The performance of Deep Neural Networks (DNNs) keeps elevating in recent years with increasing network depth and width. To enable DNNs on edge devices like mobile phones, researchers proposed several network compression methods including pruning, quantization and factorization. Among the factorization-based approaches, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple a large prediction loss. As a result, performance usually drops significantly and a sophisticated fine-tuning is required to recover accuracy. We argue that it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training. We propose Trained Rank Pruning (TRP), which iterates low rank approximation and training. TRP maintains the capacity of original network while imposes low-rank constraints during training. A stochastic sub-gradient descent optimized nuclear regularization is utilized to further encourage low rank in TRP. The TRP trained network has low-rank structure in nature, and can be approximated with negligible performance loss, eliminating fine-tuning after low rank approximation. The methods are comprehensively evaluated on CIFAR-10 and ImageNet, outperforming previous compression methods using low rank approximation. Code is available: https://github.com/yuhuixu1993/Trained-Rank-Pruning
University of Tennessee（田纳西大学）；Sun Yat-Sen University（中山大学）；Oak Ridge National Laboratory（橡树岭国家实验室）
Channel-based pruning has achieved significant successes in accelerating deep convolutional neural network, whose pipeline is an iterative three-step procedure: ranking, pruning and fine-tuning. However, this iterative procedure is computationally expensive. In this study, we present a novel computationally efficient channel pruning approach based on the coarse ranking that utilizes the intermediate results during fine-tuning to rank the importance of filters, built upon state-of-the-art works with data-driven ranking criteria. The goal of this work is not to propose a single improved approach…
To accelerate DNNs inference, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pre-trained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, this paper integrates low rank approximation and regularization into the training process. We propose Trained Rank Pruning (TRP), which alternates betw…
Transformer architecture has gained popularity due to its ability to scale with large dataset. Consequently, there is a need to reduce the model size and latency, especially for on-device deployment. We focus on vision transformer proposed for image recognition task (Dosovitskiy et al., 2021), and explore the application of different compression techniques such as low rank approximation and pruning for this purpose. Specifically, we investigate a structured pruning method proposed recently in Zhu et al. (2021) and find that mostly feedforward blocks are pruned with this approach, that too, wit…
Xiamen University（厦门大学）；Youtu Laboratory, Tencent（腾讯优图实验室）；Inception Institute of Artificial Intelligence（人工智能创想研究院）；Mohamed bin Zayed University of Artificial Intelligence（穆罕默德·本·扎耶德人工智能大学）；National Tsing Hua University（国立清华大学）
This paper focuses on filter-level network pruning. A novel pruning method, termed CLR-RNF, is proposed. We first reveal a "long-tail" long-tail pruning problem in magnitude-based weight pruning methods, and then propose a computation-aware measurement for individual weight importance, followed by a Cross-Layer Ranking (CLR) of weights to identify and remove the bottom-ranked weights. Consequently, the per-layer sparsity makes up of the pruned network structure in our filter pruning. Then, we introduce a recommendation-based filter selection scheme where each filter recommends a group of its c…
Xiamen University（厦门大学）；Peng Cheng Laboratory（鹏城实验室）；Pinterest（品趣志）；Beihang University（北京航空航天大学）；Peking University（北京大学）；Inception Institute of Artificial Intelligence（人工智能创想研究院）
Neural network pruning offers a promising prospect to facilitate deploying deep neural networks on resource-limited devices. However, existing methods are still challenged by the training inefficiency and labor cost in pruning designs, due to missing theoretical guidance of non-salient network components. In this paper, we propose a novel filter pruning method by exploring the High Rank of feature maps (HRank). Our HRank is inspired by the discovery that the average rank of multiple feature maps generated by a single filter is always the same, regardless of the number of image batches CNNs rec…
In this paper, we analyze two popular network compression techniques, i.e. filter pruning and low-rank decomposition, in a unified sense. By simply changing the way the sparsity regularization is enforced, filter pruning and low-rank decomposition can be derived accordingly. This provides another flexible choice for network compression because the techniques complement each other. For example, in popular network architectures with shortcut connections (e.g. ResNet), filter pruning cannot deal with the last convolutional layer in a ResBlock while the low-rank decomposition methods can. In addit…
Guilin University of Technology（桂林理工大学）；Southern University of Science and Technology（南方科技大学）；Sichuan University（四川大学）
