Hopfield-Amari Neural Network: Minimization of Quadratic Forms

In this research paper, the problem of minimization 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 HopfieldAmari neural network is discussed. The results are generalized to a “Complex Hopfield neural network” dynamics over the complex hypercube (using a “complex signum function”). Some structured quadratic forms are discussed.