Spike-Aware Propagation Approximation for Conductance-Based LIF Equations

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, which combines exact receptor-trace updates, analytic homogeneous membrane propagation, Gauss–Legendre quadrature, and spike localization, achieving an improvement on the accuracy-efficiency Pareto frontier. We establish an error bound and conditional convergence under consistent refinement for the proposed SAP. In million-neuron network experiments across four activity regimes, SAP achieved favorable accuracy-efficiency performance. Together, the analysis and experiments show that SAP can improve the accuracy-efficiency balance of conductance-based LIF simulation, highlighting the practical value in large-scale spiking neural network applications.