Garimella Ramamurthy

Garimella Ramamurthy, Marcos Eduardo Valle, Tata Jagannadha Swamy

This research paper introduces two novel complex-valued Hopfield neural networks (CvHNNs) that incorporate phase and magnitude quantization. The first CvHNN employs a ceiling-type activation function that operates on the rectangular coordinate representation of the complex net contribution. The second CvHNN similarly incorporates phase and magnitude quantization but utilizes a ceiling-type activation function based on the polar coordinate representation of the complex net contribution. The proposed CvHNNs, with their phase and magnitude quantization, significantly increase the number of states compared to existing models in the literature, thereby expanding the range of potential applications for CvHNNs.

Garimella Ramamurthy, Bondalapati Nischal

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.