Existing generalization measures that aim to capture a model's simplicity based on parameter counts or norms fail to explain generalization in overparameterized deep neural networks. In this paper, we introduce a new, theoretically motivated measure of a network's simplicity which we call prunability: the smallest \emph{fraction} of the network's parameters that can be kept while pruning without adversely affecting its training loss. We show that this measure is highly predictive of a model's generalization performance across a large set of convolutional networks trained on CIFAR-10, does not grow with network size unlike existing pruning-based measures, and exhibits high correlation with test set loss even in a particularly challenging double descent setting. Lastly, we show that the success of prunability cannot be explained by its relation to known complexity measures based on models' margin, flatness of minima and optimization speed, finding that our new measure is similar to -- but more predictive than -- existing flatness-based measures, and that its predictions exhibit low mutual information with those of other baselines.
Qian Xuesen Laboratory of Space Technology, China Academy of Space Technology（中国空间技术研究院钱学森空间技术实验室）；School of Mathematics and Statistics, Wuhan University（武汉大学数学与统计学院）
With the growth of interest in the attack and defense of deep neural networks, researchers are focusing more on the robustness of applying them to devices with limited memory. Thus, unlike adversarial training, which only considers the balance between accuracy and robustness, we come to a more meaningful and critical issue, i.e., the balance among accuracy, efficiency and robustness (AER). Recently, some related works focused on this issue, but with different observations, and the relations among AER remain unclear. This paper first investigates the robustness of pruned models with different c…
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…
MIT（麻省理工学院）；University of Toronto（多伦多大学）；Vector Institute（向量研究所）；MosaicML（MosaicML公司）；Google Research（谷歌研究院）
Practitioners frequently observe that pruning improves model generalization. A long-standing hypothesis based on bias-variance trade-off attributes this generalization improvement to model size reduction. However, recent studies on over-parameterization characterize a new model size regime, in which larger models achieve better generalization. Pruning models in this over-parameterized regime leads to a contradiction -- while theory predicts that reducing model size harms generalization, pruning to a range of sparsities nonetheless improves it. Motivated by this contradiction, we re-examine pru…
Network pruning has been known to produce compact models without much accuracy degradation. However, how the pruning process affects a network's robustness and the working mechanism behind remain unresolved. In this work, we theoretically prove that the sparsity of network weights is closely associated with model robustness. Through experiments on a variety of adversarial pruning methods, we find that weights sparsity will not hurt but improve robustness, where both weights inheritance from the lottery ticket and adversarial training improve model robustness in network pruning. Based on these …
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…
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…
Artificial neural networks (ANNs) may not be worth their computational/memory costs when used in mobile phones or embedded devices. Parameter-pruning algorithms combat these costs, with some algorithms capable of removing over 90% of an ANN's weights without harming the ANN's performance. Removing weights from an ANN is a form of regularization, but existing pruning algorithms do not significantly improve generalization error. We show that pruning ANNs can improve generalization if pruning targets large weights instead of small weights. Applying our pruning algorithm to an ANN leads to a highe…
The University of Tokyo（东京大学）；RIKEN（日本理化学研究所）；iPride Co., Ltd.（iPride株式会社）；NTT DATA Mathematical Systems Inc.（NTT数据数学系统公司）；NTT Data Corporation（NTT数据公司）
Compression techniques for deep neural network models are becoming very important for the efficient execution of high-performance deep learning systems on edge-computing devices. The concept of model compression is also important for analyzing the generalization error of deep learning, known as the compression-based error bound. However, there is still huge gap between a practically effective compression method and its rigorous background of statistical learning theory. To resolve this issue, we develop a new theoretical framework for model compression and propose a new pruning method called {…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；The Ohio State University（俄亥俄州立大学）；IBM Thomas.J. Watson Research Center（IBM托马斯·J·沃森研究中心）；Pinterest
It has been observed in practice that applying pruning-at-initialization methods to neural networks and training the sparsified networks can not only retain the testing performance of the original dense models, but also sometimes even slightly boost the generalization performance. Theoretical understanding for such experimental observations are yet to be developed. This work makes the first attempt to study how different pruning fractions affect the model's gradient descent dynamics and generalization. Specifically, this work considers a classification task for overparameterized two-layer neur…
