Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network
Abstract
In this research paper, the problem of optimization of quadratic forms associated with the dynamics of Hopfield-Amari neural network is considered. An elegant (and short) proof of the states at which local/global minima of quadratic form are attained is provided. A theorem associated with local/global minimization of quadratic energy function using the Hopfield-Amari neural network is discussed. The results are generalized to a "Complex Hopfield neural network" dynamics over the complex hypercube (using a "complex signum function"). It is also reasoned through two theorems that there is no loss of generality in assuming the threshold vector to be a zero vector in the case of real as well as a "Complex Hopfield neural network". Some structured quadratic forms like Toeplitz form and Complex Toeplitz form are discussed.
Keywords
Cite
@article{arxiv.1206.5651,
title = {Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network},
author = {Garimella Ramamurthy and Bondalapati Nischal},
journal= {arXiv preprint arXiv:1206.5651},
year = {2012}
}