New Insights on Learning Rules for Hopfield Networks: Memory and Objective Function Minimisation

Abstract

Hopfield neural networks are a possible basis for modelling associative memory in living organisms. After summarising previous studies in the field, we take a new look at learning rules, exhibiting them as descent-type algorithms for various cost functions. We also propose several new cost functions suitable for learning. We discuss the role of biases — the external inputs — in the learning process in Hopfield networks. Furthermore, we apply Newton's method for learning memories, and experimentally compare the performances of various learning rules. Finally, to add to the debate whether allowing connections of a neuron to itself enhances memory capacity, we numerically investigate the effect..