Recently, a race towards the simplification of deep networks has begun, showing that it is effectively possible to reduce the size of these models with minimal or no performance loss. However, there is a general lack in understanding why these pruning strategies are effective. In this work, we are going to compare and analyze pruned solutions with two different pruning approaches, one-shot and gradual, showing the higher effectiveness of the latter. In particular, we find that gradual pruning allows access to narrow, well-generalizing minima, which are typically ignored when using one-shot approaches. In this work we also propose PSP-entropy, a measure to understand how a given neuron correlates to some specific learned classes. Interestingly, we observe that the features extracted by iteratively-pruned models are less correlated to specific classes, potentially making these models a better fit in transfer learning approaches.
Magnitude pruning is a widely used strategy for reducing model size in pure supervised learning; however, it is less effective in the transfer learning regime that has become standard for state-of-the-art natural language processing applications. We propose the use of movement pruning, a simple, deterministic first-order weight pruning method that is more adaptive to pretrained model fine-tuning. We give mathematical foundations to the method and compare it to existing zeroth- and first-order pruning methods. Experiments show that when pruning large pretrained language models, movement pruning…
University of Leicester（莱斯特大学）；Lobachevsky State University（罗巴切夫斯基州立大学）
Pruning coupled with learning aims to optimize the neural network (NN) structure for solving specific problems. This optimization can be used for various purposes: to prevent overfitting, to save resources for implementation and training, to provide explainability of the trained NN, and many others. The minimal structure that cannot be pruned further is not unique. Ensemble of minimal structures can be used as a committee of intellectual agents that solves problems by voting. Each minimal NN presents an "empirical knowledge" about the problem and can be verbalized. The non-uniqueness of such k…
Systematic Characterization of Minimal Deep Learning Architectures: A Unified Analysis of Convergence, Pruning, and Quantization
School of Computing, Newcastle University（新castle大学计算机学院）；VSB-Technical University of Ostrava（奥斯特拉瓦技术大学）；Queen Mary University of London（伦敦女王玛丽大学）；University of Florida（佛罗里达大学）；University of Catania（卡塔尼亚大学）
Syracuse University（雪城大学）；North Carolina State University（北卡罗来纳州立大学）；Carnegie Mellon University（卡内基梅隆大学）
Network pruning is a widely-used compression technique that is able to significantly scale down overparameterized models with minimal loss of accuracy. This paper shows that pruning may create or exacerbate disparate impacts. The paper sheds light on the factors to cause such disparities, suggesting differences in gradient norms and distance to decision boundary across groups to be responsible for this critical issue. It analyzes these factors in detail, providing both theoretical and empirical support, and proposes a simple, yet effective, solution that mitigates the disparate impacts caused …
ETH Zürich（苏黎世联邦理工学院）；Beihang University（北京航空航天大学）；Singapore Management University（新加坡管理大学）
Many mobile applications demand selective execution of multiple correlated deep learning inference tasks on resource-constrained platforms. Given a set of deep neural networks, each pre-trained for a single task, it is desired that executing arbitrary combinations of tasks yields minimal computation cost. Pruning each network separately yields suboptimal computation cost due to task relatedness. A promising remedy is to merge the networks into a multitask network to eliminate redundancy across tasks before network pruning. However, pruning a multitask network combined by existing network mergi…
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.…
Recent studies assessing the efficacy of pruning neural networks methods uncovered a surprising finding: when conducting ablation studies on existing pruning-at-initialization methods, namely SNIP, GraSP, SynFlow, and magnitude pruning, performances of these methods remain unchanged and sometimes even improve when randomly shuffling the mask positions within each layer (Layerwise Shuffling) or sampling new initial weight values (Reinit), while keeping pruning masks the same. We attempt to understand the reason behind such network immunity towards weight/mask modifications, by studying layer-wi…
