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

Kartikay Agrawal, Vaishnavi Nagabhushana, Abhijeet Vikram, Vedant Sharma, Ayon Borthakur
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:1033-1060, 2026.

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 (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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-agrawal26c, title = {A Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model for Time Series}, author = {Agrawal, Kartikay and Nagabhushana, Vaishnavi and Vikram, Abhijeet and Sharma, Vedant and Borthakur, Ayon}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {1033--1060}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/agrawal26c/agrawal26c.pdf}, url = {https://proceedings.mlr.press/v306/agrawal26c.html}, 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 (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.} }
Endnote
%0 Conference Paper %T A Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model for Time Series %A Kartikay Agrawal %A Vaishnavi Nagabhushana %A Abhijeet Vikram %A Vedant Sharma %A Ayon Borthakur %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-agrawal26c %I PMLR %P 1033--1060 %U https://proceedings.mlr.press/v306/agrawal26c.html %V 306 %X 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.
APA
Agrawal, K., Nagabhushana, V., Vikram, A., Sharma, V. & Borthakur, A.. (2026). A Spiking Heterogeneous Harmonic Resonate-and-Fire State Space Model for Time Series. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:1033-1060 Available from https://proceedings.mlr.press/v306/agrawal26c.html.

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