基于群论的深度卷积网络分析

王溪,明扬,洪奕光

系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 219-227.

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PDF(2374 KB)
系统科学与数学 ›› 2019, Vol. 39 ›› Issue (2) : 219-227. DOI: 10.12341/jssms13584
论文

基于群论的深度卷积网络分析

    王溪,明扬,洪奕光
作者信息 +

Analysis of Deep Convolutional Networks from Group Theory Viewpoint

    WANG Xi ,MING Yang, HONG Yiguang
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文章历史 +

摘要

近年来深度学习已成为机器学习中处理大量复杂数据的有效方法, 它通过多层次的 结构从高维数据中提取特征, 从而解决分类、回归等实际任务. 文章首先回顾了深度卷积网络和自编码器的数学模型, 然后引入群论中分析对称性的一些方法, 对深度卷积网络在数据降维时的有效性进行了初步的讨论, 最后根据深度卷积网络对称群的逐层关系提出了改进神经网络的一个原则.

Abstract

Deep learning has recently become a very effective method in machine learning, which can classify data or solve practical problems from the feature of high-dimensional data. This paper first reviews the mathematical models of the deep convolutional network and the autoencoder, and then the paper introduces some very important concepts in the group theory to give a preliminary explanation of the effectiveness of the deep convolutional network. Then we propose a principle of improving neural networks according to the hierarchical relation of deep convolutional networks with symmetric groups.

关键词

深度学习 / 卷积神经网络 / 群作用 / 数据对称性.

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王溪 , 明扬 , 洪奕光. 基于群论的深度卷积网络分析. 系统科学与数学, 2019, 39(2): 219-227. https://doi.org/10.12341/jssms13584
WANG Xi , MING Yang , HONG Yiguang. Analysis of Deep Convolutional Networks from Group Theory Viewpoint. Journal of Systems Science and Mathematical Sciences, 2019, 39(2): 219-227 https://doi.org/10.12341/jssms13584
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