Unmanned aerial vehicle (UAV) tracking has wide potential applications in such as agriculture, navigation, and public security. However, the limitations of computing resources, battery capacity, and maximum load of UAV hinder the deployment of deep learning-based tracking algorithms on UAV. Consequently, discriminative correlation filters (DCF) trackers stand out in the UAV tracking community because of their high efficiency. However, their precision is usually much lower than trackers based on deep learning. Model compression is a promising way to narrow the gap (i.e., effciency, precision) b…
University of Tennessee（田纳西大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；Sun Yat-Sen University（中山大学）
Most existing channel pruning methods formulate the pruning task from a perspective of inefficiency reduction which iteratively rank and remove the least important filters, or find the set of filters that minimizes some reconstruction errors after pruning. In this work, we investigate the channel pruning from a new perspective with statistical modeling. We hypothesize that the number of filters at a certain layer reflects the level of 'redundancy' in that layer and thus formulate the pruning problem from the aspect of redundancy reduction. Based on both theoretic analysis and empirical studies…
Structured pruning techniques have achieved great compression performance on convolutional neural networks for image classification task. However, the majority of existing methods are weight-oriented, and their pruning results may be unsatisfactory when the original model is trained poorly. That is, a fully-trained model is required to provide useful weight information. This may be time-consuming, and the pruning results are sensitive to the updating process of model parameters. In this paper, we propose a metric named Average Filter Information Entropy (AFIE) to measure the importance of each…
Southern University of Science and Technology（南方科技大学）；University of Technology Sydney（悉尼科技大学）；Fudan University（复旦大学）
This paper proposed a Soft Filter Pruning (SFP) method to accelerate the inference procedure of deep Convolutional Neural Networks (CNNs). Specifically, the proposed SFP enables the pruned filters to be updated when training the model after pruning. SFP has two advantages over previous works: (1) Larger model capacity. Updating previously pruned filters provides our approach with larger optimization space than fixing the filters to zero. Therefore, the network trained by our method has a larger model capacity to learn from the training data. (2) Less dependence on the pre-trained model. Large …
Shanghai Jiao Tong University（上海交通大学）；Qualcomm AI Research（高通人工智能研究院）；Duke University（杜克大学）
To enable DNNs on edge devices like mobile phones, low-rank approximation has been widely adopted because of its solid theoretical rationale and efficient implementations. Several previous works attempted to directly approximate a pretrained model by low-rank decomposition; however, small approximation errors in parameters can ripple over a large prediction loss. As a result, performance usually drops significantly and a sophisticated effort on fine-tuning is required to recover accuracy. Apparently, it is not optimal to separate low-rank approximation from training. Unlike previous works, thi…
When approaching a novel visual recognition problem in a specialized image domain, a common strategy is to start with a pre-trained deep neural network and fine-tune it to the specialized domain. If the target domain covers a smaller visual space than the source domain used for pre-training (e.g. ImageNet), the fine-tuned network is likely to be over-parameterized. However, applying network pruning as a post-processing step to reduce the memory requirements has drawbacks: fine-tuning and pruning are performed independently; pruning parameters are set once and cannot adapt over time; and the hi…
Hong Kong University of Science and Technology（香港科技大学）；Tsinghua University（清华大学）；Megvii Technology（旷视科技）；Huazhong University of Science and Technology（华中科技大学）
In this paper, we propose a novel meta learning approach for automatic channel pruning of very deep neural networks. We first train a PruningNet, a kind of meta network, which is able to generate weight parameters for any pruned structure given the target network. We use a simple stochastic structure sampling method for training the PruningNet. Then, we apply an evolutionary procedure to search for good-performing pruned networks. The search is highly efficient because the weights are directly generated by the trained PruningNet and we do not need any finetuning at search time. With a single P…
The increasing of pre-trained models has significantly facilitated the performance on limited data tasks with transfer learning. However, progress on transfer learning mainly focuses on optimizing the weights of pre-trained models, which ignores the structure mismatch between the model and the target task. This paper aims to improve the transfer performance from another angle - in addition to tuning the weights, we tune the structure of pre-trained models, in order to better match the target task. To this end, we propose TransTailor, targeting at pruning the pre-trained model for improved tran…
