Spatio-Temporal Spectral Backpropagation for Training Spiking Neural Networks

Spiking Neural Networks (SNNs) offer significant advantages in time-series modeling due to their event-driven nature and biological plausibility, yet their training remains challenging. In existing backpropagation algorithms, parameters are deeply coupled within the temporal dimension, hindering the quantification of individual influences and limiting the analytical depth of gradient dynamics and theoretical interpretability. This paper proposes the Spatio-Temporal Spectral Backpropagation (STSBP) framework, which decomposes SNN error propagation in the spatio-temporal frequency domain into a product of four terms: (1) a spatial frequency kernel dependent on network structure and surrogate gradients; (2) a temporal frequency kernel governed by the leakage factor $\beta$; (3) an error spatio-temporal spectrum derived from task errors; and (4) an input signal spectrum. The framework reveals that SNNs prioritize low-frequency components in the spatial domain. In the temporal domain, the learning order is jointly determined by the temporal frequency kernel, the spatial-frequency integral of the error spectrum, and the input signal spectrum. Based on this theory, this paper presents the Frequency-LIF (Frequency Leaky Integrate-and-Fire) model, which comprises two core modules: the Spatial Frequency Dynamic Adjustment Mechanism (SFDAM) and the Temporal Frequency Dynamic Adjustment Mechanism (TFDAM). In the spatial domain, SFDAM detects low-frequency dominance, then attenuates low-frequency weights and enhances high-frequency learning, guiding the model from global trends to local details. In the temporal domain, TFDAM exponentially decays the leakage factor $\beta$ over timesteps, steering the model from initial low-frequency focus toward high-frequency learning. Experimental results on eight time-series prediction benchmark datasets demonstrate that Frequency-LIF outperforms current state-of-the-art methods. The relevant code is available at: https://anonymous.4open.science/r/Frequency-LIF-86F4.