Neural network pruning---the task of reducing the size of a network by removing parameters---has been the subject of a great deal of work in recent years. We provide a meta-analysis of the literature, including an overview of approaches to pruning and consistent findings in the literature. After aggregating results across 81 papers and pruning hundreds of models in controlled conditions, our clearest finding is that the community suffers from a lack of standardized benchmarks and metrics. This deficiency is substantial enough that it is hard to compare pruning techniques to one another or determine how much progress the field has made over the past three decades. To address this situation, we identify issues with current practices, suggest concrete remedies, and introduce ShrinkBench, an open-source framework to facilitate standardized evaluations of pruning methods. We use ShrinkBench to compare various pruning techniques and show that its comprehensive evaluation can prevent common pitfalls when comparing pruning methods.
Modern deep neural networks are often too large to use in many practical scenarios. Neural network pruning is an important technique for reducing the size of such models and accelerating inference. Gibbs pruning is a novel framework for expressing and designing neural network pruning methods. Combining approaches from statistical physics and stochastic regularization methods, it can train and prune a network simultaneously in such a way that the learned weights and pruning mask are well-adapted for each other. It can be used for structured or unstructured pruning and we propose a number of spe…
Facebook AI Research（脸书人工智能研究院）；Florida State University（佛罗里达州立大学）
Pruning neural network parameters is often viewed as a means to compress models, but pruning has also been motivated by the desire to prevent overfitting. This motivation is particularly relevant given the perhaps surprising observation that a wide variety of pruning approaches increase test accuracy despite sometimes massive reductions in parameter counts. To better understand this phenomenon, we analyze the behavior of pruning over the course of training, finding that pruning's benefit to generalization increases with pruning's instability (defined as the drop in test accuracy immediately fo…
Facebook AI Research（脸书人工智能研究院）；Brown University（布朗大学）
We examine how recently documented, fundamental phenomena in deep learning models subject to pruning are affected by changes in the pruning procedure. Specifically, we analyze differences in the connectivity structure and learning dynamics of pruned models found through a set of common iterative pruning techniques, to address questions of uniqueness of trainable, high-sparsity sub-networks, and their dependence on the chosen pruning method. In convolutional layers, we document the emergence of structure induced by magnitude-based unstructured pruning in conjunction with weight rewinding that r…
Deep neural networks are typically too computationally expensive to run in real-time on consumer-grade hardware and low-powered devices. In this paper, we investigate reducing the computational and memory requirements of neural networks through network pruning and quantisation. We examine their efficacy on large networks like AlexNet compared to recent compact architectures: ShuffleNet and MobileNet. Our results show that pruning and quantisation compresses these networks to less than half their original size and improves their efficiency, particularly on MobileNet with a 7x speedup. We also d…
As deep neural networks are growing in size and being increasingly deployed to more resource-limited devices, there has been a recent surge of interest in network pruning methods, which aim to remove less important weights or activations of a given network. A common limitation of most existing pruning techniques, is that they require pre-training of the network at least once before pruning, and thus we can benefit from reduction in memory and computation only at the inference time. However, reducing the training cost of neural networks with rapid structural pruning may be beneficial either to …
Deep learning architectures with a huge number of parameters are often compressed using pruning techniques to ensure computational efficiency of inference during deployment. Despite multitude of empirical advances, there is a lack of theoretical understanding of the effectiveness of different pruning methods. We inspect different pruning techniques under the statistical mechanics formulation of a teacher-student framework and derive their generalization error (GE) bounds. It has been shown that Determinantal Point Process (DPP) based node pruning method is notably superior to competing approac…
Pacific Northwest National Lab（太平洋西北国家实验室）；University of Maryland at College Park（马里兰大学帕克分校）
Large neural networks are heavily over-parameterized. This is done because it improves training to optimality. However once the network is trained, this means many parameters can be zeroed, or pruned, leaving an equivalent sparse neural network. We propose renormalizing sparse neural networks in order to improve accuracy. We prove that our method's error converges to zero as network parameters cluster or concentrate. We prove that without renormalizing, the error does not converge to zero in general. We experiment with our method on real world datasets MNIST, Fashion MNIST, and CIFAR-10 and co…
