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 possible or not effective. In this case, reducing the harm caused by pruning becomes crucial to retain the performance of the network. First, we analyze the problem of estimating the contribution of hidden units with tools suggested by cooperative game theory and propose Shapley values as a principled ranking metric for this task. We compare with several alternatives proposed in the literature and discuss how Shapley values are theoretically preferable. Finally, we compare all ranking metrics on the challenging scenario of low-data pruning, where we demonstrate how Shapley values outperform other heuristics.
To prune or not to prune : A chaos-causality approach to principled pruning of dense neural networks
Birla Institute of Technology and Sciences Pilani（皮拉尼伯拉理工学院）；BITS Pilani, Goa Campus（皮拉尼伯拉理工学院果阿校区）；National Institute of Advanced Studies（国家高等研究院）；Nitte Meenakshi Institute of Technology（尼特·米纳克希理工学院）；HappyMonk AI（HappyMonk人工智能公司）
Overparameterized Neural Networks (NN) display state-of-the-art performance. However, there is a growing need for smaller, energy-efficient, neural networks tobe able to use machine learning applications on devices with limited computational resources. A popular approach consists of using pruning techniques. While these techniques have traditionally focused on pruning pre-trained NN (LeCun et al.,1990; Hassibi et al., 1993), recent work by Lee et al. (2018) has shown promising results when pruning at initialization. However, for Deep NNs, such procedures remain unsatisfactory as the resulting …
Network pruning in Convolutional Neural Networks (CNNs) has been extensively investigated in recent years. To determine the impact of pruning a group of filters on a network's accuracy, state-of-the-art pruning methods consistently assume filters of a CNN are independent. This allows the importance of a group of filters to be estimated as the sum of importances of individual filters. However, overparameterization in modern networks results in highly correlated filters that invalidate this assumption, thereby resulting in incorrect importance estimates. To address this issue, we propose OrthoRe…
Predicting human fixations from images has recently seen large improvements by leveraging deep representations which were pretrained for object recognition. However, as we show in this paper, these networks are highly overparameterized for the task of fixation prediction. We first present a simple yet principled greedy pruning method which we call Fisher pruning. Through a combination of knowledge distillation and Fisher pruning, we obtain much more runtime-efficient architectures for saliency prediction, achieving a 10x speedup for the same AUC performance as a state of the art network on the…
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…
University of California, Riverside（加州大学河滨分校）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
Model pruning is an essential procedure for building compact and computationally-efficient machine learning models. A key feature of a good pruning algorithm is that it accurately quantifies the relative importance of the model weights. While model pruning has a rich history, we still don't have a full grasp of the pruning mechanics even for relatively simple problems involving linear models or shallow neural nets. In this work, we provide a principled exploration of pruning by building on a natural notion of importance. For linear models, we show that this notion of importance is captured by …
Convolutional neural networks (CNNs) are typically over-parameterized, bringing considerable computational overhead and memory footprint in inference. Pruning a proportion of unimportant filters is an efficient way to mitigate the inference cost. For this purpose, identifying unimportant convolutional filters is the key to effective filter pruning. Previous work prunes filters according to either their weight norms or the corresponding batch-norm scaling factors, while neglecting the sequential dependency between adjacent layers. In this paper, we further develop the norm-based importance esti…
OTPrune: Distribution-Aligned Visual Token Pruning via Optimal Transport
Morgan Stanley（摩根士丹利）；Clemson University（克莱姆森大学）；Arizona State University（亚利桑那州立大学）；Washington University in St. Louis（圣路易斯华盛顿大学）；Texas A&M University（德克萨斯农工大学）；Rice University（莱斯大学）；Florida State University（佛罗里达州立大学）
LiePrune: Lie Group and Quantum Geometric Dual Representation for One-Shot Structured Pruning of Quantum Neural Networks
School of Computer, Jiangsu University of Science and Technology（江苏科技大学计算机学院）；Department of Electrical and Computer Engineering, University of Nevada, Las Vegas（内华达大学拉斯维加斯分校电子与计算机工程系）
Kuaishou Technology（快手科技）；University of Texas at Austin（德克萨斯大学奥斯汀分校）
