A Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model for Time Series

Spiking neural networks have attracted increasing attention for their energy efficiency, multiplication-free computation, and sparse event-based processing. In parallel, state space models have emerged as a scalable alternative to transformers for long-range sequence modelling by avoiding quadratic dependence on sequence length. We propose here a spiking heterogeneous harmonic resonate-and-fire state space model (S$H^2$RFSSM), a second-order spiking SSM for classification and regression on ultra-long sequences. S$H^2$RFSSM outperforms transformers and first-order SSMs on average while eliminating matrix multiplications, making it highly suitable for resource-constrained applications. Furthermore, we introduce a kernel-based spiking regressor that enables accurate modelling of dependencies in sequences of up to 50k steps. We also observe a reduction in spiking operations and improved performance with heterogeneity and discretisation in harmonic resonate-and-fire neuronal layers. Overall, we evaluate Harmonic Resonate-and Fire layers across 17 diverse datasets, spanning sensors, time series, and classification to long-term forecasting. Our results demonstrate that S$H^2$RFSSM achieves superior long-range modelling capability with energy efficiency, positioning it as a strong candidate for signal processing on resource-constrained devices for human activity recognition, time series classification, and regression.

Modern AI systems often struggle to efficiently process very long streams of data, especially on small devices such as wearables and sensors with limited battery power. Popular models such as transformers can become increasingly expensive as sequences grow longer, making efficient long-range modelling a major challenge. In our work, we introduce a new brain-inspired AI model called the Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model (S$H^2$RFSSM). The model combines energy-efficient spiking neural networks, which communicate via sparse electrical spikes similar to neurons in the brain, with techniques for efficiently handling long sequences. Inspired by biological brains, we also study heterogeneity, in which different neurons learn and behave differently rather than sharing identical settings. Across 17 datasets involving sensor signals, time-series classification, and long-term forecasting, our approach achieved stronger average performance than existing artificial and spiking neural network approaches while requiring fewer computational resources. These results highlight the potential of brain-inspired AI for accurate and energy-efficient processing on low-power devices.