We propose a new formulation for pruning convolutional kernels in neural networks to enable efficient inference. We interleave greedy criteria-based pruning with fine-tuning by backpropagation - a computationally efficient procedure that maintains good generalization in the pruned network. We propose a new criterion based on Taylor expansion that approximates the change in the cost function induced by pruning network parameters. We focus on transfer learning, where large pretrained networks are adapted to specialized tasks. The proposed criterion demonstrates superior performance compared to o…
University of Edinburgh（爱丁堡大学）；Trinity College Dublin（都柏林三一学院）；University of Glasgow（格拉斯哥大学）
Convolutional Neural Networks (CNN) are becoming a common presence in many applications and services, due to their superior recognition accuracy. They are increasingly being used on mobile devices, many times just by porting large models designed for server space, although several model compression techniques have been considered. One model compression technique intended to reduce computations is channel pruning. Mobile and embedded systems now have GPUs which are ideal for the parallel computations of neural networks and for their lower energy cost per operation. Specialized libraries perform…
Many neural network pruning algorithms proceed in three steps: train the network to completion, remove unwanted structure to compress the network, and retrain the remaining structure to recover lost accuracy. The standard retraining technique, fine-tuning, trains the unpruned weights from their final trained values using a small fixed learning rate. In this paper, we compare fine-tuning to alternative retraining techniques. Weight rewinding (as proposed by Frankle et al., (2019)), rewinds unpruned weights to their values from earlier in training and retrains them from there using the original …
University of Toronto（多伦多大学）；Vector Institute（向量研究所）
Recent advances in the sparse neural network literature have made it possible to prune many large feed forward and convolutional networks with only a small quantity of data. Yet, these same techniques often falter when applied to the problem of recovering sparse recurrent networks. These failures are quantitative: when pruned with recent techniques, RNNs typically obtain worse performance than they do under a simple random pruning scheme. The failures are also qualitative: the distribution of active weights in a pruned LSTM or GRU network tend to be concentrated in specific neurons and gates, …
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…
Neural network pruning has been an essential technique to reduce the computation and memory requirements for using deep neural networks for resource-constrained devices. Most existing research focuses primarily on balancing the sparsity and accuracy of a pruned neural network by strategically removing insignificant parameters and retraining the pruned model. Such efforts on reusing training samples pose serious privacy risks due to increased memorization, which, however, has not been investigated yet. In this paper, we conduct the first analysis of privacy risks in neural network pruning. Spec…
Zhejiang University（浙江大学）；SUTD-ZJU IDEA（新加坡科技设计大学-浙江大学 信息与数据科学联合实验室）；Singapore University of Technology and Design（新加坡科技设计大学）
Despite enjoying extensive applications in video analysis, three-dimensional convolutional neural networks (3D CNNs)are restricted by their massive computation and storage consumption. To solve this problem, we propose a threedimensional regularization-based neural network pruning method to assign different regularization parameters to different weight groups based on their importance to the network. Further we analyze the redundancy and computation cost for each layer to determine the different pruning ratios. Experiments show that pruning based on our method can lead to 2x theoretical speedu…
Bucknell University（巴克内尔大学）；University of Utah（犹他大学）；Colby College（科尔比学院）
Pruning techniques have been successfully used in neural networks to trade accuracy for sparsity. However, the impact of network pruning is not uniform: prior work has shown that the recall for underrepresented classes in a dataset may be more negatively affected. In this work, we study such relative distortions in recall by hypothesizing an intensification effect that is inherent to the model. Namely, that pruning makes recall relatively worse for a class with recall below accuracy and, conversely, that it makes recall relatively better for a class with recall above accuracy. In addition, we …
Neural network pruning techniques reduce the number of parameters without compromising predicting ability of a network. Many algorithms have been developed for pruning both over-parameterized fully-connected networks (FCNs) and convolutional neural networks (CNNs), but analytical studies of capabilities and compression ratios of such pruned sub-networks are lacking. We theoretically study the performance of two pruning techniques (random and magnitude-based) on FCNs and CNNs. Given a target network {whose weights are independently sampled from appropriate distributions}, we provide a universal…
