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最优脑细胞凋亡

Optimal Brain Apoptosis

February 25, 2025
作者: Mingyuan Sun, Zheng Fang, Jiaxu Wang, Junjie Jiang, Delei Kong, Chenming Hu, Yuetong Fang, Renjing Xu
cs.AI

摘要

卷积神经网络(CNNs)与Transformer模型日益增长的复杂性和参数量,在计算效率和资源需求方面带来了挑战。剪枝作为一种有效策略,通过移除冗余元素如神经元、通道或连接,能在不明显影响性能的前提下提升计算效率,已被证实能有效应对这些挑战。本文在“最优脑损伤”(Optimal Brain Damage, OBD)的基础之上,进一步发展了利用Hessian矩阵进行参数重要性评估的方法。不同于以往依赖近似的方法,我们提出了“最优脑凋亡”(Optimal Brain Apoptosis, OBA),这是一种新颖的剪枝方法,直接计算每个参数的Hessian-向量积值。通过跨网络层分解Hessian矩阵,并识别层间Hessian子矩阵非零的条件,我们提出了一种高效计算参数二阶泰勒展开的技术。该方法使得剪枝过程更为精确,特别是在CNNs和Transformer的应用中,这一点在我们的实验中得到了验证,包括在CIFAR10、CIFAR100和Imagenet数据集上对VGG19、ResNet32、ResNet50及ViT-B/16模型的测试。我们的代码已公开于https://github.com/NEU-REAL/OBA。
English
The increasing complexity and parameter count of Convolutional Neural Networks (CNNs) and Transformers pose challenges in terms of computational efficiency and resource demands. Pruning has been identified as an effective strategy to address these challenges by removing redundant elements such as neurons, channels, or connections, thereby enhancing computational efficiency without heavily compromising performance. This paper builds on the foundational work of Optimal Brain Damage (OBD) by advancing the methodology of parameter importance estimation using the Hessian matrix. Unlike previous approaches that rely on approximations, we introduce Optimal Brain Apoptosis (OBA), a novel pruning method that calculates the Hessian-vector product value directly for each parameter. By decomposing the Hessian matrix across network layers and identifying conditions under which inter-layer Hessian submatrices are non-zero, we propose a highly efficient technique for computing the second-order Taylor expansion of parameters. This approach allows for a more precise pruning process, particularly in the context of CNNs and Transformers, as validated in our experiments including VGG19, ResNet32, ResNet50, and ViT-B/16 on CIFAR10, CIFAR100 and Imagenet datasets. Our code is available at https://github.com/NEU-REAL/OBA.

Summary

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论文概述

核心贡献

  • 提出了一种新的剪枝方法——Optimal Brain Apoptosis (OBA),通过直接计算Hessian-向量积来估计参数的重要性,避免了传统方法中对Hessian矩阵的近似。
  • 通过分解Hessian矩阵并分析层间Hessian子矩阵的非零条件,提出了一种高效计算参数二阶泰勒展开的方法。
  • 在CNN和Transformer模型上验证了OBA的有效性,实验表明OBA在CIFAR10、CIFAR100和ImageNet数据集上表现优异。

研究背景

  • 随着卷积神经网络(CNN)和Transformer的复杂性和参数数量的增加,计算效率和资源需求成为挑战。
  • 剪枝作为一种有效的策略,通过移除冗余的神经元、通道或连接来提高计算效率,同时尽可能保持模型性能。

关键词

  • 剪枝
  • Hessian矩阵
  • 二阶泰勒展开
  • 卷积神经网络
  • Transformer

背景

研究空白

  • 现有的剪枝方法大多依赖于对Hessian矩阵的近似,无法精确估计参数的重要性。
  • 在复杂的网络结构中,参数之间的相互依赖性使得剪枝过程更加复杂。

技术挑战

  • 计算Hessian矩阵的高计算复杂度。
  • 在剪枝过程中保持模型性能的同时,减少计算开销。

现有方法

  • 传统的剪枝方法如Optimal Brain Damage (OBD)和Optimal Brain Surgeon (OBS)通过近似Hessian矩阵来估计参数重要性。
  • 其他方法如权重剪枝和泰勒展开剪枝也常用于模型压缩。

方法论

技术架构

  • OBA通过直接计算Hessian-向量积来估计参数的重要性,避免了传统方法中的近似。
  • 通过分解Hessian矩阵并分析层间Hessian子矩阵的非零条件,提出了一种高效计算参数二阶泰勒展开的方法。

实现细节

  • 使用Jacobian-向量积前向传播(JVPF)来高效计算层间Hessian子矩阵的非零条件。
  • 在剪枝过程中,逐步移除重要性较低的参数或参数组。

创新点

  • 直接计算Hessian-向量积,避免了传统方法中的近似。
  • 提出了一种高效计算参数二阶泰勒展开的方法,适用于结构化和非结构化剪枝任务。

结果

实验设置

  • 在VGG19、ResNet32、ResNet50和ViT-B/16模型上进行了实验,数据集包括CIFAR10、CIFAR100和ImageNet。
  • 对比了OBA与其他剪枝方法在模型精度和计算效率上的表现。

主要发现

  • OBA在保持模型性能的同时,显著减少了计算开销。
  • 在结构化和非结构化剪枝任务中,OBA均表现出色,尤其是在高稀疏度情况下。

局限性

  • OBA目前适用于MLP、CNN和Transformer等网络结构,对于更复杂的网络结构如RNN和状态空间模型,计算Hessian矩阵的难度较大,需要进一步研究。

结论

  • OBA提出了一种新的剪枝方法,通过直接计算Hessian-向量积来精确估计参数的重要性,避免了传统方法中的近似。
  • 实验表明,OBA在结构化和非结构化剪枝任务中均表现出色,尤其是在高稀疏度情况下。
  • 未来的研究可以探索OBA在更复杂网络结构中的应用。

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