Retrieval Phase Diagrams of Non-monotonic Hopfield Networks

TL;DR

This paper analyzes the retrieval phase diagrams of non-monotonic Hopfield networks using mean-field approximation, showing they can store more patterns than monotonic networks and extending to general transfer functions.

Contribution

It provides a detailed analysis of non-monotonic Hopfield networks' retrieval phases and demonstrates their superior storage capacity over traditional models.

Findings

Non-monotonic networks have larger storage capacity.

Retrieval phase diagrams align with previous synchronous network results.

State-dependent synapses enhance storage capacity.

Abstract

We investigate the retrieval phase diagrams of an asynchronous fully-connected attractor network with non-monotonic transfer function by means of a mean-field approximation. We find for the noiseless zero-temperature case that this non-monotonic Hopfield network can store more patterns than a network with monotonic transfer function investigated by Amit et al. Properties of retrieval phase diagrams of non-monotonic networks agree with the results obtained by Nishimori and Opris who treated synchronous networks. We also investigate the optimal storage capacity of the non-monotonic Hopfield model with state-dependent synaptic couplings introduced by Zertuche et el. We show that the non-monotonic Hopfield model with state-dependent synapses stores more patterns than the conventional Hopfield model. Our formulation can be easily extended to a general transfer function.