Retrieval phase diagrams of non-monotonic Hopfield networks. (English) Zbl 0897.68084

Summary: 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 monotone transfer function investigated by D. J. Amit, H. Gutfreunt and H. Sompolinsky [Ann. Phys. 173, 30 (1987)]. 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 F. Zertuche, R. López and H. Waelbroeck [J. Phys. A, Math. Gen. 27, No. 5, 1575-1583 (1994; Zbl 0842.68063)]. 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.


68T05 Learning and adaptive systems in artificial intelligence
82C41 Dynamics of random walks, random surfaces, lattice animals, etc. in time-dependent statistical mechanics


Zbl 0842.68063
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