PRF: Parallel Resonate and Fire Neuron for Long Sequence Learning in Spiking Neural Networks

Abstract: Recently, there is growing demand for effective and efficient long sequence modeling, with State Space Models (SSMs) proving to be effective for long sequence tasks. To further reduce energy consumption, SSMs can be adapted to Spiking Neural Networks (SNNs) using spiking functions. However, current spiking-formalized SSMs approaches still rely on float-point matrix-vector multiplication during inference, undermining SNNs' energy advantage. In this work, we address the efficiency and performance challenges of long sequence learning in SNNs simultaneously. First, we propose a decoupled reset method for parallel spiking neuron training, reducing the typical Leaky Integrate-and-Fire (LIF) model's training time from $O(L^2)$ to $O(L\log L)$, effectively speeding up the training by $6.57 \times$ to $16.50 \times$ on sequence lengths $1,024$ to $32,768$. To our best knowledge, this is the first time that parallel computation with a reset mechanism is implemented achieving equivalence to its sequential counterpart. Secondly, to capture long-range dependencies, we propose a Parallel Resonate and Fire (PRF) neuron, which leverages an oscillating membrane potential driven by a resonate mechanism from a differentiable reset function in the complex domain. The PRF enables efficient long sequence learning while maintaining parallel training. Finally, we demonstrate that the proposed spike-driven architecture using PRF achieves performance comparable to Structured SSMs (S4), with two orders of magnitude reduction in energy consumption, outperforming Transformer on Long Range Arena tasks.