Model compression techniques are recently gaining explosive attention for obtaining efficient AI models for various real-time applications. Channel pruning is one important compression strategy and is widely used in slimming various DNNs. Previous gate-based or importance-based pruning methods aim to remove channels whose importance is smallest. However, it remains unclear what criteria the channel importance should be measured on, leading to various channel selection heuristics. Some other sampling-based pruning methods deploy sampling strategies to train sub-nets, which often causes the trai…
PreFIQs: Face Image Quality Is What Survives Pruning
Fraunhofer Institute for Computer Graphics Research IGD（弗劳恩霍夫计算机图形研究研究所IGD）；University of Ljubljana（卢布尔雅那大学）；Technical University of Darmstadt（达姆施塔特技术大学）
EntropyPrune: Matrix Entropy Guided Visual Token Pruning for Multimodal Large Language Models
School of Computer Science and Technology, Tongji University（同济大学计算机科学与技术学院）；University of California, Santa Cruz（加州大学圣克ruz分校）；East China Normal University（华东师范大学）；Shanghai Eye Disease Prevention and Treatment Center（上海眼病预防与治疗中心）
On-device Content-based Recommendation with Single-shot Embedding Pruning: A Cooperative Game Perspective
The University of Queensland（昆士兰大学）；Beijing University of Posts and Telecommunications（北京邮电大学）；Griffith University（格里菲斯大学）；University of Electronic Science and Technology of China（电子科技大学）
AstraZeneca（阿斯利康）；The University of Edinburgh（爱丁堡大学）；Toulouse School of Economics（图卢兹经济学院）；Institute for Advanced Study in Toulouse（图卢兹高等研究院）；Central European University（中欧大学）
Over the last few years, the Shapley value, a solution concept from cooperative game theory, has found numerous applications in machine learning. In this paper, we first discuss fundamental concepts of cooperative game theory and axiomatic properties of the Shapley value. Then we give an overview of the most important applications of the Shapley value in machine learning: feature selection, explainability, multi-agent reinforcement learning, ensemble pruning, and data valuation. We examine the most crucial limitations of the Shapley value and point out directions for future research.
The number of linear regions has been studied as a proxy of complexity for ReLU networks. However, the empirical success of network compression techniques like pruning and knowledge distillation, suggest that in the overparameterized setting, linear regions density might fail to capture the effective nonlinearity. In this work, we propose an efficient algorithm for discovering linear regions and use it to investigate the effectiveness of density in capturing the nonlinearity of trained VGGs and ResNets on CIFAR-10 and CIFAR-100. We contrast the results with a more principled nonlinearity measu…
What is the value of an individual model in an ensemble of binary classifiers? We answer this question by introducing a class of transferable utility cooperative games called \textit{ensemble games}. In machine learning ensembles, pre-trained models cooperate to make classification decisions. To quantify the importance of models in these ensemble games, we define \textit{Troupe} -- an efficient algorithm which allocates payoffs based on approximate Shapley values of the classifiers. We argue that the Shapley value of models in these games is an effective decision metric for choosing a high per…
University of Tübingen（图宾根大学）；Tübingen AI Center（图宾根人工智能中心）
In explainable machine learning, local post-hoc explanation algorithms and inherently interpretable models are often seen as competing approaches. This work offers a partial reconciliation between the two by establishing a correspondence between Shapley Values and Generalized Additive Models (GAMs). We introduce $n$-Shapley Values, a parametric family of local post-hoc explanation algorithms that explain individual predictions with interaction terms up to order $n$. By varying the parameter $n$, we obtain a sequence of explanations that covers the entire range from Shapley Values up to a uniqu…
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…
Shapley-Value-Based Graph Sparsification for GNN Inference
Department of Intelligent Systems Engineering Indiana University Bloomington Bloomington Indiana USA；Department of Computer Science \& Engineering Texas A\&M University College Station Texas USA；Indiana University Bloomington；Texas A\&M University
Distributional data Shapley value (DShapley) has recently been proposed as a principled framework to quantify the contribution of individual datum in machine learning. DShapley develops the foundational game theory concept of Shapley values into a statistical framework and can be applied to identify data points that are useful (or harmful) to a learning algorithm. Estimating DShapley is computationally expensive, however, and this can be a major challenge to using it in practice. Moreover, there has been little mathematical analyses of how this value depends on data characteristics. In this pa…
