| 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: Fractional Order Spiking State Space Models for Efficient Long Sequence Learning
Overview
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.
Core Innovation
Fractional-Order Dynamics
- Problem: Traditional SNNs use first-order ODEs → memoryless bottleneck → limited long-range dependency
- Solution: Extend to fractional calculus regime → hierarchical integration with long-memory kernels
- Key Insight: Fractional operators enable memory kernels that capture multi-scale temporal dependencies
f-SSM Architecture
State Transition: x_{t+α} = A x_t + B u_t (fractional order α)
Output: y_t = C x_t + D u_t
- A, B, C, D: State space matrices
- α: Fractional order (typically 0.1-0.9)
- Memory Kernel: Hierarchical integration of past states
Efficient Parallelization
- Challenge: Fractional operators → computational overhead + parallelization difficulty
- Solution: State-space formulation enables parallel training
- Result: Maintains sparse synaptic computation while supporting GPU acceleration
Key Technical Components
1. Fractional-Order Neuron Model
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)
2. Long-Memory Kernel
- Implementation: Hierarchical state integration
- Memory Horizon: Configurable (10-1000 steps)
- Sparsity: Preserved through spike-based computation
3. Training Algorithm
- Backpropagation: Through fractional states via state-space reformulation
- Gradient: Efficiently computed via parallel scan
- Spiking Mechanism: LIF threshold + fractional state accumulation
Experimental Results
