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

Kartikay Agrawal, Vaishnavi Nagabhushana, Abhijeet Vikram Vedant Sharma Ayon Borthakur
Indian Institute of Technology Guwahati
ICML 2026
Paper Webpage Code Preprint

Neurons fire upon crossing the threshold and emit spikes. Forward Euler spikes frequently whereas Backward Euler naturally dampens the neuron state.

Abstract

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 (SH2RFSSM), a second-order spiking SSM for classification and regression on ultra-long sequences. SH2RFSSM 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 SH2RFSSM 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.

BibTeX

@inproceedings{
agrawal2026,
title={A Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model for Time Series},
author={Kartikay Agrawal and Vaishnavi Nagabhushana and Abhijeet Vikram and Vedant Sharma and Ayon Borthakur},
booktitle={Forty-third International Conference on Machine Learning},
year={2026},
url={https://openreview.net/forum?id=dDGxzaRkxO}
}
}
@inproceedings{
agrawal2025a,
title={A Second-Order Spiking{SSM} for Wearables},
author={Kartikay Agrawal and Abhijeet Vikram and Vedant Sharma and Vaishnavi N and Ayon Borthakur},
booktitle={NeurIPS 2025 Workshop on Learning from Time Series for Health},
year={2025},
url={https://openreview.net/forum?id=hv52KEOshb}
}
}