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LongSpike: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning

NeurIPS 2026 · Architectures and efficiency › Spiking networks · approach: Sparse efficient spiking sequence models · 0 citations (OpenAlex)

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Proposes LongSpike, an SNN framework that replaces first-order LIF/SSM state dynamics with fractional-order SSM dynamics approximated by a sum-of-exponentials multi-timescale memory bank, enabling parallel training.

Problem

First-order (integer-order) ODE-based spiking neural networks and SSMs have short-tailed, memoryless impulse responses, limiting modeling of long-range dependencies in long-sequence tasks.

Approach

Replace integer-order state transitions with a Caputo fractional-order SSM (f-SSM), approximating the power-law kernel with a learnable sum-of-exponentials so each trace is an LTI system computable via FFT convolution, and feed its output as input current to LIF neurons (parallelized via a surrogate dynamic network CNN).

Key results

• LongSpike reaches 86.33% average accuracy on LRA, above SpikingSSM (84.33%) and the S4D-Lin ANN (85.52%).
• On WikiText-103, LongSpike (75M params) achieves 32.31 perplexity versus SpikingSSM's 33.94 and SpikeGPT's 39.75.
• On Speech Commands, LongSpike achieves 96.31% accuracy versus SpikingSSM's 96.09% at a similar parameter count (305K).

Surprising findings

• A non-spiking f-SSM variant outperforms S4 on all LRA tasks (88.06% vs 80.48% average), suggesting gains come from fractional dynamics rather than spiking.

Limitations

• Not deployed on neuromorphic hardware; energy results are theoretical spiking-rate proxies.
• Average LRA score in text (85.28%) inconsistent with table (86.33%).

Experimental setup

Datasets: Long Range Arena WikiText-103 Speech Commands sMNIST psMNIST DVS128 Gesture

Benchmarks: Long Range Arena WikiText-103 Speech Commands sMNIST psMNIST DVS128 Gesture

Metrics: accuracy perplexity spiking rate energy estimate (MAC/AC)

Baselines: Transformer LMUFormer S4 S4D-Lin Spiking LMUFormer Binary S4D P-SpikeSSM SpikingSSM SpikeGPT

Builds on: SpikingSSM S4 HiPPO Surrogate Dynamic Network Mamba

Closest papers by meaning

• SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models (AAAI 2025 · similarity 0.92)
• P-SPIKESSM: HARNESSING PROBABILISTIC SPIKING STATE SPACE MODELS FOR LONG-RANGE DEPENDENCY TASKS (ICLR 2025 · similarity 0.90)
• Fractional State Space Transition for Long Sequence Modeling (NeurIPS 2026 · similarity 0.88)
• NDOT: Neuronal Dynamics-based Online Training for Spiking Neural Networks (ICML 2024 · similarity 0.88)
• The Dormant Spiking Neuron: A State-Driven Mechanism for Efficient Spiking Neural Networks (NeurIPS 2026 · similarity 0.88)
• SpikF: Spiking Fourier Network for Efficient Long-term Prediction (ICML 2025 · similarity 0.88)