Multilayered Network Architectures for Inverse Matrix Computation
Yongfeng Miao, Yingbo Hua · International Symposium on Information Theory and its Applications · 1994
This paper develops two novel computational architectures suitable for matrix inversion using multi layered neural networks, in which the inverse matrix computation is viewed as a kind of pattern matching problem. Two isomorphic linear multilayer networks, namely the learning network (LN) and the computing network (CN) are used to implement a kind of indirect linear architecture in which the LN learns the transformation between its input and output patterns while the CN outputs the inverse matrix solution based on weights mapped from the LN. In direct non-linear architecture, a two-layered network with non-linear hidden neurons is utilized to learn the inverse transformation corresponding to the given matrix and simultaneously outputs the inverse matrix solution. Learning algorithms for the architectures are studied with an emphasis on speeding up the convergence. Performances of the two architectures are illustrated by simulation examples.