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ASecond-Order SpikingSSM for Wearables

arXiv 2510.14386 ↗First posted 16 Oct 2025cs.LG cs.NEcited by 0

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Abstract (arXiv)

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

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 30 of its 40 references that are in the map. First posted on arXiv 16 Oct 2025.

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30 of 40 references.

References · 30

  1. 2017Attention Is All You Needcited by 60,361
  2. 2023Mamba: Linear-Time Sequence Modeling with Selective State Spacescited by 4,718
  3. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,501
  4. 2021Efficiently Modeling Long Sequences with Structured State Spacescited by 2,465
  5. 2022Simplified State Space Layers for Sequence Modelingcited by 788
  6. 2019Surrogate Gradient Learning in Spiking Neural Networkscited by 626
  7. 2020Neural Controlled Differential Equations for Irregular Time Seriescited by 506
  8. 2023Resurrecting Recurrent Neural Networks for Long Sequencescited by 408
  9. 2024Titans: Learning to Memorize at Test Timecited by 328
  10. 2022Spikformer: When Spiking Neural Network Meets Transformercited by 271
  11. 2020Neural Rough Differential Equations for Long Time Seriescited by 143
  12. 2022MetaFormer Baselines for Visioncited by 132
18 more
  1. 2024Reducing Transformer Key-Value Cache Size with Cross-Layer Attentioncited by 131
  2. 2021UnICORNN: A recurrent model for learning very long time dependenciescited by 56
  3. 2016UniMiB SHAR: a new dataset for human activity recognition using acceleration data from smartphonescited by 54
  4. 2024Oscillatory State-Space Modelscited by 39
  5. 2024Log Neural Controlled Differential Equations: The Lie Brackets Make a Differencecited by 35
  6. 2023Efficient Video and Audio processing with Loihi 2cited by 29
  7. 2024State-space models are accurate and efficient neural operators for dynamical systemscited by 28
  8. 2023DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processorcited by 21
  9. 2023Learning Long Sequences in Spiking Neural Networkscited by 19
  10. 2024SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Modelscited by 19
  11. 2024Spiking Transformer with Spatial-Temporal Attentioncited by 19
  12. 2019Rapid online learning and robust recall in a neuromorphic olfactory circuitcited by 18
  13. 2024Balanced Resonate-and-Fire Neuronscited by 12
  14. 2024P-SpikeSSM: Harnessing Probabilistic Spiking State Space Models for Long-Range Dependency Taskscited by 12
  15. 2025Learning to Dissipate Energy in Oscillatory State-Space Modelscited by 9
  16. 2025Learning long range dependencies through time reversal symmetry breakingcited by 7
  17. 2022Wearable-based Human Activity Recognition with Spatio-Temporal Spiking Neural Networkscited by 6
  18. 2021Deep Spiking Neural Networks with Resonate-and-Fire Neuronscited by 5

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  1. 2024PRF: Parallel Resonate and Fire Neuron for Long Sequence Learning in Spiking Neural Networks
  2. 2024SPikE-SSM: A Sparse, Precise, and Efficient Spiking State Space Model for Long Sequences Learning
  3. 2026Phase State Space Models: Parallel, Surrogate-Free Training of Spiking Networks ↗
  4. 2026LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning
  5. 2025SiLIF: Structured State Space Model Dynamics and Parametrization for Spiking Neural Networks
  6. 2025Scaling Up Resonate-and-Fire Networks for Fast Deep Learning
  7. 2025Compute-in-Memory Implementation of State Space Models for Event Sequence Processing
  8. 2025Low-Bit Data Processing Using Multiple-Output Spiking Neurons with Non-linear Reset Feedback