With the rapid development of deep learning, the sizes of neural networks become larger and larger so that the training and inference often overwhelm the hardware resources. Given the fact that neural networks are often over-parameterized, one effective way to reduce such computational overhead is neural network pruning, by removing redundant parameters from trained neural networks. It has been recently observed that pruning can not only reduce computational overhead but also can improve empirical robustness of deep neural networks (NNs), potentially owing to removing spurious correlations whi…
Deep Neural Networks (DNNs) are the key to the state-of-the-art machine vision, sensor fusion and audio/video signal processing. Unfortunately, their computation complexity and tight resource constraints on the Edge make them hard to leverage on mobile, embedded and IoT devices. Due to great diversity of Edge devices, DNN designers have to take into account the hardware platform and application requirements during network training. In this work we introduce pruning via matrix pivoting as a way to improve network pruning by compromising between the design flexibility of architecture-oblivious a…
Lightweight model design has become an important direction in the application of deep learning technology, pruning is an effective mean to achieve a large reduction in model parameters and FLOPs. The existing neural network pruning methods mostly start from the importance of parameters, and design parameter evaluation metrics to perform parameter pruning iteratively. These methods are not studied from the perspective of model topology, may be effective but not efficient, and requires completely different pruning for different datasets. In this paper, we study the graph structure of the neural …
The rapidly growing parameter volume of deep neural networks (DNNs) hinders the artificial intelligence applications on resource constrained devices, such as mobile and wearable devices. Neural network pruning, as one of the mainstream model compression techniques, is under extensive study to reduce the number of parameters and computations. In contrast to irregular pruning that incurs high index storage and decoding overhead, structured pruning techniques have been proposed as the promising solutions. However, prior studies on structured pruning tackle the problem mainly from the perspective …
Structural pruning of neural network parameters reduces computation, energy, and memory transfer costs during inference. We propose a novel method that estimates the contribution of a neuron (filter) to the final loss and iteratively removes those with smaller scores. We describe two variations of our method using the first and second-order Taylor expansions to approximate a filter's contribution. Both methods scale consistently across any network layer without requiring per-layer sensitivity analysis and can be applied to any kind of layer, including skip connections. For modern networks trai…
Network pruning has become the de facto tool to accelerate deep neural networks for mobile and edge applications. Recently, feature-map discriminant based channel pruning has shown promising results, as it aligns well with the CNN objective of differentiating multiple classes and offers better interpretability of the pruning decision. However, existing discriminant-based methods are challenged by computation inefficiency, as there is a lack of theoretical guidance on quantifying the feature-map discriminant power. In this paper, we present a new mathematical formulation to accurately and effic…
Argonne Leadership Computing Facility（阿贡领导力计算设施）；Argonne National Laboratories（阿贡国家实验室）
Bayesian neural Networks (BNNs) are a promising method of obtaining statistical uncertainties for neural network predictions but with a higher computational overhead which can limit their practical usage. This work explores the use of high performance computing with distributed training to address the challenges of training BNNs at scale. We present a performance and scalability comparison of training the VGG-16 and Resnet-18 models on a Cray-XC40 cluster. We demonstrate that network pruning can speed up inference without accuracy loss and provide an open source software package, {\it{BPrune}}…
The learning capability of a neural network improves with increasing depth at higher computational costs. Wider layers with dense kernel connectivity patterns furhter increase this cost and may hinder real-time inference. We propose feature map and kernel level pruning for reducing the computational complexity of a deep convolutional neural network. Pruning feature maps reduces the width of a layer and hence does not need any sparse representation. Further, kernel pruning converts the dense connectivity pattern into a sparse one. Due to coarse nature, these pruning granularities can be exploit…
The University of Tennessee Knoxville（田纳西大学诺克斯维尔分校）；Sun Yat-sen University（中山大学）
