Layered neural networks with non-monotonic transfer functions

Katsuki Katayama, Yasuo Sakata and Tsuyoshi Horiguchi

Physica A: Statistical Mechanics and its Applications, 2003, vol. 317, issue 1, 270-298

Abstract: We investigate storage capacity and generalization ability for two types of fully connected layered neural networks with non-monotonic transfer functions; random patterns are embedded into the networks by a Hebbian learning rule. One of them is a layered network in which a non-monotonic transfer function of even layers is different from that of odd layers. The other is a layered network with intra-layer connections, in which the non-monotonic transfer function of inter-layer is different from that of intra-layer, and inter-layered neurons and intra-layered neurons are updated alternately. We derive recursion relations for order parameters for those layered networks by the signal-to-noise ratio method. We clarify that the storage capacity and the generalization ability for those layered networks are enhanced in comparison with those with a conventional monotonic transfer function when non-monotonicity of the transfer functions is selected optimally. We also point out that some chaotic behavior appears in the order parameters for the layered networks when non-monotonicity of the transfer functions increases.

Keywords: Layered neural network; Non-monotonic transfer function; Hebb rule; Storage capacity; Generalization ability; Signal-to-noise ratio method (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:317:y:2003:i:1:p:270-298

DOI: 10.1016/S0378-4371(02)01319-5

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