Random masks define surprisingly effective sparse neural network models, as has been shown empirically. The resulting sparse networks can often compete with dense architectures and state-of-the-art lottery ticket pruning algorithms, even though they do not rely on computationally expensive prune-train iterations and can be drawn initially without significant computational overhead. We offer a theoretical explanation of how random masks can approximate arbitrary target networks if they are wider by a logarithmic factor in the inverse sparsity $1 / \log(1/\text{sparsity})$. This overparameterization factor is necessary at least for 3-layer random networks, which elucidates the observed degrading performance of random networks at higher sparsity. At moderate to high sparsity levels, however, our results imply that sparser networks are contained within random source networks so that any dense-to-sparse training scheme can be turned into a computationally more efficient sparse-to-sparse one by constraining the search to a fixed random mask. We demonstrate the feasibility of this approach in experiments for different pruning methods and propose particularly effective choices of initial layer-wise sparsity ratios of the random source network. As a special case, we show theoretically and experimentally that random source networks also contain strong lottery tickets.
The lottery ticket hypothesis states that sparse subnetworks exist in randomly initialized dense networks that can be trained to the same accuracy as the dense network they reside in. However, the subsequent work has failed to replicate this on large-scale models and required rewinding to an early stable state instead of initialization. We show that by using a training method that is stable with respect to linear mode connectivity, large networks can also be entirely rewound to initialization. Our subsequent experiments on common vision tasks give strong credence to the hypothesis in Evci et a…
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…
MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）；Element AI（Element AI公司）；University of Toronto（多伦多大学）；Vector Institute（矢量研究院）
Recent work has explored the possibility of pruning neural networks at initialization. We assess proposals for doing so: SNIP (Lee et al., 2019), GraSP (Wang et al., 2020), SynFlow (Tanaka et al., 2020), and magnitude pruning. Although these methods surpass the trivial baseline of random pruning, they remain below the accuracy of magnitude pruning after training, and we endeavor to understand why. We show that, unlike pruning after training, randomly shuffling the weights these methods prune within each layer or sampling new initial values preserves or improves accuracy. As such, the per-weigh…
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…
Recent advances in deep learning optimization showed that just a subset of parameters are really necessary to successfully train a model. Potentially, such a discovery has broad impact from the theory to application; however, it is known that finding these trainable sub-network is a typically costly process. This inhibits practical applications: can the learned sub-graph structures in deep learning models be found at training time? In this work we explore such a possibility, observing and motivating why common approaches typically fail in the extreme scenarios of interest, and proposing an app…
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…
Robert Bosch GmbH（罗伯特·博世有限公司）；Lübeck University（吕贝克大学）
State-of-the-art deep neural network (DNN) pruning techniques, applied one-shot before training starts, evaluate sparse architectures with the help of a single criterion -- called pruning score. Pruning weights based on a solitary score works well for some architectures and pruning rates but may also fail for other ones. As a common baseline for pruning scores, we introduce the notion of a generalized synaptic score (GSS). In this work we do not concentrate on a single pruning criterion, but provide a framework for combining arbitrary GSSs to create more powerful pruning strategies. These COmb…
Insights into the Lottery Ticket Hypothesis and Iterative Magnitude Pruning
Indian Institute of Technology Delhi（印度理工学院德里分校）；Bharti School of Telecommunication Technology and Management（巴蒂电信技术与管理学院）；Foundation for Innovation and Technology Transfer（创新与技术转移基金会）；On Semiconductors (India)（安森半导体（印度）公司）；Cadence Design Systems（楷登电子公司）；Indian National Science Academy (INSA)（印度国家科学院）
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 …
University of Oxford（牛津大学）；University of Cambridge（剑桥大学）；Samsung AI Center（三星人工智能中心）
