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arXiv · 1206.5651

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

Garimella Ramamurthy·Bondalapati Nischal
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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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Garimella Ramamurthy, Bondalapati Nischal. 2012-07-14. Optimization of Real, Hermitian Quadratic Forms: Real, Complex Hopfield-Amari Neural Network. https://arxiv.org/abs/1206.5651

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