Deep Neural nets (NNs) with millions of parameters are at the heart of many state-of-the-art computer vision systems today. However, recent works have shown that much smaller models can achieve similar levels of performance. In this work, we address the problem of pruning parameters in a trained NN model. Instead of removing individual weights one at a time as done in previous works, we remove one neuron at a time. We show how similar neurons are redundant, and propose a systematic way to remove them. Our experiments in pruning the densely connected layers show that we can remove upto 85\% of …
University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
This paper presents a method for adding multiple tasks to a single deep neural network while avoiding catastrophic forgetting. Inspired by network pruning techniques, we exploit redundancies in large deep networks to free up parameters that can then be employed to learn new tasks. By performing iterative pruning and network re-training, we are able to sequentially "pack" multiple tasks into a single network while ensuring minimal drop in performance and minimal storage overhead. Unlike prior work that uses proxy losses to maintain accuracy on older tasks, we always optimize for the task at han…
Bar-Ilan University（巴伊兰大学）；College of Law and Business（法律与商业学院）
The rise of neural network (NN) applications has prompted an increased interest in compression, with a particular focus on channel pruning, which does not require any additional hardware. Most pruning methods employ either single-layer operations or global schemes to determine which channels to remove followed by fine-tuning of the network. In this paper we present Gator, a channel-pruning method which temporarily adds learned gating mechanisms for pruning of individual channels, and which is trained with an additional auxiliary loss, aimed at reducing the computational cost due to memory, (th…
George Mason University（乔治梅森大学）；Clarkson University（克拉克森大学）
Based on filter magnitude ranking (e.g. L1 norm), conventional filter pruning methods for Convolutional Neural Networks (CNNs) have been proved with great effectiveness in computation load reduction. Although effective, these methods are rarely analyzed in a perspective of filter functionality. In this work, we explore the filter pruning and the retraining through qualitative filter functionality interpretation. We find that the filter magnitude based method fails to eliminate the filters with repetitive functionality. And the retraining phase is actually used to reconstruct the remained filte…
ETH Zurich（苏黎世联邦理工学院）；University of Cambridge（剑桥大学）
Structured pruning is a well-known technique to reduce the storage size and inference cost of neural networks. The usual pruning pipeline consists of ranking the network internal filters and activations with respect to their contributions to the network performance, removing the units with the lowest contribution, and fine-tuning the network to reduce the harm induced by pruning. Recent results showed that random pruning performs on par with other metrics, given enough fine-tuning resources. In this work, we show that this is not true on a low-data regime when fine-tuning is either not possibl…
Xiamen University（厦门大学）；University of Chinese Academy of Sciences（中国科学院大学）；Peking University（北京大学）；Huawei Technologies Co. Ltd.（华为技术有限公司）
We propose a novel network pruning approach by information preserving of pre-trained network weights (filters). Network pruning with the information preserving is formulated as a matrix sketch problem, which is efficiently solved by the off-the-shelf Frequent Direction method. Our approach, referred to as FilterSketch, encodes the second-order information of pre-trained weights, which enables the representation capacity of pruned networks to be recovered with a simple fine-tuning procedure. FilterSketch requires neither training from scratch nor data-driven iterative optimization, leading to a…
This paper presents an efficient and robust approach for reducing the size of deep neural networks by pruning entire neurons. It exploits maxout units for combining neurons into more complex convex functions and it makes use of a local relevance measurement that ranks neurons according to their activation on the training set for pruning them. Additionally, a parameter reduction comparison between neuron and weight pruning is shown. It will be empirically shown that the proposed neuron pruning reduces the number of parameters dramatically. The evaluation is performed on two tasks, the MNIST han…
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）
Network pruning is widely used to compress Deep Neural Networks (DNNs). The Soft Filter Pruning (SFP) method zeroizes the pruned filters during training while updating them in the next training epoch. Thus the trained information of the pruned filters is completely dropped. To utilize the trained pruned filters, we proposed a SofteR Filter Pruning (SRFP) method and its variant, Asymptotic SofteR Filter Pruning (ASRFP), simply decaying the pruned weights with a monotonic decreasing parameter. Our methods perform well across various networks, datasets and pruning rates, also transferable to weig…
Structural pruning can simplify network architecture and improve inference speed. We propose Hardware-Aware Latency Pruning (HALP) that formulates structural pruning as a global resource allocation optimization problem, aiming at maximizing the accuracy while constraining latency under a predefined budget on targeting device. For filter importance ranking, HALP leverages latency lookup table to track latency reduction potential and global saliency score to gauge accuracy drop. Both metrics can be evaluated very efficiently during pruning, allowing us to reformulate global structural pruning un…