Pruning neural networks at initialization would enable us to find sparse models that retain the accuracy of the original network while consuming fewer computational resources for training and inference. However, current methods are insufficient to enable this optimization and lead to a large degradation in model performance. In this paper, we identify a fundamental limitation in the formulation of current methods, namely that their saliency criteria look at a single step at the start of training without taking into account the trainability of the network. While pruning iteratively and graduall…
Random Forest (RF) is an ensemble classification technique that was developed by Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe that there is still room for enhancing and improving its performance in terms of predictive accuracy. This explains why, over the past decade, there have been many extensions of RF where each extension employed a variety of techniques and strategies to improve certain aspect(s) of RF. Since it has been proven empirically that ensembles tend to yield better results when …
Politecnico di Torino（都灵理工大学）；University of Bologna（博洛尼亚大学）
Temporal Convolutional Networks (TCNs) are promising Deep Learning models for time-series processing tasks. One key feature of TCNs is time-dilated convolution, whose optimization requires extensive experimentation. We propose an automatic dilation optimizer, which tackles the problem as a weight pruning on the time-axis, and learns dilation factors together with weights, in a single training. Our method reduces the model size and inference latency on a real SoC hardware target by up to 7.4x and 3x, respectively with no accuracy drop compared to a network without dilation. It also yields a ric…
Mila, McGill University（麦吉尔大学 Mila 研究院）；Georgia Institute of Technology（佐治亚理工学院）；Georgia State University（佐治亚州立大学）；DeepMind
Deep Reinforcement Learning (RL) is a powerful framework for solving complex real-world problems. Large neural networks employed in the framework are traditionally associated with better generalization capabilities, but their increased size entails the drawbacks of extensive training duration, substantial hardware resources, and longer inference times. One way to tackle this problem is to prune neural networks leaving only the necessary parameters. State-of-the-art concurrent pruning techniques for imposing sparsity perform demonstrably well in applications where data distributions are fixed. …
IDEAS Research Institute, Robert Gordon University（罗伯特戈登大学IDEAS研究院）
Random Forest (RF) is an ensemble supervised machine learning technique that was developed by Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe that there is still room for enhancing and improving its performance accuracy. This explains why, over the past decade, there have been many extensions of RF where each extension employed a variety of techniques and strategies to improve certain aspect(s) of RF. Since it has been proven empiricallthat ensembles tend to yield better results when there is a s…
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…
Modern-day neural networks are famously large, yet also highly redundant and compressible; there exist numerous pruning strategies in the deep learning literature that yield over 90% sparser sub-networks of fully-trained, dense architectures while still maintaining their original accuracies. Amongst these many methods though -- thanks to its conceptual simplicity, ease of implementation, and efficacy -- Iterative Magnitude Pruning (IMP) dominates in practice and is the de facto baseline to beat in the pruning community. However, theoretical explanations as to why a simplistic method such as IM…
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 app…
MIT EECS（麻省理工学院电气工程与计算机科学系）；MIT CSAIL（麻省理工学院计算机科学与人工智能实验室）
Magnitude pruning is a common, effective technique to identify sparse subnetworks at little cost to accuracy. In this work, we ask whether a particular architecture's accuracy-sparsity tradeoff can be improved by combining pruning information across multiple runs of training. From a shared ResNet-20 initialization, we train several network copies (\emph{siblings}) to completion using different SGD data orders on CIFAR-10. While the siblings' pruning masks are naively not much more similar than chance, starting sibling training after a few epochs of shared pretraining significantly increases pr…
