loss and accuracy drop, necessitating a following finetuning step for recovery. In this paper, we propose to manipulate the redundancy during training to facilitate network pruning. To this e…
Boğaziçi University（海峡大学）；Télécom Paris（巴黎电信学院）；Institut Polytechnique de Paris（巴黎理工学院）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；INRIA（法国国家信息与自动化研究所）；École Normale Supérieure（巴黎高等师范学院）；PSL Research University（巴黎文理研究大学）
Neural network compression techniques have become increasingly popular as they can drastically reduce the storage and computation requirements for very large networks. Recent empirical studies have illustrated that even simple pruning strategies can be surprisingly effective, and several theoretical studies have shown that compressible networks (in specific senses) should achieve a low generalization error. Yet, a theoretical characterization of the underlying cause that makes the networks amenable to such simple compression schemes is still missing. In this study, we address this fundamental …
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…
Idiap Research Institute（IDIAP研究所）；EPFL（洛桑联邦理工学院）；Qualcomm AI Research（高通人工智能研究院）
Current methods for pruning neural network weights iteratively apply magnitude-based pruning on the model weights and re-train the resulting model to recover lost accuracy. In this work, we show that such strategies do not allow for the recovery of erroneously pruned weights. To enable weight recovery, we propose a simple strategy called \textit{cyclical pruning} which requires the pruning schedule to be periodic and allows for weights pruned erroneously in one cycle to recover in subsequent ones. Experimental results on both linear models and large-scale deep neural networks show that cyclica…
Beihang University（北京航空航天大学）；The University of Tokyo（东京大学）；RIKEN Center for AIP（理化学研究所人工智能研究中心）
People usually believe that network pruning not only reduces the computational cost of deep networks, but also prevents overfitting by decreasing model capacity. However, our work surprisingly discovers that network pruning sometimes even aggravates overfitting. We report an unexpected sparse double descent phenomenon that, as we increase model sparsity via network pruning, test performance first gets worse (due to overfitting), then gets better (due to relieved overfitting), and gets worse at last (due to forgetting useful information). While recent studies focused on the deep double descent …
This paper describes a channel-selection approach for simplifying deep neural networks. Specifically, we propose a new type of generic network layer, called pruning layer, to seamlessly augment a given pre-trained model for compression. Each pruning layer, comprising $1 \times 1$ depth-wise kernels, is represented with a dual format: one is real-valued and the other is binary. The former enables a two-phase optimization process of network pruning to operate with an end-to-end differentiable network, and the latter yields the mask information for channel selection. Our method progressively perf…
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…
Robert Bosch GmbH（罗伯特·博世有限公司）；University of Lübeck（吕贝克大学）
Unstructured pruning is well suited to reduce the memory footprint of convolutional neural networks (CNNs), both at training and inference time. CNNs contain parameters arranged in $K \times K$ filters. Standard unstructured pruning (SP) reduces the memory footprint of CNNs by setting filter elements to zero, thereby specifying a fixed subspace that constrains the filter. Especially if pruning is applied before or during training, this induces a strong bias. To overcome this, we introduce interspace pruning (IP), a general tool to improve existing pruning methods. It uses filters represented i…
Since the convolutional neural networks are often trained with redundant parameters, it is possible to reduce redundant kernels or filters to obtain a compact network without dropping the classification accuracy. In this paper, we propose a filter pruning method using the hierarchical group sparse regularization. It is shown in our previous work that the hierarchical group sparse regularization is effective in obtaining sparse networks in which filters connected to unnecessary channels are automatically close to zero. After training the convolutional neural network with the hierarchical group …
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…
Georgia Institute of Technology（佐治亚理工学院）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Reducing communication in training large-scale machine learning applications on distributed platform is still a big challenge. To address this issue, we propose a distributed hierarchical averaging stochastic gradient descent (Hier-AVG) algorithm with infrequent global reduction by introducing local reduction. As a general type of parallel SGD, Hier-AVG can reproduce several popular synchronous parallel SGD variants by adjusting its parameters. We show that Hier-AVG with infrequent global reduction can still achieve standard convergence rate for non-convex optimization problems. In addition, w…
Harvard University（哈佛大学）；Microsoft Research（微软研究院）；University of Pennsylvania（宾夕法尼亚大学）；Hebrew University of Jerusalem（希伯来大学）
There is mounting evidence of emergent phenomena in the capabilities of deep learning methods as we scale up datasets, model sizes, and training times. While there are some accounts of how these resources modulate statistical capacity, far less is known about their effect on the computational problem of model training. This work conducts such an exploration through the lens of learning a $k$-sparse parity of $n$ bits, a canonical discrete search problem which is statistically easy but computationally hard. Empirically, we find that a variety of neural networks successfully learn sparse paritie…
University of Texas at Austin（德克萨斯大学奥斯汀分校）；Carnegie Mellon University（卡内基梅隆大学）
Sparse shrunk additive models and sparse random feature models have been developed separately as methods to learn low-order functions, where there are few interactions between variables, but neither offers computational efficiency. On the other hand, $\ell_2$-based shrunk additive models are efficient but do not offer feature selection as the resulting coefficient vectors are dense. Inspired by the success of the iterative magnitude pruning technique in finding lottery tickets of neural networks, we propose a new method -- Sparser Random Feature Models via IMP (ShRIMP) -- to efficiently fit hi…
