About spikeDE
Traditional SNNs, governed by integer-order differential equations, often struggle to capture long-range temporal dependencies without resorting to deep, computationally expensive architectures. Our team recognized that biological neurons operate with complex, non-Markovian dynamics—properties naturally described by fractional calculus.
The goal of spikeDE is to bridge the gap between advanced mathematical theory and practical deep learning applications. By providing a robust, PyTorch-native implementation of Fractional-Order SNNs (f-SNNs), we aim to empower researchers and engineers to build more expressive, robust, and biologically plausible neural models with minimal effort.
The Research Behind spikeDE
The core algorithms and theoretical foundations of spikeDE are based on our paper, "Fractional-order Spiking Neural Network", which has been accepted by ICLR 2026 (International Conference on Learning Representations).
Paper Highlights
Our work introduces a paradigm shift from Markovian integer-order dynamics to non-Markovian fractional-order dynamics. Here are the key contributions:
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Capturing Long-Range Dependencies
Unlike traditional LIF neurons that rely on exponential decay, our f-LIF neurons utilize power-law relaxation via the Mittag-Leffler function. This allows the membrane potential to retain a "heavy-tailed" memory of past inputs, naturally modeling the complex temporal correlations observed in biological neurons.
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Proven Robustness & Stability
We provide theoretical guarantees showing that fractional-order dynamics suppress perturbation accumulation sub-linearly (\(t^\alpha\) vs \(t\)). Experiments confirm that spikeDE models maintain superior accuracy under heavy noise injection, occlusion, and temporal jitter compared to integer-order baselines.
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Strict Generalization
The spikeDE framework is a strict superset of traditional SNNs. By setting the fractional order \(\alpha=1\), it recovers standard IF/LIF dynamics. This ensures seamless compatibility with existing architectures like CNNs, Transformers, and GNNs, requiring only a drop-in replacement of the neuron module.
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Efficiency Without Compromise
Despite the added expressivity, our optimized solvers (using short-memory principles and FFT-based convolution) ensure that f-SNNs achieve comparable energy efficiency to traditional SNNs while delivering state-of-the-art performance on neuromorphic vision and graph learning tasks.
Key Theoretical Insight
A single fractional-order neuron represents a continuum of timescales that would require infinitely many integer-order units for exact equivalence. This irreducibility grants f-SNNs fundamentally richer expressive power.
Citation
If you use spikeDE in your research or applications, please consider citing our paper.
@misc{ge2026fractionalorderspikingneuralnetwork,
title={Fractional-order Spiking Neural Network},
author={Chengjie Ge and Yufeng Peng and Zihao Li and Qiyu Kang and Xueyang Fu and Xuhao Li and Qixin Zhang and Junhao Ren and Zheng-Jun Zha},
year={2026},
eprint={2507.16937},
archivePrefix={arXiv},
primaryClass={cs.NE},
url={https://arxiv.org/abs/2507.16937},
}
Community & Contribution
spikeDE is an open-source project licensed under the MIT License. We welcome contributions from the community!
Whether you find a bug, have a feature request, want to improve documentation, or wish to contribute new fractional solvers/neuron models, please feel free to open an issue or submit a Pull Request on our GitHub Repository.
Let's build the future of Spiking Neural Networks together.