Deep Neural Networks are highly over-parameterized and the size of the neural networks can be reduced significantly after training without any decrease in performance. One can clearly see this phenomenon in a wide range of architectures trained for various problems. Weight/channel pruning, distillation, quantization, matrix factorization are some of the main methods one can use to remove the redundancy to come up with smaller and faster models. This work starts with a short informative chapter, where we motivate the pruning idea and provide the necessary notation. In the second chapter, we com…
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 …
We propose a simultaneous learning and pruning algorithm capable of identifying and eliminating irrelevant structures in a neural network during the early stages of training. Thus, the computational cost of subsequent training iterations, besides that of inference, is considerably reduced. Our method, based on variational inference principles using Gaussian scale mixture priors on neural network weights, learns the variational posterior distribution of Bernoulli random variables multiplying the units/filters similarly to adaptive dropout. Our algorithm, ensures that the Bernoulli parameters pr…
Learning on Transformers is Provable Low-Rank and Sparse: A One-layer Analysis
Rensselaer Polytechnic Institute（伦斯勒理工学院）；New Jersey Institute of Technology（新泽西理工学院）；Michigan State University（密歇根州立大学）；IBM Thomas J. Watson Research Center（IBM托马斯·J·沃森研究中心）
Is Complexity Required for Neural Network Pruning? A Case Study on Global Magnitude Pruning
Institute for Infocomm Research (I2 R), A*STAR（资讯通信研究院 (I2R)，新加坡科技研究局 (A*STAR)）；National University of Singapore（新加坡国立大学）；Nanyang Technological University（南洋理工大学）
University of Oxford（牛津大学）；ServiceNow；Google Brain；MILA（MILA（蒙特利尔学习算法研究所））
We study an approach to learning pruning masks by optimizing the expected loss of stochastic pruning masks, i.e., masks which zero out each weight independently with some weight-specific probability. We analyze the training dynamics of the induced stochastic predictor in the setting of linear regression, and observe a data-adaptive L1 regularization term, in contrast to the dataadaptive L2 regularization term known to underlie dropout in linear regression. We also observe a preference to prune weights that are less well-aligned with the data labels. We evaluate probabilistic fine-tuning for op…
Pruning the parameters of deep neural networks has generated intense interest due to potential savings in time, memory and energy both during training and at test time. Recent works have identified, through an expensive sequence of training and pruning cycles, the existence of winning lottery tickets or sparse trainable subnetworks at initialization. This raises a foundational question: can we identify highly sparse trainable subnetworks at initialization, without ever training, or indeed without ever looking at the data? We provide an affirmative answer to this question through theory driven …
Today a canonical approach to reduce the computation cost of Deep Neural Networks (DNNs) is to pre-define an over-parameterized model before training to guarantee the learning capacity, and then prune unimportant learning units (filters and neurons) during training to improve model compactness. We argue it is unnecessary to introduce redundancy at the beginning of the training but then reduce redundancy for the ultimate inference model. In this paper, we propose a Continuous Growth and Pruning (CGaP) scheme to minimize the redundancy from the beginning. CGaP starts the training from a small ne…
the University of Texas, Austin（得克萨斯大学奥斯汀分校）；the University of Chicago（芝加哥大学）；Google Research（谷歌研究院）
Recent empirical works show that large deep neural networks are often highly redundant and one can find much smaller subnetworks without a significant drop of accuracy. However, most existing methods of network pruning are empirical and heuristic, leaving it open whether good subnetworks provably exist, how to find them efficiently, and if network pruning can be provably better than direct training using gradient descent. We answer these problems positively by proposing a simple greedy selection approach for finding good subnetworks, which starts from an empty network and greedily adds importa…
On How Iterative Magnitude Pruning Discovers Local Receptive Fields in Fully Connected Neural Networks
UC Santa Barbara（加州大学圣芭芭拉分校）；Johns Hopkins Applied Physics Lab（约翰霍普金斯应用物理实验室）；UT Austin（得克萨斯大学奥斯汀分校）；International Centre for Theoretical Physics（国际理论物理中心）；Radboud University（拉德堡德大学）；International School of Advanced Studies（国际高级研究学院）
Deep neural networks (DNN) are prone to miscalibrated predictions, often exhibiting a mismatch between the predicted output and the associated confidence scores. Contemporary model calibration techniques mitigate the problem of overconfident predictions by pushing down the confidence of the winning class while increasing the confidence of the remaining classes across all test samples. However, from a deployment perspective, an ideal model is desired to (i) generate well-calibrated predictions for high-confidence samples with predicted probability say >0.95, and (ii) generate a higher proportio…
Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology（麻省理工学院计算机科学与人工智能实验室）
Neural network pruning is a popular technique used to reduce the inference costs of modern, potentially overparameterized, networks. Starting from a pre-trained network, the process is as follows: remove redundant parameters, retrain, and repeat while maintaining the same test accuracy. The result is a model that is a fraction of the size of the original with comparable predictive performance (test accuracy). Here, we reassess and evaluate whether the use of test accuracy alone in the terminating condition is sufficient to ensure that the resulting model performs well across a wide spectrum of…
INSA Lyon, CNRS, Ecole Centrale de Lyon, Universite Claude Bernard Lyon 1, Université Lumière Lyon 2, LIRIS, UMR5205（里昂国立应用科学学院、国家科学研究中心、里昂中央理工学院、克莱尔伯恩大学里昂1分校、里昂2大学、LIRIS、UMR5205）
Network pruning and knowledge distillation are two widely-known model compression methods that efficiently reduce computation cost and model size. A common problem in both pruning and distillation is to determine compressed architecture, i.e., the exact number of filters per layer and layer configuration, in order to preserve most of the original model capacity. In spite of the great advances in existing works, the determination of an excellent architecture still requires human interference or tremendous experimentations. In this paper, we propose an architecture slimming method that automates…
Channel pruning is one of the predominant approaches for accelerating deep neural networks. Most existing pruning methods either train from scratch with a sparsity inducing term such as group lasso, or prune redundant channels in a pretrained network and then fine tune the network. Both strategies suffer from some limitations: the use of group lasso is computationally expensive, difficult to converge and often suffers from worse behavior due to the regularization bias. The methods that start with a pretrained network either prune channels uniformly across the layers or prune channels based on …
Pruning AMR: Efficient Visualization of Implicit Neural Representations via Weight Matrix Analysis
Center for Applied Mathematics, Cornell University（应用数学中心，康奈尔大学）；Center for Applied Scientific Computing, Lawrence Livermore National Laboratory（应用科学计算中心，劳伦斯·利弗莫尔国家实验室）
CERC, Polytechnique Montréal（蒙特利尔理工学院计算与工程研究中心）；University of Pisa（比萨大学）；Huawei Montreal Research Centre（华为蒙特利尔研究中心）；Jacobs Technion-Cornell Institute（雅各布斯泰克尼翁-康奈尔研究所）；Cornell Tech（康奈尔理工学院）；Technion - IIT（以色列理工学院）
In Machine Learning, Artificial Neural Networks (ANNs) are a very powerful tool, broadly used in many applications. Often, the selected (deep) architectures include many layers, and therefore a large amount of parameters, which makes training, storage and inference expensive. This motivated a stream of research about compressing the original networks into smaller ones without excessively sacrificing performances. Among the many proposed compression approaches, one of the most popular is \emph{pruning}, whereby entire elements of the ANN (links, nodes, channels, \ldots) and the corresponding we…
Filter pruning has been widely used for neural network compression because of its enabled practical acceleration. To date, most of the existing filter pruning works explore the importance of filters via using intra-channel information. In this paper, starting from an inter-channel perspective, we propose to perform efficient filter pruning using Channel Independence, a metric that measures the correlations among different feature maps. The less independent feature map is interpreted as containing less useful information$/$knowledge, and hence its corresponding filter can be pruned without affe…
Department of Electrical Engineering Yale University（耶鲁大学电气工程系）
Neural network pruning with suitable retraining can yield networks with considerably fewer parameters than the original with comparable degrees of accuracy. Typical pruning methods require large, fully trained networks as a starting point from which they perform a time-intensive iterative pruning and retraining procedure to regain the original accuracy. We propose a novel pruning method that prunes a network real-time during training, reducing the overall training time to achieve an efficient compressed network. We introduce an activation density based analysis to identify the optimal relative…