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）
Deep convolutional neural networks (CNNs) are deployed in various applications but demand immense computational requirements. Pruning techniques and Winograd convolution are two typical methods to reduce the CNN computation. However, they cannot be directly combined because Winograd transformation fills in the sparsity resulting from pruning. Li et al. (2017) propose sparse Winograd convolution in which weights are directly pruned in the Winograd domain, but this technique is not very practical because Winograd-domain retraining requires low learning rates and hence significantly longer traini…
Beihang University（北京航空航天大学）；Guangzhou University（广州大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）
High-dimensional and sparse (HiDS) matrices are frequently adopted to describe the complex relationships in various big data-related systems and applications. A Position-transitional Latent Factor Analysis (PLFA) model can accurately and efficiently represent an HiDS matrix. However, its involved latent factors are optimized by stochastic gradient descent with the specific gradient direction step-by-step, which may cause a suboptimal solution. To address this issue, this paper proposes a Sequential-Group-Differential- Evolution (SGDE) algorithm to refine the latent factors optimized by a PLFA …
The merged-staircase property: a necessary and nearly sufficient condition for SGD learning of sparse functions on two-layer neural networks
Mathematics Institute, EPFL（EPFL数学研究所）；Department of Electrical Engineering and Computer Science, MIT（MIT电气工程与计算机科学系）；Department of Statistics, Stanford University（斯坦福大学统计系）
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）；Kwai Inc.（快手公司）；Aberystwyth University（阿伯里斯特威斯大学）
We propose ResRep, a novel method for lossless channel pruning (a.k.a. filter pruning), which slims down a CNN by reducing the width (number of output channels) of convolutional layers. Inspired by the neurobiology research about the independence of remembering and forgetting, we propose to re-parameterize a CNN into the remembering parts and forgetting parts, where the former learn to maintain the performance and the latter learn to prune. Via training with regular SGD on the former but a novel update rule with penalty gradients on the latter, we realize structured sparsity. Then we equivalen…
University of Washington（华盛顿大学）；New York University（纽约大学）；Unipart Group（优尼帕特集团）
Deep Neural Networks have been used in a wide variety of applications with significant success. However, their highly complex nature owing to comprising millions of parameters has lead to problems during deployment in pipelines with low latency requirements. As a result, it is more desirable to obtain lightweight neural networks which have the same performance during inference time. In this work, we propose a weight based pruning approach in which the weights are pruned gradually based on their momentum of the previous iterations. Each layer of the neural network is assigned an importance valu…
Ozyegin University（厄兹耶金大学）；Imperial College London（帝国理工学院）
Distributed learning, particularly variants of distributed stochastic gradient descent (DSGD), are widely employed to speed up training by leveraging computational resources of several workers. However, in practise, communication delay becomes a bottleneck due to the significant amount of information that needs to be exchanged between the workers and the parameter server. One of the most efficient strategies to mitigate the communication bottleneck is top-K sparsification. However, top-K sparsification requires additional communication load to represent the sparsity pattern, and the mismatch b…
We introduce hybrid pruning which combines both coarse-grained channel and fine-grained weight pruning to reduce model size, computation and power demands with no to little loss in accuracy for enabling modern networks deployment on resource-constrained devices, such as always-on security cameras and drones. Additionally, to effectively perform channel pruning, we propose a fast sensitivity test that helps us quickly identify the sensitivity of within and across layers of a network to the output accuracy for target multiplier accumulators (MACs) or accuracy tolerance. Our experiment shows sign…
The sheer size of modern neural networks makes model serving a serious computational challenge. A popular class of compression techniques overcomes this challenge by pruning or sparsifying the weights of pretrained networks. While useful, these techniques often face serious tradeoffs between computational requirements and compression quality. In this work, we propose a novel optimization-based pruning framework that considers the combined effect of pruning (and updating) multiple weights subject to a sparsity constraint. Our approach, CHITA, extends the classical Optimal Brain Surgeon framewor…
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.…
Robert Bosch GmbH（罗伯特·博世有限公司）；Lübeck University（吕贝克大学）
State-of-the-art deep neural network (DNN) pruning techniques, applied one-shot before training starts, evaluate sparse architectures with the help of a single criterion -- called pruning score. Pruning weights based on a solitary score works well for some architectures and pruning rates but may also fail for other ones. As a common baseline for pruning scores, we introduce the notion of a generalized synaptic score (GSS). In this work we do not concentrate on a single pruning criterion, but provide a framework for combining arbitrary GSSs to create more powerful pruning strategies. These COmb…
Sparse methods and the use of Winograd convolutions are two orthogonal approaches, each of which significantly accelerates convolution computations in modern CNNs. Sparse Winograd merges these two and thus has the potential to offer a combined performance benefit. Nevertheless, training convolution layers so that the resulting Winograd kernels are sparse has not hitherto been very successful. By introducing a Winograd layer in place of a standard convolution layer, we can learn and prune Winograd coefficients "natively" and obtain sparsity level beyond 90% with only 0.1% accuracy loss with Ale…
