Parallel Fixed-Point Spiking Neurons for Efficient Training of Spiking Neural Networks

Spiking Neural Networks (SNNs) are inherently sequential due to temporal state dependencies, limiting the efficiency of parallel hardware such as GPUs and resulting in high training cost. In this work, we propose the Parallel Fixed-Point Spiking Neurons (PFSN), which reformulates the dynamics of leaky integrate-and-fire neurons into a unified fixed-point mapping, enabling parallel computation across all time steps. Unlike conventional sequential unrolling, the proposed formulation decouples temporal dependencies through iterative fixed-point updates, significantly improving computational efficiency. Furthermore, we introduce a learnable temporal propagation operator that generalizes predefined dynamics and allows adaptive modeling of task-specific temporal interactions without relying on explicit temporal recursion. Extensive experiments across diverse domains, including event-based recognition, sequential image classification, speech processing, and time-series forecasting, demonstrate that PFSN consistently achieves superior efficiency while maintaining or improving predictive performance compared to existing parallel SNN approaches. These results highlight the effectiveness of combining fixed-point formulations with learnable temporal structures for scalable and efficient SNN training. Code is available at https://anonymous.4open.science/r/PFSN.