Critical dynamics in associative memory networks

Maximilian Uhlig,J. Michael Herrmann,Anna Levina,Theo Geisel

doi:10.3389/fncom.2013.00087

Abstract

Critical behavior in neural networks is characterized by scale-free avalanche size distributions and can be explained by self-regulatory mechanisms. Theoretical and experimental evidence indicates that information storage capacity reaches its maximum in the critical regime. We study the effect of structural connectivity formed by Hebbian learning on the criticality of network dynamics. The network only endowed with Hebbian learning does not allow for simultaneous information storage and criticality. However, the critical regime can be stabilized by short-term synaptic dynamics in the form of synaptic depression and facilitation or, alternatively, by homeostatic adaptation of the synaptic weights. We show that a heterogeneous distribution of maximal synaptic strengths does not preclude criticality if the Hebbian learning is alternated with periods of critical dynamics recovery. We discuss the relevance of these findings for the flexibility of memory in aging and with respect to the recent theory of synaptic plasticity.

Highlights

Critical dynamics in neural networks is an experimentally and conceptually established phenomenon which has been shown to be important for information processing in the brain
We have studied earlier the effect of dynamical synapses (Markram and Tsodyks, 1996) in associative memory networks (Bibitchkov et al, 2002), we are interested in the criticalizing role of dynamical synapses
We have described the dynamics of the neural network in the critical regime

Summary

Introduction

Critical dynamics in neural networks is an experimentally and conceptually established phenomenon which has been shown to be important for information processing in the brain. At the same time the theoretical understanding of neural avalanches has been developed starting from sandpile-like systems (Herz and Hopfield, 1995) and homogeneous networks (Eurich et al, 2002), but later including particular structural connectivity (Lin and Chen, 2005; Teramae and Fukai, 2007; Larremore et al, 2011). There are, other influences that shape the connectivity structure and weighting. Most prominently, this includes Hebbian learning, and homeostatic effects or pathological changes. We study how such structural changes influence criticality in neural networks

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