On Lipschitz Bounds of General Convolutional Neural Networks
On Lipschitz Bounds of General Convolutional Neural Networks
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DOI：
10.1109/tit.2019.2961812
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发表时间：
2018-08
影响因子：
2.5
通讯作者：
Dongmian Zou;R. Balan;Maneesh Kumar Singh
中科院分区：
文献类型：
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作者：
Dongmian Zou;R. Balan;Maneesh Kumar Singh
许多卷积神经网络(CNN)都具有前馈结构。在这篇文章中，我们建立了一个分析CNN的Lipschitz界的一般框架，并提出了一个估计这些界的线性规划。对几种CNN，包括散射网络、AlexNet和GoogLeNet进行了数值研究。在这些实际的数值例子中，将局部Lipschitz界的估计与这些理论界进行了比较。在Lipschitz界的基础上，我们接下来建立了关于平稳随机输入信号的输出分布的浓度不等式。在此基础上，进一步利用Lipschitz界进行非线性判别分析，以衡量不同类别特征之间的分离程度。
Many convolutional neural networks (CNN’s) have a feed-forward structure. In this paper, we model a general framework for analyzing the Lipschitz bounds of CNN’s and propose a linear program that estimates these bounds. Several CNN’s, including the scattering networks, the AlexNet and the GoogleNet, are studied numerically. In these practical numerical examples, estimations of local Lipschitz bounds are compared to these theoretical bounds. Based on the Lipschitz bounds, we next establish concentration inequalities for the output distribution with respect to a stationary random input signal. The Lipschitz bound is further used to perform nonlinear discriminant analysis that measures the separation between features of different classes.