Convolutional neural networks (CNN) play a major role in image processing tasks like image classification, object detection, semantic segmentation. Very often CNN networks have from several to hundred stacked layers with several megabytes of weights. One of the possible methods to reduce complexity and memory footprint is pruning. Pruning is a process of removing weights which connect neurons from two adjacent layers in the network. The process of finding near optimal solution with specified drop in accuracy can be more sophisticated when DL model has higher number of convolutional layers. In the paper few approaches based on retraining and no retraining are described and compared together.
Zuse Institute Berlin（柏林祖斯研究所）；Technische Universität Berlin（柏林工业大学）
Many Neural Network Pruning approaches consist of several iterative training and pruning steps, seemingly losing a significant amount of their performance after pruning and then recovering it in the subsequent retraining phase. Recent works of Renda et al. (2020) and Le & Hua (2021) demonstrate the significance of the learning rate schedule during the retraining phase and propose specific heuristics for choosing such a schedule for IMP (Han et al., 2015). We place these findings in the context of the results of Li et al. (2020) regarding the training of models within a fixed training budget an…
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…
Network pruning is an effective method to reduce the computational expense of over-parameterized neural networks for deployment on low-resource systems. Recent state-of-the-art techniques for retraining pruned networks such as weight rewinding and learning rate rewinding have been shown to outperform the traditional fine-tuning technique in recovering the lost accuracy (Renda et al., 2020), but so far it is unclear what accounts for such performance. In this work, we conduct extensive experiments to verify and analyze the uncanny effectiveness of learning rate rewinding. We find that the reaso…
Modern deep networks have millions to billions of parameters, which leads to high memory and energy requirements during training as well as during inference on resource-constrained edge devices. Consequently, pruning techniques have been proposed that remove less significant weights in deep networks, thereby reducing their memory and computational requirements. Pruning is usually performed after training the original network, and is followed by further retraining to compensate for the accuracy loss incurred during pruning. The prune-and-retrain procedure is repeated iteratively until an optimu…
The most common method for DNN pruning is hard thresholding of network weights, followed by retraining to recover any lost accuracy. Recently developed smart pruning algorithms use the DNN response over the training set for a variety of cost functions to determine redundant network weights, leading to less accuracy degradation and possibly less retraining time. For experiments on the total pruning time (pruning time + retraining time) we show that hard thresholding followed by retraining remains the most efficient way of reducing the number of network parameters. However smart pruning algorith…
Olica: Efficient Structured Pruning of Large Language Models without Retraining
Center of Statistical Research, School of Statistics（统计研究中心、统计学与数据科学学院）；New Cornerstone Science Laboratory, Southwestern University of Finance（新基石科学实验室、西南财经大学）
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 …
Building compact convolutional neural networks (CNNs) with reliable performance is a critical but challenging task, especially when deploying them in real-world applications. As a common approach to reduce the size of CNNs, pruning methods delete part of the CNN filters according to some metrics such as $l1$-norm. However, previous methods hardly leverage the information variance in a single feature map and the similarity characteristics among feature maps. In this paper, we propose a novel filter pruning method, which incorporates two kinds of feature map selections: diversity-aware selection…
Pruning and quantization are proven methods for improving the performance and storage efficiency of convolutional neural networks (CNNs). Pruning removes near-zero weights in tensors and masks weak connections between neurons in neighbouring layers. Quantization reduces the precision of weights by replacing them with numerically similar values that require less storage. In this paper, we identify another form of redundancy in CNN weight tensors, in the form of repeated patterns of similar values. We observe that pruning and quantization both tend to drastically increase the number of repeated …
The Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州））；The Hong Kong University of Science and Technology（香港科技大学）
Pruning is an effective technique for convolutional neural networks (CNNs) model compression, but it is difficult to find the optimal pruning policy due to the large design space. To improve the usability of pruning, many auto pruning methods have been developed. Recently, Bayesian optimization (BO) has been considered to be a competitive algorithm for auto pruning due to its solid theoretical foundation and high sampling efficiency. However, BO suffers from the curse of dimensionality. The performance of BO deteriorates when pruning deep CNNs, since the dimension of the design spaces increase…