Department of Computer Science and Engineering（计算机科学与工程系）；Robert Bosch Centre for Data Science and AI (RBC-DSAI)（罗伯特·博世数据科学与人工智能中心（RBC-DSAI））；Indian Institute of Technology Madras（印度理工学院马德拉斯分校）
Recently there has been a lot of work on pruning filters from deep convolutional neural networks (CNNs) with the intention of reducing computations. The key idea is to rank the filters based on a certain criterion (say, $l_1$-norm, average percentage of zeros, etc) and retain only the top ranked filters. Once the low scoring filters are pruned away the remainder of the network is fine tuned and is shown to give performance comparable to the original unpruned network. In this work, we report experiments which suggest that the comparable performance of the pruned network is not due to the specif…
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 Pisa（比萨大学）；TU Graz（格拉茨工业大学）；CSH Vienna（维也纳复杂科学中心）
We study the impact of different pruning techniques on the representation learned by deep neural networks trained with contrastive loss functions. Our work finds that at high sparsity levels, contrastive learning results in a higher number of misclassified examples relative to models trained with traditional cross-entropy loss. To understand this pronounced difference, we use metrics such as the number of PIEs (Hooker et al., 2019), Q-Score (Kalibhat et al., 2022), and PD-Score (Baldock et al., 2021) to measure the impact of pruning on the learned representation quality. Our analysis suggests …
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…
Osaka University（大阪大学）；University of Electronic Science and Technology of China（电子科技大学）
Recently, tile pruning has been widely studied to accelerate the inference of deep neural networks (DNNs). However, we found that the loss due to tile pruning, which can eliminate important elements together with unimportant elements, is large on trained DNNs. In this study, we propose a one-shot reparameterization method, called TileTrans, to reduce the loss of tile pruning. Specifically, we repermute the rows or columns of the weight matrix such that the model architecture can be kept unchanged after reparameterization. This repermutation realizes the reparameterization of the DNN model with…
Neural networks are both computationally intensive and memory intensive, making them difficult to deploy on embedded systems with limited hardware resources. To address this limitation, we introduce "deep compression", a three stage pipeline: pruning, trained quantization and Huffman coding, that work together to reduce the storage requirement of neural networks by 35x to 49x without affecting their accuracy. Our method first prunes the network by learning only the important connections. Next, we quantize the weights to enforce weight sharing, finally, we apply Huffman coding. After the first …
Structured pruning is a popular method for compressing a neural network: given a large trained network, one alternates between removing channel connections and fine-tuning; reducing the overall width of the network. However, the efficacy of structured pruning has largely evaded scrutiny. In this paper, we examine ResNets and DenseNets obtained through structured pruning-and-tuning and make two interesting observations: (i) reduced networks---smaller versions of the original network trained from scratch---consistently outperform pruned networks; (ii) if one takes the architecture of a pruned ne…
Facebook AI Research（脸书人工智能研究院）；Univ. Grenoble Alpes（格勒诺布尔阿尔卑斯大学）；Inria（法国国家信息与自动化研究所）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立理工学院）
Convolutional neural networks trained without supervision come close to matching performance with supervised pre-training, but sometimes at the cost of an even higher number of parameters. Extracting subnetworks from these large unsupervised convnets with preserved performance is of particular interest to make them less computationally intensive. Typical pruning methods operate during training on a task while trying to maintain the performance of the pruned network on the same task. However, in self-supervised feature learning, the training objective is agnostic on the representation transfera…
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…
Adversarial pruning compresses models while preserving robustness. Current methods require access to adversarial examples during pruning. This significantly hampers training efficiency. Moreover, as new adversarial attacks and training methods develop at a rapid rate, adversarial pruning methods need to be modified accordingly to keep up. In this work, we propose a novel framework to prune a previously trained robust neural network while maintaining adversarial robustness, without further generating adversarial examples. We leverage concurrent self-distillation and pruning to preserve knowledg…
The computation and memory needed for Convolutional Neural Network (CNN) inference can be reduced by pruning weights from the trained network. Pruning is guided by a pruning saliency, which heuristically approximates the change in the loss function associated with the removal of specific weights. Many pruning signals have been proposed, but the performance of each heuristic depends on the particular trained network. This leaves the data scientist with a difficult choice. When using any one saliency metric for the entire pruning process, we run the risk of the metric assumptions being invalidat…
