Exact ensemble dynamics for spike-timing-dependent plasticity

Spike‑timing‑dependent plasticity (STDP) describes activity‑dependent synaptic changes driven by the relative timing of pre‑ and postsynaptic spikes and is a fundamental mechanism of neural plasticity. Synaptic weight dynamics under STDP can be modeled as a stochastic Markov process governed by a master equation. While previous work approximated equilibrium behavior using a truncated Fokker–Planck equation, this approach is not always accurate. This study shows that when jump moments satisfy specific polynomial conditions, the Kramers–Moyal expansion yields closed‑form recurrences for synaptic weight moments. Applying this method to an antisymmetric STDP model yields exact equilibrium moments, which are validated through simulations across a broad parameter range.