University College Dublin（都柏林大学）；National University of Singapore（新加坡国立大学）
Using smart wearable devices to monitor patients electrocardiogram (ECG) for real-time detection of arrhythmias can significantly improve healthcare outcomes. Convolutional neural network (CNN) based deep learning has been used successfully to detect anomalous beats in ECG. However, the computational complexity of existing CNN models prohibits them from being implemented in low-powered edge devices. Usually, such models are complex with lots of model parameters which results in large number of computations, memory, and power usage in edge devices. Network pruning techniques can reduce model co…
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…
Institute of Computing Technology, Chinese Academy of Sciences（中国科学院计算技术研究所）；University of Chinese Academy of Sciences（中国科学院大学）
In this work, we propose a heuristic genetic algorithm (GA) for pruning convolutional neural networks (CNNs) according to the multi-objective trade-off among error, computation and sparsity. In our experiments, we apply our approach to prune pre-trained LeNet across the MNIST dataset, which reduces 95.42% parameter size and achieves 16$\times$ speedups of convolutional layer computation with tiny accuracy loss by laying emphasis on sparsity and computation, respectively. Our empirical study suggests that GA is an alternative pruning approach for obtaining a competitive compression performance.…
Tight Compression: Compressing CNN Through Fine-Grained Pruning and Weight Permutation for Efficient Implementation
ACCESS - AI Chip Center for Emerging Smart Systems（ACCESS——新兴智能系统人工智能芯片中心）；Hong Kong University of Science and Technology (HKUST)（香港科技大学）；NVIDIA Corporation（英伟达公司）
Convolutional neural networks (CNNs) have succeeded in many practical applications. However, their high computation and storage requirements often make them difficult to deploy on resource-constrained devices. In order to tackle this issue, many pruning algorithms have been proposed for CNNs, but most of them can't prune CNNs to a reasonable level. In this paper, we propose a novel algorithm for training and pruning CNNs based on the recursive least squares (RLS) optimization. After training a CNN for some epochs, our algorithm combines inverse input autocorrelation matrices and weight matrice…
Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this problem, we propose Network Implosion, it erases multiple layers from Residual Networks without degrading accuracy. Our key idea is to introduce a priority term that identifies the importance of a layer; we can select unimportant layers according to the priority and erase them after…
In recent years, most of the deep learning solutions are targeted to be deployed in mobile devices. This makes the need for development of lightweight models all the more imminent. Another solution is to optimize and prune regular deep learning models. In this paper, we tackle the problem of CNN model pruning with the help of Self-Similarity Matrix (SSM) computed from the 2D CNN filters. We propose two novel algorithms to rank and prune redundant filters which contribute similar activation maps to the output. One of the key features of our method is that there is no need of finetuning after tr…
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…
PERP: Rethinking the Prune-Retrain Paradigm in the Era of LLMs
Department for AI in Society, Science, and Technology, Zuse Institute Berlin, Germany（人工智能与社会、科学与技术部门，柏林Zuse研究所）；Institute of Mathematics, Technische Universität Berlin, Germany（数学研究所，柏林技术大学）
Centre for Vision, Speech and Signal Processing (CVSSP)（视觉、语音与信号处理中心（CVSSP））；University of Surrey（萨里大学）
Convolution neural networks (CNNs) have shown great success in various applications. However, the computational complexity and memory storage of CNNs is a bottleneck for their deployment on resource-constrained devices. Recent efforts towards reducing the computation cost and the memory overhead of CNNs involve similarity-based passive filter pruning methods. Similarity-based passive filter pruning methods compute a pairwise similarity matrix for the filters and eliminate a few similar filters to obtain a small pruned CNN. However, the computational complexity of computing the pairwise similar…
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.…
LTS2 Laboratory, EPFL（洛桑联邦理工学院LTS2实验室）；IDCOM Laboratory, University of Edinburgh（爱丁堡大学IDCOM实验室）
Recent DNN pruning algorithms have succeeded in reducing the number of parameters in fully connected layers, often with little or no drop in classification accuracy. However, most of the existing pruning schemes either have to be applied during training or require a costly retraining procedure after pruning to regain classification accuracy. We start by proposing a cheap pruning algorithm for fully connected DNN layers based on difference of convex functions (DC) optimisation, that requires little or no retraining. We then provide a theoretical analysis for the growth in the Generalization Err…
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））；Tsinghua University（清华大学）；University of Warwick（华威大学）；Hangzhou Dianzi University（杭州电子科技大学）