Convolutional neural network (CNN) pruning has become one of the most successful network compression approaches in recent years. Existing works on network pruning usually focus on removing the least important filters in the network to achieve compact architectures. In this study, we claim that identifying structural redundancy plays a more essential role than finding unimportant filters, theoretically and empirically. We first statistically model the network pruning problem in a redundancy reduction perspective and find that pruning in the layer(s) with the most structural redundancy outperfor…
We report, for the first time, on the cascade weight shedding phenomenon in deep neural networks where in response to pruning a small percentage of a network's weights, a large percentage of the remaining is shed over a few epochs during the ensuing fine-tuning phase. We show that cascade weight shedding, when present, can significantly improve the performance of an otherwise sub-optimal scheme such as random pruning. This explains why some pruning methods may perform well under certain circumstances, but poorly under others, e.g., ResNet50 vs. MobileNetV3. We provide insight into why the glob…
The state of neural network pruning has been noticed to be unclear and even confusing for a while, largely due to "a lack of standardized benchmarks and metrics" [3]. To standardize benchmarks, first, we need to answer: what kind of comparison setup is considered fair? This basic yet crucial question has barely been clarified in the community, unfortunately. Meanwhile, we observe several papers have used (severely) sub-optimal hyper-parameters in pruning experiments, while the reason behind them is also elusive. These sub-optimal hyper-parameters further exacerbate the distorted benchmarks, re…
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…
University of Liverpool（利物浦大学）；Huawei Ireland Research Center（华为爱尔兰研究中心）
Pruning aims to reduce the number of parameters while maintaining performance close to the original network. This work proposes a novel \emph{self-distillation} based pruning strategy, whereby the representational similarity between the pruned and unpruned versions of the same network is maximized. Unlike previous approaches that treat distillation and pruning separately, we use distillation to inform the pruning criteria, without requiring a separate student network as in knowledge distillation. We show that the proposed {\em cross-correlation objective for self-distilled pruning} implicitly …
To prune or not to prune : A chaos-causality approach to principled pruning of dense neural networks
Birla Institute of Technology and Sciences Pilani（皮拉尼伯拉理工学院）；BITS Pilani, Goa Campus（皮拉尼伯拉理工学院果阿校区）；National Institute of Advanced Studies（国家高等研究院）；Nitte Meenakshi Institute of Technology（尼特·米纳克希理工学院）；HappyMonk AI（HappyMonk人工智能公司）
Adaptive Pruning of Deep Neural Networks for Resource-Aware Embedded Intrusion Detection on the Edge
Computer Science University of Massachusetts Dartmouth（计算机科学大学马萨诸塞大学达特茅斯分校）；United States Military Academy（美国军事学院）；University of Massachusetts Dartmouth（马萨诸塞大学达特茅斯分校）
University of Toronto（多伦多大学）；York University（约克大学）
In this work, PRUNIX, a framework for training and pruning convolutional neural networks is proposed for deployment on memristor crossbar based accelerators. PRUNIX takes into account the numerous non-ideal effects of memristor crossbars including weight quantization, state-drift, aging and stuck-at-faults. PRUNIX utilises a novel Group Sawtooth Regularization intended to improve non-ideality tolerance as well as sparsity, and a novel Adaptive Pruning Algorithm (APA) intended to minimise accuracy loss by considering the sensitivity of different layers of a CNN to pruning. We compare our regula…
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…
Centrum Wiskunde & Informatica（数学与计算机科学中心）；Leiden Institute of Advanced Computer Science（莱顿高级计算机科学研究所）
Neural network pruning techniques can substantially reduce the computational cost of applying convolutional neural networks (CNNs). Common pruning methods determine which convolutional filters to remove by ranking the filters individually, i.e., without taking into account their interdependence. In this paper, we advocate the viewpoint that pruning should consider the interdependence between series of consecutive operators. We propose the LongEst-chAiN (LEAN) method that prunes CNNs by using graph-based algorithms to select relevant chains of convolutions. A CNN is interpreted as a graph, with…
University of Genoa（热那亚大学）；Imperial College London（伦敦帝国理工学院）；University of Sassari（萨萨里大学）
Verification of deep neural networks has witnessed a recent surge of interest, fueled by success stories in diverse domains and by abreast concerns about safety and security in envisaged applications. Complexity and sheer size of such networks are challenging for automated formal verification techniques which, on the other hand, could ease the adoption of deep networks in safety- and security-critical contexts. In this paper we focus on enabling state-of-the-art verification tools to deal with neural networks of some practical interest. We propose a new training pipeline based on network pruni…
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…
Deep neural networks have evolved to become power demanding and consequently difficult to apply to small-size mobile platforms. Network parameter reduction methods have been introduced to systematically deal with the computational and memory complexity of deep networks. We propose to examine the ability of attentive connection pruning to deal with redundancy reduction in neural networks as a contribution to the reduction of computational demand. In this work, we describe a Top-Down attention mechanism that is added to a Bottom-Up feedforward network to select important connections and subseque…
