Spatiotemporal learning in analog neural networks using spike-timing-dependent synaptic plasticity

Incorporating the spike-timing-dependent synaptic plasticity (STDP) into a learning rule, we study spatiotemporal learning in analog neural networks. First, we study learning of a finite number of periodic spatiotemporal patterns by deriving the dynamics of the order parameters. When a pattern is retrieved successfully, the order parameters exhibit periodic oscillation. Analyzing this oscillation of the order parameters, we elucidate the relation of the STDP time window to the properties of the retrieval state; the phase of the Fourier transform of the STDP time window determines the retrieval frequency and the time average of the STDP time window crucially affects the storage capacity. We also evaluate the stability of the order parameter oscillation and identify the retrieval state that is stable in single-pattern learning but unstable in multiple-pattern learning even when the retrieval state is independent of a pattern number. To examine the further applicability of the STDP-based learning rule, we also study learning of nonperiodic spatiotemporal Poisson patterns. Our numerical simulations demonstrate that the Poisson patterns are memorized successfully not only in analog neural networks but also in spiking neural networks