The ability of Deep Neural Networks to approximate highly complex functions is key to their success. This benefit, however, comes at the expense of a large model size, which challenges its deployment in resource-constrained environments. Pruning is an effective technique used to limit this issue, but often comes at the cost of reduced accuracy and adversarial robustness. This paper addresses these shortcomings and introduces Deadwooding, a novel global pruning technique that exploits a Lagrangian Dual method to encourage model sparsity while retaining accuracy and ensuring robustness. The resu…
Deep neural networks have achieved impressive performance in many applications but their large number of parameters lead to significant computational and storage overheads. Several recent works attempt to mitigate these overheads by designing compact networks using pruning of connections. However, we observe that most of the existing strategies to design compact networks fail to preserve network robustness against adversarial examples. In this work, we rigorously study the extension of network pruning strategies to preserve both benign accuracy and robustness of a network. Starting with a form…
Recent studies show that even highly biased dense networks contain an unbiased substructure that can achieve better out-of-distribution (OOD) generalization than the original model. Existing works usually search the invariant subnetwork using modular risk minimization (MRM) with out-domain data. Such a paradigm may bring about two potential weaknesses: 1) Unfairness, due to the insufficient observation of out-domain data during training; and 2) Sub-optimal OOD generalization, due to the feature-untargeted model pruning on the whole data distribution. In this paper, we propose a novel Spurious …
Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike other works, our method pays special attention to the quality of the solution in the compressed model and inference computation time by pruning neurons. The proposed algorithm directs the parameters of the compressed model toward a flatter solution by exploring the spectral radius of Hessian which results in better generalization on unseen data. Moreover, t…
Adversarial Pruning: A Survey and Benchmark of Pruning Methods for Adversarial Robustness
University of Cagliari（卡利亚里大学）；Sapienza University of Rome（罗马大学）；University of Genova（热那亚大学）；CINI, National Cybersecurity Lab, Consorzio Interuniversitario Nazionale per l’Informatica（意大利国家跨大学信息学联盟国家网络安全实验室）
Amazon AI（亚马逊人工智能）；UT Austin（得克萨斯大学奥斯汀分校）；UC Irvine（加利福尼亚大学欧文分校）；CMU（卡内基梅隆大学）；Caltech（加州理工学院）；Imperial College London（伦敦帝国理工学院）
Neural networks are known to be vulnerable to adversarial examples. Carefully chosen perturbations to real images, while imperceptible to humans, induce misclassification and threaten the reliability of deep learning systems in the wild. To guard against adversarial examples, we take inspiration from game theory and cast the problem as a minimax zero-sum game between the adversary and the model. In general, for such games, the optimal strategy for both players requires a stochastic policy, also known as a mixed strategy. In this light, we propose Stochastic Activation Pruning (SAP), a mixed st…
University of Technology Sydney（悉尼科技大学）；Baidu Research（百度研究院）
The great success of deep learning heavily relies on increasingly larger training data, which comes at a price of huge computational and infrastructural costs. This poses crucial questions that, do all training data contribute to model's performance? How much does each individual training sample or a sub-training-set affect the model's generalization, and how to construct the smallest subset from the entire training data as a proxy training set without significantly sacrificing the model's performance? To answer these, we propose dataset pruning, an optimization-based sample selection method t…
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…
Nanjing University of Information Science and Technology（南京信息工程大学）；JD Finance America Corporation（京东金融美国公司）
Meta-learning is a powerful paradigm for few-shot learning. Although with remarkable success witnessed in many applications, the existing optimization based meta-learning models with over-parameterized neural networks have been evidenced to ovetfit on training tasks. To remedy this deficiency, we propose a network pruning based meta-learning approach for overfitting reduction via explicitly controlling the capacity of network. A uniform concentration analysis reveals the benefit of network capacity constraint for reducing generalization gap of the proposed meta-learner. We have implemented our…
University of California, Irvine（加州大学欧文分校）；University of California, Los Angeles（加州大学洛杉矶分校）
Deep neural nets (DNNs) compression is crucial for adaptation to mobile devices. Though many successful algorithms exist to compress naturally trained DNNs, developing efficient and stable compression algorithms for robustly trained DNNs remains widely open. In this paper, we focus on a co-design of efficient DNN compression algorithms and sparse neural architectures for robust and accurate deep learning. Such a co-design enables us to advance the goal of accommodating both sparsity and robustness. With this objective in mind, we leverage the relaxed augmented Lagrangian based algorithms to pr…
University of Science and Technology of China (USTC)（中国科学技术大学）
Ensembles, as a widely used and effective technique in the machine learning community, succeed within a key element -- "diversity." The relationship between diversity and generalization, unfortunately, is not entirely understood and remains an open research issue. To reveal the effect of diversity on the generalization of classification ensembles, we investigate three issues on diversity, i.e., the measurement of diversity, the relationship between the proposed diversity and the generalization error, and the utilization of this relationship for ensemble pruning. In the diversity measurement, w…
Nanyang Technological University（南洋理工大学）；City University of Hong Kong（香港城市大学）
