Piecewise Few-Spikes Neurons: Nonlinear Function Approximation for Provable and Efficient ANN-to-SNN Conversion

Due to their potential for energy-efficient deployment on neuromorphic hardware, Spiking Neural Networks (SNNs) have gained significant attention. While conversion from pre-trained Artificial Neural Networks (ANNs) serves as a popular route for constructing deep spiking models, its theoretical capabilities and underlying approximation dynamics remain insufficiently understood. In this paper, we categorize common conversion methods into two main paradigms and analyze their core mechanics, exposing their primary limitations concerning non-linear representations and activation resolution. To address these constraints, we propose Piecewise Few-Spike (PWFS) neurons, which introduce time-dependent parameter dynamics to enable accurate nonlinear function approximation without excessive spike counts. Unlike existing approaches that rely on heuristic optimizations, PWFS provides an explicit theoretical convergence guarantee with provable error bounds, establishing a precise mathematical trade-off between approximation accuracy and inference latency. We conduct comprehensive experiments to validate the efficacy of PWFS, showcasing its favorable accuracy in ANN-to-SNN conversion.