# ASecond-Order SpikingSSM for Wearables

arXiv: https://arxiv.org/abs/2510.14386 · HTML: https://mlsanity.com/paper/2510.14386/

## 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.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2208.04933/) (2022)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Resurrecting Recurrent Neural Networks for Long Sequences](https://mlsanity.com/paper/2303.06349/) (2023)
- [Titans: Learning to Memorize at Test Time](https://mlsanity.com/paper/2501.00663/) (2024)
- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [MetaFormer Baselines for Vision](https://mlsanity.com/paper/2210.13452/) (2022)
- [Reducing Transformer Key-Value Cache Size with Cross-Layer Attention](https://mlsanity.com/paper/2405.12981/) (2024)
- [UnICORNN: A recurrent model for learning very long time dependencies](https://mlsanity.com/paper/2103.05487/) (2021)
- [UniMiB SHAR: a new dataset for human activity recognition using acceleration data from smartphones](https://mlsanity.com/paper/1611.07688/) (2016)
- [Oscillatory State-Space Models](https://mlsanity.com/paper/2410.03943/) (2024)
- [Log Neural Controlled Differential Equations: The Lie Brackets Make a Difference](https://mlsanity.com/paper/2402.18512/) (2024)
- [Efficient Video and Audio processing with Loihi 2](https://mlsanity.com/paper/2310.03251/) (2023)
- [State-space models are accurate and efficient neural operators for dynamical systems](https://mlsanity.com/paper/2409.03231/) (2024)
- [DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processor](https://mlsanity.com/paper/2310.00564/) (2023)
- [Learning Long Sequences in Spiking Neural Networks](https://mlsanity.com/paper/2401.00955/) (2023)
- [SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models](https://mlsanity.com/paper/2408.14909/) (2024)
- [Spiking Transformer with Spatial-Temporal Attention](https://mlsanity.com/paper/2409.19764/) (2024)
- [Rapid online learning and robust recall in a neuromorphic olfactory circuit](https://mlsanity.com/paper/1906.07067/) (2019)
- [Balanced Resonate-and-Fire Neurons](https://mlsanity.com/paper/2402.14603/) (2024)
- [P-SpikeSSM: Harnessing Probabilistic Spiking State Space Models for Long-Range Dependency Tasks](https://mlsanity.com/paper/2406.02923/) (2024)
- [Learning to Dissipate Energy in Oscillatory State-Space Models](https://mlsanity.com/paper/2505.12171/) (2025)
- [Learning long range dependencies through time reversal symmetry breaking](https://mlsanity.com/paper/2506.05259/) (2025)
- [Wearable-based Human Activity Recognition with Spatio-Temporal Spiking Neural Networks](https://mlsanity.com/paper/2212.02233/) (2022)
- [Deep Spiking Neural Networks with Resonate-and-Fire Neurons](https://mlsanity.com/paper/2109.08234/) (2021)

## 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