Pruning is one of the predominant approaches for compressing deep neural networks (DNNs). Lately, coresets (provable data summarizations) were leveraged for pruning DNNs, adding the advantage of theoretical guarantees on the trade-off between the compression rate and the approximation error. However, coresets in this domain were either data-dependent or generated under restrictive assumptions on both the model's weights and inputs. In real-world scenarios, such assumptions are rarely satisfied, limiting the applicability of coresets. To this end, we suggest a novel and robust framework for computing such coresets under mild assumptions on the model's weights and without any assumption on the training data. The idea is to compute the importance of each neuron in each layer with respect to the output of the following layer. This is achieved by a combination of Löwner ellipsoid and Caratheodory theorem. Our method is simultaneously data-independent, applicable to various networks and datasets (due to the simplified assumptions), and theoretically supported. Experimental results show that our method outperforms existing coreset based neural pruning approaches across a wide range of networks and datasets. For example, our method achieved a $62\%$ compression rate on ResNet50 on ImageNet with $1.09\%$ drop in accuracy.
Model compression is crucial for deployment of neural networks on devices with limited computational and memory resources. Many different methods show comparable accuracy of the compressed model and similar compression rates. However, the majority of the compression methods are based on heuristics and offer no worst-case guarantees on the trade-off between the compression rate and the approximation error for an arbitrarily new sample. We propose the first efficient structured pruning algorithm with a provable trade-off between its compression rate and the approximation error for any future tes…
One-shot coreset selection aims to select a representative subset of the training data, given a pruning rate, that can later be used to train future models while retaining high accuracy. State-of-the-art coreset selection methods pick the highest importance examples based on an importance metric and are found to perform well at low pruning rates. However, at high pruning rates, they suffer from a catastrophic accuracy drop, performing worse than even random sampling. This paper explores the reasons behind this accuracy drop both theoretically and empirically. We first propose a novel metric to…
University of Haifa（海法大学）；Johns Hopkins University（约翰斯·霍普金斯大学）；Carnegie Mellon University（卡内基梅隆大学）
Previous work showed empirically that large neural networks can be significantly reduced in size while preserving their accuracy. Model compression became a central research topic, as it is crucial for deployment of neural networks on devices with limited computational and memory resources. The majority of the compression methods are based on heuristics and offer no worst-case guarantees on the trade-off between the compression rate and the approximation error for an arbitrarily new sample. We propose the first efficient, data-independent neural pruning algorithm with a provable trade-off betw…
Coreset is usually a small weighted subset of $n$ input points in $\mathbb{R}^d$, that provably approximates their loss function for a given set of queries (models, classifiers, etc.). Coresets become increasingly common in machine learning since existing heuristics or inefficient algorithms may be improved by running them possibly many times on the small coreset that can be maintained for streaming distributed data. Coresets can be obtained by sensitivity (importance) sampling, where its size is proportional to the total sum of sensitivities. Unfortunately, computing the sensitivity of each p…
Coreset of a given dataset and loss function is usually a small weighed set that approximates this loss for every query from a given set of queries. Coresets have shown to be very useful in many applications. However, coresets construction is done in a problem dependent manner and it could take years to design and prove the correctness of a coreset for a specific family of queries. This could limit coresets use in practical applications. Moreover, small coresets provably do not exist for many problems. To address these limitations, we propose a generic, learning-based algorithm for constructio…
Training machine learning models on massive datasets incurs substantial computational costs. To alleviate such costs, there has been a sustained effort to develop data-efficient training methods that can carefully select subsets of the training examples that generalize on par with the full training data. However, existing methods are limited in providing theoretical guarantees for the quality of the models trained on the extracted subsets, and may perform poorly in practice. We propose AdaCore, a method that leverages the geometry of the data to extract subsets of the training examples for eff…
University of California, Los Angeles（加州大学洛杉矶分校）；University of Washington（华盛顿大学）；Stanford University（斯坦福大学）
