Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network

2012/06/25 by Garimella Ramamurthy, Ramamurthy, Garimella, Bondalapati Nischal +1
Computer Science · #FOS: Computer and information sciences #Fuzzy Logic and Control Systems #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #cs.NE

paper · pdf · doi:10.48550/arxiv.1206.5651

openalex publication_date 2012/06/25 · arxiv created 2012/07/14 · arxiv updated 2012/07/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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