Filter pruning has been widely used for compressing convolutional neural networks to reduce computation costs during the deployment stage. Recent studies have shown that filter pruning techniques can achieve lossless compression of deep neural networks, reducing redundant filters (kernels) without sacrificing accuracy performance. However, the evaluation is done when the training and testing data are from similar environmental conditions (independent and identically distributed), and how the filter pruning techniques would affect the cross-domain generalization (out-of-distribution) performanc…
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…
New Jersey Institute of Technology（新泽西理工学院）；Microsoft Research（微软研究院）；Rice University（莱斯大学）
Recent work has focused on compressing pre-trained language models (PLMs) like BERT where the major focus has been to improve the in-distribution performance for downstream tasks. However, very few of these studies have analyzed the impact of compression on the generalizability and robustness of compressed models for out-of-distribution (OOD) data. Towards this end, we study two popular model compression techniques including knowledge distillation and pruning and show that the compressed models are significantly less robust than their PLM counterparts on OOD test sets although they obtain simi…
Neural network pruning is frequently used to compress over-parameterized networks by large amounts, while incurring only marginal drops in generalization performance. However, the impact of pruning on networks that have been highly optimized for efficient inference has not received the same level of attention. In this paper, we analyze the effect of pruning for computer vision, and study state-of-the-art ConvNets, such as the FBNetV3 family of models. We show that model pruning approaches can be used to further optimize networks trained through NAS (Neural Architecture Search). The resulting f…
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…
Tsinghua University（清华大学）；IBM Research（IBM研究院）；University of California, Los Angeles（加州大学洛杉矶分校）；SenseTime Research（商汤科技研究院）；Northeastern University（东北大学）
It is well known that deep neural networks (DNNs) are vulnerable to adversarial attacks, which are implemented by adding crafted perturbations onto benign examples. Min-max robust optimization based adversarial training can provide a notion of security against adversarial attacks. However, adversarial robustness requires a significantly larger capacity of the network than that for the natural training with only benign examples. This paper proposes a framework of concurrent adversarial training and weight pruning that enables model compression while still preserving the adversarial robustness a…
In safety-critical but computationally resource-constrained applications, deep learning faces two key challenges: lack of robustness against adversarial attacks and large neural network size (often millions of parameters). While the research community has extensively explored the use of robust training and network pruning independently to address one of these challenges, only a few recent works have studied them jointly. However, these works inherit a heuristic pruning strategy that was developed for benign training, which performs poorly when integrated with robust training techniques, includ…
University of Massachusetts Amherst（马萨诸塞大学阿默斯特分校）；State University of Rio de Janeiro（里约热内卢州立大学）
The prevalence and success of Deep Neural Network (DNN) applications in recent years have motivated research on DNN compression, such as pruning and quantization. These techniques accelerate model inference, reduce power consumption, and reduce the size and complexity of the hardware necessary to run DNNs, all with little to no loss in accuracy. However, since DNNs are vulnerable to adversarial inputs, it is important to consider the relationship between compression and adversarial robustness. In this work, we investigate the adversarial robustness of models produced by several irregular pruni…
We propose a simple and easy to implement neural network compression algorithm that achieves results competitive with more complicated state-of-the-art methods. The key idea is to modify the original optimization problem by adding K independent Gaussian priors (corresponding to the k-means objective) over the network parameters to achieve parameter quantization, as well as an L1 penalty to achieve pruning. Unlike many existing quantization-based methods, our method uses hard clustering assignments of network parameters, which adds minimal change or overhead to standard network training. We als…
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 Texas at Austin（德克萨斯大学奥斯汀分校）；Carnegie Mellon University（卡内基梅隆大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）；Michigan State University（密歇根州立大学）；MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
Certifiable robustness is a highly desirable property for adopting deep neural networks (DNNs) in safety-critical scenarios, but often demands tedious computations to establish. The main hurdle lies in the massive amount of non-linearity in large DNNs. To trade off the DNN expressiveness (which calls for more non-linearity) and robustness certification scalability (which prefers more linearity), we propose a novel solution to strategically manipulate neurons, by "grafting" appropriate levels of linearity. The core of our proposal is to first linearize insignificant ReLU neurons, to eliminate t…
GPrune-LLM: Generalization-Aware Structured Pruning for Large Language Models
Department of Computing, The Hong Kong Polytechnic University, Hong Kong（香港理工大学计算机系）；School of Artificial Intelligence and Data Science, IIT Jodhpur（IIT朱罗浦人工智能与数据科学学院）
