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Mean-field analysis of a neural network with stochastic spike-timing-dependent plasticity

Pascal Helson*

Etienne Tanré

Romain Veltz

  • *Contact author: pascal.helson@u-bordeaux.fr
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Phys. Rev. E 114, 024405 – Published 19 August, 2026

DOI: https://doi.org/10.1103/fh5w-3zx4

Abstract

Synaptic plasticity is the biological foundation of learning and memory and a key inspiration for efficient, spike-based neuromorphic computing. In both contexts, spike-timing-dependent plasticity (STDP) is a crucial adaptive rule. However, while analytical tools exist for spiking networks with fixed connections, they fail when STDP is introduced, creating a long-standing theoretical impasse. In this work, we demonstrate how mean-field theory can successfully bridge this gap. We derive the first McKean-Vlasov mean-field limit for a network of stochastic spiking units with discrete-state STDP synapses, providing a rigorous, low-dimensional description of a system previously considered analytically intractable due to strong heterogeneity and adaptive couplings. While motivated by neuroscience—introducing plasticity into a stochastic Wilson-Cowan model—our framework establishes a general theoretical tool for studying the collective dynamics of large systems of interacting spiking (as opposed to rate-based) units with adaptation. This result provides a new methodological avenue in statistical physics for analyzing a wide class of complex systems with plastic interactions.

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Phys. Rev. E 114, 024405– Published 19 August, 2026
  • Received 2 October 2025
  • Accepted 25 June 2026
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