It is not easy to design and run Convolutional Neural Networks (CNNs) due to: 1) finding the optimal number of filters (i.e., the width) at each layer is tricky, given an architecture; and 2) the computational intensity of CNNs impedes the deployment on computationally limited devices. Oracle Pruning is designed to remove the unimportant filters from a well-trained CNN, which estimates the filters' importance by ablating them in turn and evaluating the model, thus delivers high accuracy but suffers from intolerable time complexity, and requires a given resulting width but cannot automatically …
Parameter pruning is a promising approach for CNN compression and acceleration by eliminating redundant model parameters with tolerable performance loss. Despite its effectiveness, existing regularization-based parameter pruning methods usually drive weights towards zero with large and constant regularization factors, which neglects the fact that the expressiveness of CNNs is fragile and needs a more gentle way of regularization for the networks to adapt during pruning. To solve this problem, we propose a new regularization-based pruning method (named IncReg) to incrementally assign different …
Tsinghua University（清华大学）；Northeastern University（东北大学）；Xi’an Jiaotong University（西安交通大学）；Institute for Interdisciplinary Information Core Technology（交叉信息核心技术研究院）
Weight pruning is a powerful technique to realize model compression. We propose PCNN, a fine-grained regular 1D pruning method. A novel index format called Sparsity Pattern Mask (SPM) is presented to encode the sparsity in PCNN. Leveraging SPM with limited pruning patterns and non-zero sequences with equal length, PCNN can be efficiently employed in hardware. Evaluated on VGG-16 and ResNet-18, our PCNN achieves the compression rate up to 8.4X with only 0.2% accuracy loss. We also implement a pattern-aware architecture in 55nm process, achieving up to 9.0X speedup and 28.39 TOPS/W efficiency wi…
Sparsification is an efficient approach to accelerate CNN inference, but it is challenging to take advantage of sparsity in training procedure because the involved gradients are dynamically changed. Actually, an important observation shows that most of the activation gradients in back-propagation are very close to zero and only have a tiny impact on weight-updating. Hence, we consider pruning these very small gradients randomly to accelerate CNN training according to the statistical distribution of activation gradients. Meanwhile, we theoretically analyze the impact of pruning algorithm on the…
Object trackers deployed on low-power devices need to be light-weight, however, most of the current state-of-the-art (SOTA) methods rely on using compute-heavy backbones built using CNNs or transformers. Large sizes of such models do not allow their deployment in low-power conditions and designing compressed variants of large tracking models is of great importance. This paper demonstrates how highly compressed light-weight object trackers can be designed using neural architectural pruning of large CNN and transformer based trackers. Further, a comparative study on architectural choices best su…
College of Information Sciences and Technology（信息科学与技术学院）；The Pennsylvania State University（宾夕法尼亚州立大学）；Adobe Research（奥多比研究院）
Model pruning has become a useful technique that improves the computational efficiency of deep learning, making it possible to deploy solutions in resource-limited scenarios. A widely-used practice in relevant work assumes that a smaller-norm parameter or feature plays a less informative role at the inference time. In this paper, we propose a channel pruning technique for accelerating the computations of deep convolutional neural networks (CNNs) that does not critically rely on this assumption. Instead, it focuses on direct simplification of the channel-to-channel computation graph of a CNN wi…
With the general trend of increasing Convolutional Neural Network (CNN) model sizes, model compression and acceleration techniques have become critical for the deployment of these models on edge devices. In this paper, we provide a comprehensive survey on Pruning, a major compression strategy that removes non-critical or redundant neurons from a CNN model. The survey covers the overarching motivation for pruning, different strategies and criteria, their advantages and drawbacks, along with a compilation of major pruning techniques. We conclude the survey with a discussion on alternatives to pr…
Zhejiang University（浙江大学）；University of Sydney（悉尼大学）
Parameter pruning is a promising approach for CNN compression and acceleration by eliminating redundant model parameters with tolerable performance degrade. Despite its effectiveness, existing regularization-based parameter pruning methods usually drive weights towards zero with large and constant regularization factors, which neglects the fragility of the expressiveness of CNNs, and thus calls for a more gentle regularization scheme so that the networks can adapt during pruning. To achieve this, we propose a new and novel regularization-based pruning method, named IncReg, to incrementally ass…
Channel Pruning, widely used for accelerating Convolutional Neural Networks, is an NP-hard problem due to the inter-layer dependency of channel redundancy. Existing methods generally ignored the above dependency for computation simplicity. To solve the problem, under the Bayesian framework, we here propose a layer-wise Recursive Bayesian Pruning method (RBP). A new dropout-based measurement of redundancy, which facilitate the computation of posterior assuming inter-layer dependency, is introduced. Specifically, we model the noise across layers as a Markov chain and target its posterior to refl…
