DMFT analysis of Hopfield network with plasticity

TL;DR

This paper develops a dynamical mean-field theory for Hopfield networks with activity-dependent plasticity, revealing how plasticity influences memory capacity and stability.

Contribution

It extends DMFT analysis to networks with coevolving neural states and synapses, highlighting the effects of plasticity on memory retrieval.

Findings

Moderate plasticity enlarges the basin of attraction.

Optimal plasticity balances memory stability and cue imprinting.

Excessive plasticity causes spurious attractors.

Abstract

We study a fully connected Hopfield-type associative memory network with online activity-dependent synaptic plasticity, where neural states and synaptic couplings coevolve during retrieval. Using the generating-functional formalism, we derive a dynamical mean-field theory (DMFT) in the large-system limit with extensively many stored random patterns, and show that the many-body dynamics reduces to an effective single-site stochastic process with colored Gaussian crosstalk noise and delayed feedback terms. Numerical solutions of the DMFT equations agree well with direct simulations. We find that moderate plasticity enlarges the basin of attraction and increases the maximum retrievable memory load by generating a positive delayed feedback that stabilizes retrieval against crosstalk noise. However, excessively strong plasticity causes the network to imprint the imperfect initial cue itself, leading to spurious attractors and degraded retrieval performance. Consequently, an optimal plasticity strength emerges from the trade-off between memory stabilization and premature cue imprinting. These results extend the DMFT description of associative memory to networks with coevolving neural and synaptic dynamics.