Second-order information, in the form of Hessian- or Inverse-Hessian-vector products, is a fundamental tool for solving optimization problems. Recently, there has been significant interest in utilizing this information in the context of deep neural networks; however, relatively little is known about the quality of existing approximations in this context. Our work examines this question, identifies issues with existing approaches, and proposes a method called WoodFisher to compute a faithful and efficient estimate of the inverse Hessian.
Our main application is to neural network compression, where we build on the classic Optimal Brain Damage/Surgeon framework. We demonstrate that WoodFisher significantly outperforms popular state-of-the-art methods for one-shot pruning. Further, even when iterative, gradual pruning is considered, our method results in a gain in test accuracy over the state-of-the-art approaches, for pruning popular neural networks (like ResNet-50, MobileNetV1) trained on standard image classification datasets such as ImageNet ILSVRC. We examine how our method can be extended to take into account first-order information, as well as illustrate its ability to automatically set layer-wise pruning thresholds and perform compression in the limited-data regime. The code is available at the following link, https://github.com/IST-DASLab/WoodFisher.
Model compression has been introduced to reduce the required hardware resources while maintaining the model accuracy. Lots of techniques for model compression, such as pruning, quantization, and low-rank approximation, have been suggested along with different inference implementation characteristics. Adopting model compression is, however, still challenging because the design complexity of model compression is rapidly increasing due to additional hyper-parameters and computation overhead in order to achieve a high compression ratio. In this paper, we propose a simple and efficient model compre…
Connectionist models such as neural networks suffer from catastrophic forgetting. In this work, we study this problem from the perspective of information theory and define forgetting as the increase of description lengths of previous data when they are compressed with a sequentially learned model. In addition, we show that continual learning approaches based on variational posterior approximation and generative replay can be considered as approximations to two prequential coding methods in compression, namely, the Bayesian mixture code and maximum likelihood (ML) plug-in code. We compare these…
The goal of model compression is to reduce the size of a large neural network while retaining a comparable performance. As a result, computation and memory costs in resource-limited applications may be significantly reduced by dropping redundant weights, neurons, or layers. There have been many model compression algorithms proposed that provide impressive empirical success. However, a theoretical understanding of model compression is still limited. One problem is understanding if a network is more compressible than another of the same structure. Another problem is quantifying how much one can …
CSAIL（麻省理工学院计算机科学与人工智能实验室）；Massachusetts Institute of Technology（麻省理工学院）；University of British Columbia（英属哥伦比亚大学）；Harvard University（哈佛大学）
Kernel methods offer the flexibility to learn complex relationships in modern, large data sets while enjoying strong theoretical guarantees on quality. Unfortunately, these methods typically require cubic running time in the data set size, a prohibitive cost in the large-data setting. Random feature maps (RFMs) and the Nystrom method both consider low-rank approximations to the kernel matrix as a potential solution. But, in order to achieve desirable theoretical guarantees, the former may require a prohibitively large number of features J+, and the latter may be prohibitively expensive for hig…
We propose tensorial neural networks (TNNs), a generalization of existing neural networks by extending tensor operations on low order operands to those on high order ones. The problem of parameter learning is challenging, as it corresponds to hierarchical nonlinear tensor decomposition. We propose to solve the learning problem using stochastic gradient descent by deriving nontrivial backpropagation rules in generalized tensor algebra we introduce. Our proposed TNNs has three advantages over existing neural networks: (1) TNNs naturally apply to high order input object and thus preserve the mult…
Low-rank approximation is an effective model compression technique to not only reduce parameter storage requirements, but to also reduce computations. For convolutional neural networks (CNNs), however, well-known low-rank approximation methods, such as Tucker or CP decomposition, result in degraded model accuracy because decomposed layers hinder training convergence. In this paper, we propose a new training technique that finds a flat minimum in the view of low-rank approximation without a decomposed structure during training. By preserving the original model structure, 2-dimensional low-rank …
We introduce a class of fully-connected neural networks whose activation functions, rather than being pointwise, rescale feature vectors by a function depending only on their norm. We call such networks radial neural networks, extending previous work on rotation equivariant networks that considers rescaling activations in less generality. We prove universal approximation theorems for radial neural networks, including in the more difficult cases of bounded widths and unbounded domains. Our proof techniques are novel, distinct from those in the pointwise case. Additionally, radial neural network…
Clustering-Based Low-Rank Matrix Approximation for Medical Image Compression
Department of Statistics, Rhodes University（统计学系，罗德斯大学）；Department of Mathematics, Rhodes University（数学系，罗德斯大学）；National Institute for Theoretical and Computational Sciences (NITheCS)（理论与计算科学国家研究所）
D-QRELO: Training- and Data-Free Delta Compression for Large Language Models via Quantization and Residual Low-Rank Approximation
Harbin Institute of Technology, Shenzhen, China（哈尔滨工业大学（深圳））；TeleAI of China Telecom（中国电信TeleAI）；The Hong Kong Polytechnic University（香港理工大学）；The University of Hong Kong（香港大学）
We propose `Dracula', a new framework for unsupervised feature selection from sequential data such as text. Dracula learns a dictionary of $n$-grams that efficiently compresses a given corpus and recursively compresses its own dictionary; in effect, Dracula is a `deep' extension of Compressive Feature Learning. It requires solving a binary linear program that may be relaxed to a linear program. Both problems exhibit considerable structure, their solution paths are well behaved, and we identify parameters which control the depth and diversity of the dictionary. We also discuss how to derive fea…
University of California, Davis（加州大学戴维斯分校）；Google Research（谷歌研究院）
Model compression is essential for serving large deep neural nets on devices with limited resources or applications that require real-time responses. As a case study, a state-of-the-art neural language model usually consists of one or more recurrent layers sandwiched between an embedding layer used for representing input tokens and a softmax layer for generating output tokens. For problems with a very large vocabulary size, the embedding and the softmax matrices can account for more than half of the model size. For instance, the bigLSTM model achieves state-of- the-art performance on the One-B…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Innopolis University（Innopolis 大学）
The low-rank tensor approximation is very promising for the compression of deep neural networks. We propose a new simple and efficient iterative approach, which alternates low-rank factorization with a smart rank selection and fine-tuning. We demonstrate the efficiency of our method comparing to non-iterative ones. Our approach improves the compression rate while maintaining the accuracy for a variety of tasks.
