Learning of spatiotemporal patterns in Ising-spin neural networks: analysis of storage capacity by path integral methods.

We encode periodic spatiotemporal patterns in Ising-spin neural networks, using the simple learning rule inspired by the spike-timing-dependent synaptic plasticity. It is then found that periodically oscillating spin neurons successfully reproduce phase differences of the encoded periodic patterns. The storage capacity of this associative memory neural network is enhanced with an adequate level of asymmetry in synapse connections. To understand the properties of these nonequilibrium retrieval states of the neural network, we carry out an analysis based on a path integral method. The relation of a dynamic crosstalk term to time-persistent oscillation of a correlation function well explains the enhancement of the storage capacity in spite of our approximation on nonpersistent terms. We investigate the accuracy of this approximation further by detailed comparison with numerical simulations.

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