Fermi National Accelerator Laboratory（费米国家加速器实验室）；University of California San Diego（加州大学圣地亚哥分校）；Xilinx Research（赛灵思研究院）；Northwestern University（西北大学）
Efficient machine learning implementations optimized for inference in hardware have wide-ranging benefits, depending on the application, from lower inference latency to higher data throughput and reduced energy consumption. Two popular techniques for reducing computation in neural networks are pruning, removing insignificant synapses, and quantization, reducing the precision of the calculations. In this work, we explore the interplay between pruning and quantization during the training of neural networks for ultra low latency applications targeting high energy physics use cases. Techniques dev…
Regularization has long been utilized to learn sparsity in deep neural network pruning. However, its role is mainly explored in the small penalty strength regime. In this work, we extend its application to a new scenario where the regularization grows large gradually to tackle two central problems of pruning: pruning schedule and weight importance scoring. (1) The former topic is newly brought up in this work, which we find critical to the pruning performance while receives little research attention. Specifically, we propose an L2 regularization variant with rising penalty factors and show it …
University of Maryland（马里兰大学）；Shandong University（山东大学）
Network compression is crucial to making the deep networks to be more efficient, faster, and generalizable to low-end hardware. Current network compression methods have two open problems: first, there lacks a theoretical framework to estimate the maximum compression rate; second, some layers may get over-prunned, resulting in significant network performance drop. To solve these two problems, this study propose a gradient-matrix singularity analysis-based method to estimate the maximum network redundancy. Guided by that maximum rate, a novel and efficient hierarchical network pruning algorithm …
We present a post-training weight pruning method for deep neural networks that achieves accuracy levels tolerable for the production setting and that is sufficiently fast to be run on commodity hardware such as desktop CPUs or edge devices. We propose a data-free extension of the approach for computer vision models based on automatically-generated synthetic fractal images. We obtain state-of-the-art results for data-free neural network pruning, with ~1.5% top@1 accuracy drop for a ResNet50 on ImageNet at 50% sparsity rate. When using real data, we are able to get a ResNet50 model on ImageNet w…
Network pruning is a widely used technique to reduce computation cost and model size for deep neural networks. However, the typical three-stage pipeline, i.e., training, pruning and retraining (fine-tuning) significantly increases the overall training trails. In this paper, we develop a systematic weight-pruning optimization approach based on Surrogate Lagrangian relaxation (SLR), which is tailored to overcome difficulties caused by the discrete nature of the weight-pruning problem while ensuring fast convergence. We further accelerate the convergence of the SLR by using quadratic penalties. M…
The vulnerability of deep neural networks against adversarial examples - inputs with small imperceptible perturbations - has gained a lot of attention in the research community recently. Simultaneously, the number of parameters of state-of-the-art deep learning models has been growing massively, with implications on the memory and computational resources required to train and deploy such models. One approach to control the size of neural networks is retrospectively reducing the number of parameters, so-called neural network pruning. Available research on the impact of neural network pruning on…
Many recent works have shown trainability plays a central role in neural network pruning -- unattended broken trainability can lead to severe under-performance and unintentionally amplify the effect of retraining learning rate, resulting in biased (or even misinterpreted) benchmark results. This paper introduces trainability preserving pruning (TPP), a scalable method to preserve network trainability against pruning, aiming for improved pruning performance and being more robust to retraining hyper-parameters (e.g., learning rate). Specifically, we propose to penalize the gram matrix of convolu…
The advancement of convolutional neural networks (CNNs) on various vision applications has attracted lots of attention. Yet the majority of CNNs are unable to satisfy the strict requirement for real-world deployment. To overcome this, the recent popular network pruning is an effective method to reduce the redundancy of the models. However, the ranking of filters according to their "importance" on different pruning criteria may be inconsistent. One filter could be important according to a certain criterion, while it is unnecessary according to another one, which indicates that each criterion is…
