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.

翻译：近年来，对高效长序列建模的需求日益增长，其中状态空间模型（SSMs）已被证明在长序列任务中表现优异。为进一步降低能耗，可通过引入脉冲函数将SSMs适配至脉冲神经网络（SNNs）。然而，当前基于脉冲形式化的SSMs方法在推理过程中仍依赖浮点数矩阵向量乘法，这削弱了SNNs的能耗优势。本研究同时应对SNNs中长序列学习在效率与性能方面的挑战。首先，我们提出一种用于并行脉冲神经元训练的**解耦重置方法**，将典型的泄漏积分发放（LIF）模型训练时间从$O(L^2)$降低至$O(L\log L)$，在序列长度$1,024$至$32,768$上实现了$6.57 \times$至$16.50 \times$的有效加速。据我们所知，这是首次实现**含重置机制的并行计算**，且其等效于对应的串行计算。其次，为捕捉长程依赖关系，我们提出**并行谐振发放（PRF）神经元**，该神经元利用复数域可微重置函数产生的谐振机制驱动振荡膜电位。PRF在保持并行训练的同时，实现了高效的长序列学习。最后，我们证明所提出的基于PRF的脉冲驱动架构在性能上可比肩结构化SSMs（S4），同时能耗降低两个数量级，并在Long Range Arena任务上超越Transformer。