How much can pruning algorithms teach us about the fundamentals of learning representations in neural networks? And how much can these fundamentals help while devising new pruning techniques? A lot, it turns out. Neural network pruning has become a topic of great interest in recent years, and many different techniques have been proposed to address this problem. The decision of what to prune and when to prune necessarily forces us to confront our assumptions about how neural networks actually learn to represent patterns in data. In this work, we set out to test several long-held hypotheses abou…
We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network parameters to achieve parameter quantization, as well as an L1 penalty to achieve pruning. Unlike many existing quantization-based methods, our method uses hard clustering assignments of network parameters, which adds minimal change or overhead to standard network training. We als…
Pruning neural networks has regained interest in recent years as a means to compress state-of-the-art deep neural networks and enable their deployment on resource-constrained devices. In this paper, we propose a robust compressive learning framework that efficiently prunes network parameters during training with minimal computational overhead. We incorporate fast mechanisms to prune individual layers and build upon these to automatically prune the entire network under a user-defined budget constraint. Key to our end-to-end network pruning approach is the formulation of an intuitive and easy-to…
Model pruning seeks to induce sparsity in a deep neural network's various connection matrices, thereby reducing the number of nonzero-valued parameters in the model. Recent reports (Han et al., 2015; Narang et al., 2017) prune deep networks at the cost of only a marginal loss in accuracy and achieve a sizable reduction in model size. This hints at the possibility that the baseline models in these experiments are perhaps severely over-parameterized at the outset and a viable alternative for model compression might be to simply reduce the number of hidden units while maintaining the model's dens…
EECS Department（EECS系）；University of Michigan（密歇根大学）；Ann Arbor, MI 48105, USA（美国密歇根州安娜堡市48105（注意：这部分按要求不应提取，此处为错误识别，正确应为仅保留大学/学院/公司/研究院级别，即仅提取University of Michigan，而EECS Department是系别，不应提取，Ann Arbor是城市，不应提取。修正后正确输出应为{）
Recent network pruning methods focus on pruning models early-on in training. To estimate the impact of removing a parameter, these methods use importance measures that were originally designed to prune trained models. Despite lacking justification for their use early-on in training, such measures result in surprisingly low accuracy loss. To better explain this behavior, we develop a general framework that uses gradient flow to unify state-of-the-art importance measures through the norm of model parameters. We use this framework to determine the relationship between pruning measures and evoluti…
Computer Science and Artificial Intelligence Laboratory, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室）；Robotics and Big Data Laboratory, University of Haifa（海法大学机器人与大数据实验室）
We introduce a pruning algorithm that provably sparsifies the parameters of a trained model in a way that approximately preserves the model's predictive accuracy. Our algorithm uses a small batch of input points to construct a data-informed importance sampling distribution over the network's parameters, and adaptively mixes a sampling-based and deterministic pruning procedure to discard redundant weights. Our pruning method is simultaneously computationally efficient, provably accurate, and broadly applicable to various network architectures and data distributions. Our empirical comparisons sh…
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…
University of Minnesota（明尼苏达大学）；Sumo Logic（Sumo Logic公司）
A number of recent approaches have been proposed for pruning neural network parameters at initialization with the goal of reducing the size and computational burden of models while minimally affecting their training dynamics and generalization performance. While each of these approaches have some amount of well-founded motivation, a rigorous analysis of the effect of these pruning methods on network training dynamics and their formal relationship to each other has thus far received little attention. Leveraging recent theoretical approximations provided by the Neural Tangent Kernel, we unify a …
Amazon AI（亚马逊人工智能）；UT Austin（得克萨斯大学奥斯汀分校）；UC Irvine（加利福尼亚大学欧文分校）；CMU（卡内基梅隆大学）；Caltech（加州理工学院）；Imperial College London（伦敦帝国理工学院）
Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed st…
Iowa State University（爱荷华州立大学）；Technical University of Darmstadt（达姆施塔特工业大学）