Incremental gradient (IG) methods, such as stochastic gradient descent and its variants are commonly used for large scale optimization in machine learning. Despite the sustained effort to make IG methods more data-efficient, it remains an open question how to select a training data subset that can theoretically and practically perform on par with the full dataset. Here we develop CRAIG, a method to select a weighted subset (or coreset) of training data that closely estimates the full gradient by maximizing a submodular function. We prove that applying IG to this subset is guaranteed to converg…
The increasing availability of massive data sets poses a series of challenges for machine learning. Prominent among these is the need to learn models under hardware or human resource constraints. In such resource-constrained settings, a simple yet powerful approach is to operate on small subsets of the data. Coresets are weighted subsets of the data that provide approximation guarantees for the optimization objective. However, existing coreset constructions are highly model-specific and are limited to simple models such as linear regression, logistic regression, and $k$-means. In this work, we…
Scalable Learning of Multivariate Distributions via Coresets
Lamarr Institute for ML & AI, TU Dortmund（拉马尔人工智能与机器学习研究所，多特蒙德技术大学）；Scientific Computing Center, Karlsruhe Institute of Technology（卡尔斯鲁厄理工学院科学计算中心）；Department of Statistics, TU Dortmund（多特蒙德技术大学统计学系）
University of Oxford（牛津大学）；University of Southampton（南安普顿大学）
In the wake of the explosive growth in smartphones and cyberphysical systems, there has been an accelerating shift in how data is generated away from centralised data towards on-device generated data. In response, machine learning algorithms are being adapted to run locally on board, potentially hardware limited, devices to improve user privacy, reduce latency and be more energy efficient. However, our understanding of how these device orientated algorithms behave and should be trained is still fairly limited. To address this issue, a method to automatically synthesize reduced-order neural net…
Robinson College of Business, Georgia State University（佐治亚州立大学罗宾逊商学院）；School of Electrical and Computer Engineering, Georgia Tech（佐治亚理工学院电气与计算机工程学院）
We develop a fast, tractable technique called Net-Trim for simplifying a trained neural network. The method is a convex post-processing module, which prunes (sparsifies) a trained network layer by layer, while preserving the internal responses. We present a comprehensive analysis of Net-Trim from both the algorithmic and sample complexity standpoints, centered on a fast, scalable convex optimization program. Our analysis includes consistency results between the initial and retrained models before and after Net-Trim application and guarantees on the number of training samples needed to discover…
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…
IBM T.J. Watson Research Center（IBM T.J. Watson 研究中心）；Georgia State School of Business（佐治亚州立大学商学院）；Georgia Institute of Technology（佐治亚理工学院）
We introduce and analyze a new technique for model reduction for deep neural networks. While large networks are theoretically capable of learning arbitrarily complex models, overfitting and model redundancy negatively affects the prediction accuracy and model variance. Our Net-Trim algorithm prunes (sparsifies) a trained network layer-wise, removing connections at each layer by solving a convex optimization program. This program seeks a sparse set of weights at each layer that keeps the layer inputs and outputs consistent with the originally trained model. The algorithms and associated analysi…
Structured weight pruning is a representative model compression technique of DNNs for hardware efficiency and inference accelerations. Previous works in this area leave great space for improvement since sparse structures with combinations of different structured pruning schemes are not exploited fully and efficiently. To mitigate the limitations, we propose SS-Auto, a single-shot, automatic structured pruning framework that can achieve row pruning and column pruning simultaneously. We adopt soft constraint-based formulation to alleviate the strong non-convexity of l0-norm constraints used in s…
Syracuse University（雪城大学）；Northeastern University（东北大学）；George Mason University（乔治梅森大学）；MIT-IBM Watson AI Lab, IBM Research（IBM研究院MIT-IBM沃森人工智能实验室）
Deep neural networks (DNNs) although achieving human-level performance in many domains, have very large model size that hinders their broader applications on edge computing devices. Extensive research work have been conducted on DNN model compression or pruning. However, most of the previous work took heuristic approaches. This work proposes a progressive weight pruning approach based on ADMM (Alternating Direction Method of Multipliers), a powerful technique to deal with non-convex optimization problems with potentially combinatorial constraints. Motivated by dynamic programming, the proposed…
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；National Technical University of Athens（雅典国立技术大学）
In this paper we study an emerging class of neural networks based on the morphological operators of dilation and erosion. We explore these networks mathematically from a tropical geometry perspective as well as mathematical morphology. Our contributions are threefold. First, we examine the training of morphological networks via Difference-of-Convex programming methods and extend a binary morphological classifier to multiclass tasks. Second, we focus on the sparsity of dense morphological networks trained via gradient descent algorithms and compare their performance to their linear counterparts…
