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

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.