Spiking neural networks have garnered increasing attention due to their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as scalable alternatives to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose SHaRe-SSM (Spiking Harmonic Resonate-and-Fire State Space Model), a second-order spiking SSM for classification and regression on ultra-long sequences. SHaRe-SSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. To ensure fast computation over tens of thousands of time steps, we leverage a parallel scan formulation of the underlying dynamical system. Furthermore, we introduce a kernel-based spiking regressor, which enables the accurate modelling of dependencies in sequences of up to 50k steps. Our results demonstrate that SHaRe-SSM achieves superior long-range modelling capability with energy efficiency (52.1x less than ANN-based second order SSM), positioning it as a strong candidate for resource-constrained devices such as wearables
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