New Insights on Learning Rules for Hopfield Networks: Memory and Objective Function Minimisation
This work addresses incremental improvements in associative memory models for computational neuroscience and AI, focusing on specific learning bottlenecks.
The authors tackled the problem of improving memory capacity and learning efficiency in Hopfield networks by proposing new cost functions and applying Newton's method, resulting in experimental comparisons of various learning rules and numerical investigation of self-coupling effects.
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 Newtons 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 effects of self coupling. Keywords: Hopfield Networks, associative memory, content addressable memory, learning rules, gradient descent, attractor networks