Linear stability analysis of retrieval state in associative memory neural networks of spiking neurons

TL;DR

This paper analyzes the stability of retrieval states in spiking neuron networks with spike-timing-dependent plasticity, revealing conditions for pattern stability and phase transitions using Floquet theory and numerical methods.

Contribution

It introduces a stability analysis framework for Hodgkin-Huxley type spiking neural networks with STDP, identifying conditions for pattern crosstalk elimination and phase transitions.

Findings

Crosstalk vanishes when negative and positive parts of the STDP window are balanced.

Phase transition occurs due to loss of periodic solution stability.

Explicit critical points are obtained via Floquet theory and numerical integration.

Abstract

We study associative memory neural networks of the Hodgkin-Huxley type of spiking neurons in which multiple periodic spatio-temporal patterns of spike timing are memorized as limit-cycle-type attractors. In encoding the spatio-temporal patterns, we assume the spike-timing-dependent synaptic plasticity with the asymmetric time window. Analysis for periodic solution of retrieval state reveals that if the area of the negative part of the time window is equivalent to the positive part, then crosstalk among encoded patterns vanishes. Phase transition due to the loss of the stability of periodic solution is observed when we assume fast alpha-function for direct interaction among neurons. In order to evaluate the critical point of this phase transition, we employ Floquet theory in which the stability problem of the infinite number of spiking neurons interacting with alpha-function is reduced into the eigenvalue problem with the finite size of matrix. Numerical integration of the single-body dynamics yields the explicit value of the matrix, which enables us to determine the critical point of the phase transition with a high degree of precision.