While convolutional neural networks (CNN) have achieved impressive performance on various classification/recognition tasks, they typically consist of a massive number of parameters. This results in significant memory requirement as well as computational overheads. Consequently, there is a growing need for filter-level pruning approaches for compressing CNN based models that not only reduce the total number of parameters but reduce the overall computation as well. We present a new min-max framework for filter-level pruning of CNNs. Our framework, called Play and Prune (PP), jointly prunes and f…
Kernel pruning methods have been proposed to speed up, simplify, and improve explanation of convolutional neural network (CNN) models. However, the effectiveness of a simplified model is often below the original one. In this letter, we present new methods based on objective and subjective relevance criteria for kernel elimination in a layer-by-layer fashion. During the process, a CNN model is retrained only when the current layer is entirely simplified, by adjusting the weights from the next layer to the first one and preserving weights of subsequent layers not involved in the process. We call…
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…
Centre for Vision, Speech；Signal Processing (CVSSP) University of Surrey, UK
We present a method to develop low-complexity convolutional neural networks (CNNs) for acoustic scene classification (ASC). The large size and high computational complexity of typical CNNs is a bottleneck for their deployment on resource-constrained devices. We propose a passive filter pruning framework, where a few convolutional filters from the CNNs are eliminated to yield compressed CNNs. Our hypothesis is that similar filters produce similar responses and give redundant information allowing such filters to be eliminated from the network. To identify similar filters, a cosine distance based…
University of Pittsburgh（匹兹堡大学）；University of Notre Dame（圣母大学）
This work aims to enable on-device training of convolutional neural networks (CNNs) by reducing the computation cost at training time. CNN models are usually trained on high-performance computers and only the trained models are deployed to edge devices. But the statically trained model cannot adapt dynamically in a real environment and may result in low accuracy for new inputs. On-device training by learning from the real-world data after deployment can greatly improve accuracy. However, the high computation cost makes training prohibitive for resource-constrained devices. To tackle this probl…
Singapore University of Technology and Design（新加坡科技设计大学）
Even though the Convolutional Neural Networks (CNN) has shown superior results in the field of computer vision, it is still a challenging task to implement computer vision algorithms in real-time at the edge, especially using a low-cost IoT device due to high memory consumption and computation complexities in a CNN. Network compression methodologies such as weight pruning, filter pruning, and quantization are used to overcome the above mentioned problem. Even though filter pruning methodology has shown better performances compared to other techniques, irregularity of the number of filters prun…
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…
Recent results have revealed an interesting observation in a trained convolutional neural network (CNN), namely, the rank of a feature map channel matrix remains surprisingly constant despite the input images. This has led to an effective rank-based channel pruning algorithm, yet the constant rank phenomenon remains mysterious and unexplained. This work aims at demystifying and interpreting such rank behavior from a frequency-domain perspective, which as a bonus suggests an extremely efficient Fast Fourier Transform (FFT)-based metric for measuring channel importance without explicitly computi…
Don't Be Greedy, Just Relax! Pruning LLMs via Frank-Wolfe
Department for AI in Society, Science, and Technology, Zuse Institute Berlin（人工智能、科学与技术部门，柏林Zuse研究所）；Institute of Mathematics, Technische Universität Berlin（数学研究所，柏林技术大学）；CNRS & D.I. École Normale Supérieure, Paris, France（法国巴黎国家科学研究中心及École Normale Supérieure）
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…
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…
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…
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…
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 Maryland（马里兰大学）；NEC Labs America（NEC美国实验室）
The success of CNNs in various applications is accompanied by a significant increase in the computation and parameter storage costs. Recent efforts toward reducing these overheads involve pruning and compressing the weights of various layers without hurting original accuracy. However, magnitude-based pruning of weights reduces a significant number of parameters from the fully connected layers and may not adequately reduce the computation costs in the convolutional layers due to irregular sparsity in the pruned networks. We present an acceleration method for CNNs, where we prune filters from CN…
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…
