Retrieval Phase Diagrams of Non-monotonic Hopfield Networks

Details Retrieval Phase Diagrams of Non-monotonic Hopfield Networks Retrieval Phase Diagrams of Non-monotonic Hopfield Networks

1996-04-11

arxiv.org/abs/cond-mat/9604065v2

J.Phys.A: Math.Gen. 29 (1996) 4815-4826

Physics

Condensed Matter

Disordered Systems and Neural Networks

Latex 13 pages using IOP style file

Scientific paper

10.1088/0305-4470/29/16/008

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.

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