The Kernel Dynamics of Convolutional Neural Networks in Manifolds  

作　　者：WU Wei JING Xiaoyuan DU Wencai 

机构地区：[1]School of Computer Science,Wuhan University,Wuhan 430072,China [2]Institute of Deep-sea Science and Engineering,Chinese Academy of Sciences,Sanya 572000,China [3]Institute of Data Science,City University of Macao,Macao 999078,China

出　　处：《Chinese Journal of Electronics》2020年第6期1185-1192,共8页电子学报（英文版）

基　　金：supported by the National Natural Science Foundation of China(No.61933013,No.U1736211);the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA22030301);the Foundation of Macao(No.MF1809,No.MF1713).

摘　　要：We propose a novel expression from manifolds to define Convolutional neural network(CNN).The layered structure is proceeded by integration in limited space continuously,with weights adjusted including value and direction in neural manifolds.Status transfer functions are proposed to simulate the kernel dynamics as a control matrix.We theoretically analyze the stability and controllability of kernel-based CNNs,and verify our findings by numerical experiments.

关 键 词：Convolutional neural networks Kernelbased convolution Learning dynamics Neural manifolds 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]