Precise Spike Timing Meets Discrete Time

Abstract

Spiking neural networks (SNNs) are inspired by the continuous-time dynamics of biological neurons, yet their practical implementations typically rely on discrete-time approximations to accommodate digital hardware and time-stepped neuromorphic systems. This discretization, while necessary, introduces numerical errors that may affect training dynamics and model performance, especially in systems where precise spike timing encodes critical information. Recent work has proposed gradient-based training methods that treat spike times as differentiable continuous variables, enabling temporally precise learning. However, the impact of discretizing these spike times during deployment remains poorly understood. In this paper, we systematically investigate the effects of spike time discretization using a representative multi-spike model as a case study. We propose a causal discretization scheme and analyze its quantization error both theoretically and empirically. Our results show that this error depends not only on the time step size Δt but also on the temporal structure of the input. We demonstrate that certain structured inputs can produce local minima in discretization error, and we explore whether such minima correspond to optimal choices of Δt for real datasets. Experiments on MNIST, Fashion MNIST, and EMNIST reveal that discretization can influence both classification accuracy and network sparsity. Finally, we compare training and evaluation under mismatched and aligned time regimes, examining how consistency in spike time discretization affects performance and sparsity in spike-timing-based SNNs.