Beijing University of Posts and Telecommunications（北京邮电大学）
In this letter, we study a wireless federated learning (FL) system where network pruning is applied to local users with limited resources. Although pruning is beneficial to reduce FL latency, it also deteriorates learning performance due to the information loss. Thus, a trade-off problem between communication and learning is raised. To address this challenge, we quantify the effects of network pruning and packet error on the learning performance by deriving the convergence rate of FL with a non-convex loss function. Then, closed-form solutions for pruning control and bandwidth allocation are p…
Northeastern University（东北大学）；Syracuse University（雪城大学）；SUNY University at Buffalo（纽约州立大学布法罗分校）；University of Southern California（南加利福尼亚大学）
To facilitate efficient embedded and hardware implementations of deep neural networks (DNNs), two important categories of DNN model compression techniques: weight pruning and weight quantization are investigated. The former leverages the redundancy in the number of weights, whereas the latter leverages the redundancy in bit representation of weights. However, there lacks a systematic framework of joint weight pruning and quantization of DNNs, thereby limiting the available model compression ratio. Moreover, the computation reduction, energy efficiency improvement, and hardware performance over…
Lightweight Federated Learning over Wireless Edge Networks
Department of Electronic Engineering, Tsinghua University（电子工程系，清华大学）；School of Cyber Science and Technology, Beihang University（信息科学与技术学院，北航）；Tsinghua Space Center, Tsinghua University（清华大学空间中心）；College of Computing and Data Science, Nanyang Technological University（计算与数据科学学院，南洋理工大学）
The Larger the Merrier? Efficient Large AI Model Inference in Wireless Edge Networks
Department of Information Science and Engineering, KTH Royal Institute of Technology（信息科学与工程系，皇家理工学院）；School of Science and Engineering, the Shenzhen Future Network of Intelligence Institute, and the Guangdong Provincial Key Laboratory of Future Networks of Intelligence（科学与工程学院，深圳未来网络智能研究所，广东省未来网络智能重点实验室）；Université Paris-Saclay, CNRS, CentraleSupélec, Laboratoire des Signaux et Systèmes（巴黎-萨克雷大学，CNRS，CentraleSupélec，信号与系统实验室）；King’s College London, Centre for Telecommunications Research – Department of Engineering（伦敦国王学院，电信研究中心——工程学院）
Due to data privacy issues, accelerating networks with tiny training sets has become a critical need in practice. Previous methods achieved promising results empirically by filter-level pruning. In this paper, we both study this problem theoretically and propose an effective algorithm aligning well with our theoretical results. First, we propose the finetune convexity hypothesis to explain why recent few-shot compression algorithms do not suffer from overfitting problems. Based on it, a theory is further established to explain these methods for the first time. Compared to naively finetuning a …
Differentiable Entropy Regularization: A Complexity-Aware Approach for Neural Optimization
Department of Computer Science Iowa State University（计算机科学系爱荷华州立大学）；Department of Civil, Construction and Environmental Engineering Iowa State University（土木、建设与环境工程系爱荷华州立大学）
We propose a data-driven approach for deep convolutional neural network compression that achieves high accuracy with high throughput and low memory requirements. Current network compression methods either find a low-rank factorization of the features that requires more memory, or select only a subset of features by pruning entire filter channels. We propose the Cascaded Projection (CaP) compression method that projects the output and input filter channels of successive layers to a unified low dimensional space based on a low-rank projection. We optimize the projection to minimize classificatio…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；University of Oxford（牛津大学）；Zalando SE（Zalando公司）；itemis AG（itemis股份公司）
This work tackles the problem of characterizing and understanding the decision boundaries of neural networks with piecewise linear non-linearity activations. We use tropical geometry, a new development in the area of algebraic geometry, to characterize the decision boundaries of a simple network of the form (Affine, ReLU, Affine). Our main finding is that the decision boundaries are a subset of a tropical hypersurface, which is intimately related to a polytope formed by the convex hull of two zonotopes. The generators of these zonotopes are functions of the network parameters. This geometric c…
Rensselaer Polytechnic Institute（伦斯勒理工学院）；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）；University at Buffalo（布法罗大学）
The \textit{lottery ticket hypothesis} (LTH) states that learning on a properly pruned network (the \textit{winning ticket}) improves test accuracy over the original unpruned network. Although LTH has been justified empirically in a broad range of deep neural network (DNN) involved applications like computer vision and natural language processing, the theoretical validation of the improved generalization of a winning ticket remains elusive. To the best of our knowledge, our work, for the first time, characterizes the performance of training a pruned neural network by analyzing the geometric st…