Model compression is an essential technique for deploying deep neural networks (DNNs) on power and memory-constrained resources. However, existing model-compression methods often rely on human expertise and focus on parameters' local importance, ignoring the rich topology information within DNNs. In this paper, we propose a novel multi-stage graph embedding technique based on graph neural networks (GNNs) to identify DNN topologies and use reinforcement learning (RL) to find a suitable compression policy. We performed resource-constrained (i.e., FLOPs) channel pruning and compared our approach …
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 …
Existing generalization measures that aim to capture a model's simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically motivated measure of a network's simplicity which we call prunability: the smallest \emph{fraction} of the network's parameters that can be kept while pruning without adversely affecting its training loss. We show that this measure is highly predictive of a model's generalization performance across a large set of convolutional networks trained on CIFAR-10, does not …
State-of-the-art computer vision models are rapidly increasing in capacity, where the number of parameters far exceeds the number required to fit the training set. This results in better optimization and generalization performance. However, the huge size of contemporary models results in large inference costs and limits their use on resource-limited devices. In order to reduce inference costs, convolutional filters in trained neural networks could be pruned to reduce the run-time memory and computational requirements during inference. However, severe post-training pruning results in degraded p…
Yuanpei College, Peking University（北京大学元培学院）；School of Mathematical Sciences, Peking University（北京大学数学科学学院）；Department of Electrical Engineering, Princeton University（普林斯顿大学电气工程系）；Zhongguancun Haihua Institute for Frontier Information Technology（中关村海华前沿信息技术研究院）；Key Laboratory of Machine Perception, MOE, School of EECS, Peking University（北京大学信息科学技术学院机器感知教育部重点实验室）
Network pruning is a method for reducing test-time computational resource requirements with minimal performance degradation. Conventional wisdom of pruning algorithms suggests that: (1) Pruning methods exploit information from training data to find good subnetworks; (2) The architecture of the pruned network is crucial for good performance. In this paper, we conduct sanity checks for the above beliefs on several recent unstructured pruning methods and surprisingly find that: (1) A set of methods which aims to find good subnetworks of the randomly-initialized network (which we call "initial tic…
Spiking Neural Networks (SNNs) have been attached great importance due to their biological plausibility and high energy-efficiency on neuromorphic chips. As these chips are usually resource-constrained, the compression of SNNs is thus crucial along the road of practical use of SNNs. Most existing methods directly apply pruning approaches in artificial neural networks (ANNs) to SNNs, which ignore the difference between ANNs and SNNs, thus limiting the performance of the pruned SNNs. Besides, these methods are only suitable for shallow SNNs. In this paper, inspired by synaptogenesis and synapse …
Northeastern University（东北大学）；University of Connecticut（康涅狄格大学）；George Mason University（乔治梅森大学）
During the deployment of deep neural networks (DNNs) on edge devices, many research efforts are devoted to the limited hardware resource. However, little attention is paid to the influence of dynamic power management. As edge devices typically only have a budget of energy with batteries (rather than almost unlimited energy support on servers or workstations), their dynamic power management often changes the execution frequency as in the widely-used dynamic voltage and frequency scaling (DVFS) technique. This leads to highly unstable inference speed performance, especially for computation-inten…
Despite the promising results of convolutional neural networks (CNNs), their application on devices with limited resources is still a big challenge; this is mainly due to the huge memory and computation requirements of the CNN. To counter the limitation imposed by the network size, we use pruning to reduce the network size and -- implicitly -- the number of floating point operations (FLOPs). Contrary to the filter norm method -- used in ``conventional`` network pruning -- based on the assumption that a smaller norm implies ``less importance'' to its associated component, we develop a novel fil…
SGLP: A Similarity Guided Fast Layer Partition Pruning for Compressing Large Deep Models
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；Zhejiang University of Technology（浙江工业大学）；Nanyang Technological University（南洋理工大学）；Zhejiang University（浙江大学）；Southwest University（西南大学）；The City College of New York（纽约城市学院）；Shenzhen University of Advanced Technology（深圳大学）