Structural pruning can simplify network architecture and improve inference speed. We propose Hardware-Aware Latency Pruning (HALP) that formulates structural pruning as a global resource allocation optimization problem, aiming at maximizing the accuracy while constraining latency under a predefined budget. For filter importance ranking, HALP leverages latency lookup table to track latency reduction potential and global saliency score to gauge accuracy drop. Both metrics can be evaluated very efficiently during pruning, allowing us to reformulate global structural pruning under a reward maximiz…
Pruning enables appealing reductions in network memory footprint and time complexity. Conventional post-training pruning techniques lean towards efficient inference while overlooking the heavy computation for training. Recent exploration of pre-training pruning at initialization hints on training cost reduction via pruning, but suffers noticeable performance degradation. We attempt to combine the benefits of both directions and propose a policy that prunes as early as possible during training without hurting performance. Instead of pruning at initialization, our method exploits initial dense t…
Center for Applied Scientific Computing（应用科学计算中心）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
Recently, Frankle & Carbin (2019) demonstrated that randomly-initialized dense networks contain subnetworks that once found can be trained to reach test accuracy comparable to the trained dense network. However, finding these high performing trainable subnetworks is expensive, requiring iterative process of training and pruning weights. In this paper, we propose (and prove) a stronger Multi-Prize Lottery Ticket Hypothesis: A sufficiently over-parameterized neural network with random weights contains several subnetworks (winning tickets) that (a) have comparable accuracy to a dense target netwo…
Unstructured neural network pruning algorithms have achieved impressive compression rates. However, the resulting - typically irregular - sparse matrices hamper efficient hardware implementations, leading to additional memory usage and complex control logic that diminishes the benefits of unstructured pruning. This has spurred structured coarse-grained pruning solutions that prune entire filters or even layers, enabling efficient implementation at the expense of reduced flexibility. Here we propose a flexible new pruning mechanism that facilitates pruning at different granularities (weights, k…
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…
SenseTime Research（商汤科技研究院）；The University of Hong Kong（香港大学）；Sun Yat-Sen University（中山大学）；The Chinese University of Hong Kong（香港中文大学）
Channel pruning is a popular technique for compressing convolutional neural networks (CNNs), where various pruning criteria have been proposed to remove the redundant filters. From our comprehensive experiments, we found two blind spots in the study of pruning criteria: (1) Similarity: There are some strong similarities among several primary pruning criteria that are widely cited and compared. According to these criteria, the ranks of filters'Importance Score are almost identical, resulting in similar pruned structures. (2) Applicability: The filters'Importance Score measured by some pruning c…
In recent years, deep neural networks have known a wide success in various application domains. However, they require important computational and memory resources, which severely hinders their deployment, notably on mobile devices or for real-time applications. Neural networks usually involve a large number of parameters, which correspond to the weights of the network. Such parameters, obtained with the help of a training process, are determinant for the performance of the network. However, they are also highly redundant. The pruning methods notably attempt to reduce the size of the parameter …
Budgeted pruning is the problem of pruning under resource constraints. In budgeted pruning, how to distribute the resources across layers (i.e., sparsity allocation) is the key problem. Traditional methods solve it by discretely searching for the layer-wise pruning ratios, which lacks efficiency. In this paper, we propose Differentiable Sparsity Allocation (DSA), an efficient end-to-end budgeted pruning flow. Utilizing a novel differentiable pruning process, DSA finds the layer-wise pruning ratios with gradient-based optimization. It allocates sparsity in continuous space, which is more effici…
Pruning Deep Neural Networks (DNNs) is a prominent field of study in the goal of inference runtime acceleration. In this paper, we introduce a novel data-free pruning protocol RED++. Only requiring a trained neural network, and not specific to DNN architecture, we exploit an adaptive data-free scalar hashing which exhibits redundancies among neuron weight values. We study the theoretical and empirical guarantees on the preservation of the accuracy from the hashing as well as the expected pruning ratio resulting from the exploitation of said redundancies. We propose a novel data-free pruning te…
