Spike-Aware Propagation Approximation for Conductance-Based LIF Equations

Abstract

Large-scale spiking neural network simulation requires numerical integration that preserves membrane dynamics and spike timing without making fine-resolution updates prohibitively expensive. This balance is difficult for conductance-based leaky integrate-and-fire (LIF) networks because synaptic decay, threshold crossings, resets, and refractory periods form a hybrid dynamical system. To address this difficulty, we introduce a spike-aware propagation (SAP) approximation method that combines exact receptor-trace updates, analytic homogeneous membrane propagation, Gauss–Legendre quadrature, and spike localization, improving the accuracy–efficiency Pareto frontier. We establish an error bound and conditional convergence under consistent refinement for the proposed SAP. At h = 1 ms, the single-realization T = 1000 ms comparison showed a lower voltage RMSE for SAP than for Euler at the same width in the two high-activity regimes. The five-seed T = 200 ms robustness experiment likewise showed lower voltage RMSE for SAP than for NEST at the same width. At the highest drive, the paired mean reduction was 3.91 mV (95% CI, 3.85–3.97 mV). This quantified gain supports SAP as a practical route to an improved accuracy–efficiency balance in large-scale conductance-based LIF simulation while underscoring the method’s configuration-dependent and regime-dependent scope.