Layered neural network with intra-layer connections using Q-states clock neurons

Katsuki Katayama and Tsuyoshi Horiguchi

Physica A: Statistical Mechanics and its Applications, 2001, vol. 297, issue 3, 532-548

Abstract: We investigate storage capacity of a fully connected layered neural network with Q(⩾2)-states clock neurons, including Q=∞ (corresponding to oscillatory neurons) and with intra-layer connections, where random Q-values patterns are embedded into the network by the Hebbian learning rule. We assume that both of inter-layered neurons and intra-layered neurons are updated simultaneously. We are able to treat a recurrent network, a feed-forward network and a layered network with the intra-layer connections within the same framework by adjusting a parameter. We analyze an energy function of the network by using the replica method. We clarify that the storage capacity of the layered network with the intra-layer connections is enhanced in comparison with that of the recurrent network and that of the feed-forward network for Q=2,3,4 and 5 at zero temperature; this is due to the competition between the inter-layer connections and the intra-layer connections. For ⩾6, including Q=∞, the storage capacity at zero temperature is maximum for the feed-forward network. We obtain phase diagrams in a load-parameter versus temperature plane for the layered network with the intra-layer connections.

Keywords: Neural network; Hebb rule; Q-states clock neuron; Oscillatory neuron; Storage capacity; Replica method (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:297:y:2001:i:3:p:532-548

DOI: 10.1016/S0378-4371(01)00264-3

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