As the industry deploys increasingly large and complex neural networks to mobile devices, more pressure is put on the memory and compute resources of those devices. Deep compression, or compression of deep neural network weight matrices, is a technique to stretch resources for such scenarios. Existing compression methods cannot effectively compress models smaller than 1-2% of their original size. We develop a new compression technique, DeepThin, building on existing research in the area of low rank factorization. We identify and break artificial constraints imposed by low rank approximations b…
BayzAI；Volkswagen Group of America（美国大众汽车集团）；Innovation Center California（加州创新中心）
Finding methods for making generalizable predictions is a fundamental problem of machine learning. By looking into similarities between the prediction problem for unknown data and the lossless compression we have found an approach that gives a solution. In this paper we propose a compression principle that states that an optimal predictive model is the one that minimizes a total compressed message length of all data and model definition while guarantees decodability. Following the compression principle we use Bayesian approach to build probabilistic models of data and network definitions. A me…
We approximated the evaluation function for the game Tic-Tac-Toe by singular value decomposition (SVD) and investigated the effect of approximation accuracy on winning rate. We first prepared the perfect evaluation function of Tic-Tac-Toe and performed low-rank approximation by considering the evaluation function as a ninth-order tensor. We found that we can reduce the amount of information of the evaluation function by 70% without significantly degrading the performance. Approximation accuracy and winning rate were strongly correlated but not perfectly proportional. We also investigated how t…
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…
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…
We consider the problem of lossy image compression with deep latent variable models. State-of-the-art methods build on hierarchical variational autoencoders (VAEs) and learn inference networks to predict a compressible latent representation of each data point. Drawing on the variational inference perspective on compression, we identify three approximation gaps which limit performance in the conventional approach: an amortization gap, a discretization gap, and a marginalization gap. We propose remedies for each of these three limitations based on ideas related to iterative inference, stochastic…
Model compression is generally performed by using quantization, low-rank approximation or pruning, for which various algorithms have been researched in recent years. One fundamental question is: what types of compression work better for a given model? Or even better: can we improve by combining compressions in a suitable way? We formulate this generally as a problem of optimizing the loss but where the weights are constrained to equal an additive combination of separately compressed parts; and we give an algorithm to learn the corresponding parts' parameters. Experimentally with deep neural ne…
A popular approach to learning encoders for lossy compression is to use additive uniform noise during training as a differentiable approximation to test-time quantization. We demonstrate that a uniform noise channel can also be implemented at test time using universal quantization (Ziv, 1985). This allows us to eliminate the mismatch between training and test phases while maintaining a completely differentiable loss function. Implementing the uniform noise channel is a special case of the more general problem of communicating a sample, which we prove is computationally hard if we do not make a…
In the era of big data, learning from categorical features with very large vocabularies (e.g., 28 million for the Criteo click prediction dataset) has become a practical challenge for machine learning researchers and practitioners. We design a highly-scalable vocabulary compression algorithm that seeks to maximize the mutual information between the compressed categorical feature and the target binary labels and we furthermore show that its solution is guaranteed to be within a $1-1/e \approx 63\%$ factor of the global optimal solution. To achieve this, we introduce a novel re-parametrization o…
Tensor Train Low-rank Approximation (TT-LoRA): Democratizing AI with Accelerated LLMs
Theoretical Division, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室理论分部）；Advanced Research in Cyber Systems, Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室网络系统高级研究分部）；University of Texas at Arlington（德克萨斯大学阿灵顿分校）
Differentiable Earth Mover's Distance for Data Compression at the High-Luminosity LHC
University of California at San Diego（加利福尼亚大学圣迭戈分校）；Fermi National Accelerator Laboratory（费米国家加速器实验室）；European Organization for Nuclear Research (CERN)（欧洲核子研究中心）
Theoretical Guarantees for Low-Rank Compression of Deep Neural Networks
Department of Mathematics, University of California San Diego（加州大学圣地亚哥分校数学系）；Department of Mathematics（数学系）；Hal c o g lu Data Science Institute, University of California San Diego（Hal c o g lu数据科学研究所，加州大学圣地亚哥分校）
Mobiprox: Supporting Dynamic Approximate Computing on Mobiles
Cosylab（科西拉布公司）；Faculty of Computer and Information Science, University of Ljubljana（卢布尔雅那大学计算机与信息科学学院）；Department of Computer Science at the University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校计算机科学系）；Institute Jozef Stefan（约瑟夫·斯蒂芬研究所）
Efficient Wireless Federated Learning via Low-Rank Gradient Factorization
School of Information Science and Technology, ShanghaiTech University（上海科技大学信息科学与技术学院）；School of Computing Science, University of Glasgow（格拉斯哥大学计算科学学院）
