The USC Andrew and Erna Viterbi School of Engineering USC Signal and Image Processing Institute USC Ming Hsieh Department of Electrical Engineering University of Southern California

Technical Report USC-SIPI-320

“Theoretical Observations About the Hysteretic Hopfield Neural Network”

by Sunil Bharitkar and Jerry M. Mendel

June 1998

Several neuron activation functions have been proposed (e.g., linear, binary, sigmoid) for recurrent and multilayer Artificial Neural Networks. In this report we present a hysteretic neuron activation function for optimization and learning. We include this neuron within the framework of the Hopfield network to form the Hysteretic Hopfield Neural Network (HHNN). We then propose a dynamical equation, and an energy equation for this model using the well known Cohen-Grossberg theorem. Finally, these equations are used to prove Lyapunov stability of the HHNN.

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