While vision transformers have achieved impressive results, effectively and efficiently accelerating these models can further boost performances. In this work, we propose a dense/sparse training framework to obtain a unified model, enabling weight sharing across various token densities. Thus one model offers a range of accuracy and throughput tradeoffs for different applications. Besides, we introduce adaptive token pruning to optimize the patch token sparsity based on the input image. In addition, we investigate knowledge distillation to enhance token selection capability in early transformer…
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…
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…
Intel Labs（英特尔实验室）；University of Pittsburgh（匹兹堡大学）；Duke University（杜克大学）
Phenomenally successful in practical inference problems, convolutional neural networks (CNN) are widely deployed in mobile devices, data centers, and even supercomputers. The number of parameters needed in CNNs, however, are often large and undesirable. Consequently, various methods have been developed to prune a CNN once it is trained. Nevertheless, the resulting CNNs offer limited benefits. While pruning the fully connected layers reduces a CNN's size considerably, it does not improve inference speed noticeably as the compute heavy parts lie in convolutions. Pruning CNNs in a way that increa…
With rise of machine learning (ML) and the proliferation of smart mobile devices, recent years have witnessed a surge of interest in performing ML in wireless edge networks. In this paper, we consider the problem of jointly improving data privacy and communication efficiency of distributed edge learning, both of which are critical performance metrics in wireless edge network computing. Toward this end, we propose a new decentralized stochastic gradient method with sparse differential Gaussian-masked stochastic gradients (SDM-DSGD) for non-convex distributed edge learning. Our main contribution…
University of California, Irvine（加利福尼亚大学尔湾分校）；Department of Mathematics（数学系）
We propose an adaptive projection-gradient descent-shrinkage-splitting method (APGDSSM) to integrate penalty based channel pruning into quantization-aware training (QAT). APGDSSM concurrently searches weights in both the quantized subspace and the sparse subspace. APGDSSM uses shrinkage operator and a splitting technique to create sparse weights, as well as the Group Lasso penalty to push the weight sparsity into channel sparsity. In addition, we propose a novel complementary transformed l1 penalty to stabilize the training for extreme compression.
Synchronous stochastic gradient descent (SGD) is the most common method used for distributed training of deep learning models. In this algorithm, each worker shares its local gradients with others and updates the parameters using the average gradients of all workers. Although distributed training reduces the computation time, the communication overhead associated with the gradient exchange forms a scalability bottleneck for the algorithm. There are many compression techniques proposed to reduce the number of gradients that needs to be communicated. However, compressing the gradients introduces…
Hong Kong Baptist University（香港浸会大学）；Shenzhen District Block Technology Co., Ltd.（深圳区块科技有限公司）
Distributed synchronous stochastic gradient descent (S-SGD) has been widely used in training large-scale deep neural networks (DNNs), but it typically requires very high communication bandwidth between computational workers (e.g., GPUs) to exchange gradients iteratively. Recently, Top-$k$ sparsification techniques have been proposed to reduce the volume of data to be exchanged among workers. Top-$k$ sparsification can zero-out a significant portion of gradients without impacting the model convergence. However, the sparse gradients should be transferred with their irregular indices, which makes…
University of Minnesota, Twin Cities（明尼苏达大学双城分校）；University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
Recent empirical work on stochastic gradient descent (SGD) applied to over-parameterized deep learning has shown that most gradient components over epochs are quite small. Inspired by such observations, we rigorously study properties of Truncated SGD (T-SGD), that truncates the majority of small gradient components to zeros. Considering non-convex optimization problems, we show that the convergence rate of T-SGD matches the order of vanilla SGD. We also establish the generalization error bound for T-SGD. Further, we propose Noisy Truncated SGD (NT-SGD), which adds Gaussian noise to the truncat…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Element AI；University of Toronto（多伦多大学）；Vector Institute
We study whether a neural network optimizes to the same, linearly connected minimum under different samples of SGD noise (e.g., random data order and augmentation). We find that standard vision models become stable to SGD noise in this way early in training. From then on, the outcome of optimization is determined to a linearly connected region. We use this technique to study iterative magnitude pruning (IMP), the procedure used by work on the lottery ticket hypothesis to identify subnetworks that could have trained in isolation to full accuracy. We find that these subnetworks only reach full a…
How Pruning Reshapes Features: Sparse Autoencoder Analysis of Weight-Pruned Language Models
organization= VRAIN -- Valencian Research Institute for Artificial Intelligence, Universitat Polit\`ecnica de Val\`encia , city= Valencia , country= Spain；organization= Department of Economics；organization= Department of Business Organisation, Universitat Polit\`ecnica de Val\`encia , city= Valencia , country= Spain
Layer-Aware Position Embeddings for Visual Token Pruning in Multimodal Large Language Models
Tongji University（同济大学）；University of California, Santa Cruz（加州大学圣克鲁兹分校）；East China Normal University（华东师范大学）；Shanghai Eye Disease Prevention and Treatment Center（上海市眼病防治中心）
