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LongSpike fractional-order SSM for SNNs — enables efficient long-range dependency learning through fractional calculus while preserving sparse synaptic computation
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| name | longspike-fractional-order-snn-state-space |
| description | LongSpike fractional-order SSM for SNNs — enables efficient long-range dependency learning through fractional calculus while preserving sparse synaptic computation |
| authors | Xinrui He, Qiyu Kang, Xuecheng Wang |
| arxiv_id | 2606.12895v1 |
| submitted | 2026-06-11T00:00:00.000Z |
| categories | cs.LG |
| keywords | fractional-order SNN, long sequence, spiking state space model, f-SSM, fractional calculus, neuromorphic, long-memory kernel |
| activation_words | fractional-order SNN, long sequence SNN, f-SSM, LongSpike, fractional calculus neural networks, spiking state space models, long-memory SNN |
LongSpike introduces fractional-order State Space Models (f-SSM) into spiking neural networks to overcome the "memoryless bottleneck" of first-order ODE dynamics, enabling efficient long-range dependency capture while preserving sparse synaptic computation.
State Transition: x_{t+α} = A x_t + B u_t (fractional order α)
Output: y_t = C x_t + D u_t
# Fractional derivative (Grünwald-Letnikov approximation)
Δ^α x_t = lim_{h→0} h^{-α} Σ_{k=0}^n w_k^{(α)} x_{t-kh}
where w_k^{(α)} = (-1)^k binomial(α, k)
| Task | LongSpike | Best SNN Baseline | Improvement |
|---|---|---|---|
| Long Range Arena (LRA) | 58.2% | 53.1% | +5.1% |
| WikiText-103 | 32.4 perplexity | 38.7 | -6.3 |
| Speech Commands | 94.7% | 91.2% | +3.5% |
| Method | Memory | Parallelization | Energy | Accuracy |
|---|---|---|---|---|
| LongSpike | ✓ Long | ✓ GPU | ✓ Sparse | ✓ High |
| Spiking Transformer | △ Medium | ✓ GPU | ✓ Sparse | △ Medium |
| Spiking LSTM | ✗ Short | ✗ Sequential | ✓ Sparse | ✗ Low |