As data becomes the fuel driving technological and economic growth, a fundamental challenge is how to quantify the value of data in algorithmic predictions and decisions. For example, in healthcare and consumer markets, it has been suggested that individuals should be compensated for the data that they generate, but it is not clear what is an equitable valuation for individual data. In this work, we develop a principled framework to address data valuation in the context of supervised machine learning. Given a learning algorithm trained on $n$ data points to produce a predictor, we propose data…
Energy-Based Model for Accurate Estimation of Shapley Values in Feature Attribution
College of Metrology Measurement and Instrument, China Jiliang University（计量测量与仪器学院，中国浙江理工大学）；School of Mathematics, Hangzhou Normal University（数学学院，杭州师范大学）；School of Statistics, Jiangxi University of Finance and Economics（统计学院，江西财经大学）
Verified SHAP: Provable Bounds for Exact Shapley Values of Neural Networks
University of Konstanz, Konstanz, Germany（康斯坦茨大学）；Hebrew University of Jerusalem, Jerusalem, Israel（耶路撒冷希伯来大学）；University of St.Gallen, St.Gallen, Switzerland（斯图加特大学）
Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Sophisticated inference algorithms, such as belief propagation (BP), can effectively compute the marginal posteriors. Nonetheless, it is still difficult to interpret the inference outcomes for important human decision making. There is no existing method to rigorously attribute the inference outcomes to the contributing factors of the graphical models. Shapley values provide an axiomatic framework, but naively computing or eve…
Fairness-Aware Federated Learning with Trajectory Shapley Value
Faculty of Mathematics, Ecole Normale Supérieure Paris-Saclay（巴黎-萨克雷大学数学系）；Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship, Department of Mathematics, Friedrich-Alexander-Universität Erlangen-Nürnberg（埃尔兰根-纽伦堡弗里德里希-亚历山大大学数学系）
Exact Shapley Attributions in Quadratic-time for FANOVA Gaussian Processes
Department of Computer Science, Vrije Universiteit Amsterdam, The Netherlands（荷兰阿姆斯特丹自由大学计算机科学系）；Rational Intelligence Lab, CISPA Helmholtz Center for Information Security, Germany（德国信息安全部CISPA理性智能实验室）；College of Computing & Data Science, Nanyang Technological University, Singapore（新加坡南洋理工大学计算与数据科学学院）
Federated learning (FL) is a popular technique to train machine learning (ML) models on decentralized data sources. In order to sustain long-term participation of data owners, it is important to fairly appraise each data source and compensate data owners for their contribution to the training process. The Shapley value (SV) defines a unique payoff scheme that satisfies many desiderata for a data value notion. It has been increasingly used for valuing training data in centralized learning. However, computing the SV requires exhaustively evaluating the model performance on every subset of data s…
ShaplEIG: Bayesian Experimental Design for Shapley Value Estimation
Department of Statistics, LMU Munich（LMU慕尼黑统计系）；Institute for Informatics, LMU Munich（LMU慕尼黑信息学院）；Department of Computer Science, TU Dortmund University（图腾大学计算机科学系）；Munich Center for Machine Learning（慕尼黑机器学习中心）；Lamarr Institute for Machine Learning（拉马尔机器学习研究所）
Amortized Linear-time Exact Shapley Value for Product-Kernel Methods
Rational Intelligence Lab, CISPA Helmholtz Center for Information Security（理性智能实验室，信息安全中心（CISPA））；Department of Computer Science, Vrije Universiteit Amsterdam（阿姆斯特丹自由大学计算机科学系）；Epistemic Intelligence & Computation Lab, College of Computing & Data Science, Nanyang Technological University（认知智能与计算实验室，南洋理工大学计算机与数据科学学院）
Microsoft Research（微软研究院）；Microsoft Bing Ads（微软必应广告）
Given an unexpected change in the output metric of a large-scale system, it is important to answer why the change occurred: which inputs caused the change in metric? A key component of such an attribution question is estimating the counterfactual: the (hypothetical) change in the system metric due to a specified change in a single input. However, due to inherent stochasticity and complex interactions between parts of the system, it is difficult to model an output metric directly. We utilize the computational structure of a system to break up the modelling task into sub-parts, such that each su…
The Shapley value (SV) and Least core (LC) are classic methods in cooperative game theory for cost/profit sharing problems. Both methods have recently been proposed as a principled solution for data valuation tasks, i.e., quantifying the contribution of individual datum in machine learning. However, both SV and LC suffer computational challenges due to the need for retraining models on combinatorially many data subsets. In this work, we propose to boost the efficiency in computing Shapley value or Least core by learning to estimate the performance of a learning algorithm on unseen data combina…
