Skip to content

Introducing spikeDE: Where Fractional Calculus Meets Spiking Neural Networks

Today marks a significant milestone for our research team. We are incredibly proud to announce the public release of spikeDE, an open-source PyTorch based library designed to bring Fractional-Order Dynamics to the world of Spiking Neural Networks (SNNs).

For years, SNNs have been celebrated for their biological plausibility and energy efficiency. However, traditional models like the Leaky Integrate-and-Fire (LIF) neuron rely on integer-order differential equations (\(\alpha=1\)), which assume Markovian dynamics—meaning the neuron's current state depends only on its immediate past. This simplification fails to capture the rich, complex temporal dependencies observed in real biological neurons, which exhibit long-term memory and power-law relaxation.

With spikeDE, we change the paradigm.

The Core Idea: Beyond Integer Orders

As detailed in our upcoming paper at ICLR 2026, "Fractional-order Spiking Neural Network", biological systems often operate on multiple time scales simultaneously. A single integer-order neuron cannot efficiently represent this spectrum without stacking infinite layers.

spikeDE introduces the Caputo fractional derivative (\(D^\alpha\), where \(0 < \alpha \leq 1\)) into the membrane potential dynamics:

\[ \tau D^\alpha U(t) = f(t, U(t), I(t)) \]

By tuning the fractional order \(\alpha\), our f-LIF neurons naturally exhibit:

  1. Heavy-tailed Memory: Past inputs influence the current state via a Mittag-Leffler function decay, not just a simple exponential.
  2. Non-Markovian Behavior: The system inherently "remembers" its history, capturing long-range dependencies crucial for processing temporal data like event-based vision or dynamic graphs.
  3. Enhanced Robustness: Our theoretical analysis shows that fractional dynamics suppress noise accumulation sub-linearly (\(t^\alpha\) vs \(t\)), making f-SNNs significantly more robust to input perturbations.

What's New in spikeDE?

The initial release of spikeDE is built from the ground up to be flexible, efficient, and strictly compatible with the PyTorch ecosystem.

Native Fractional Solvers

We integrate optimized solvers directly into the computational graph. This allows for end-to-end training, even with non-local fractional operators.

Per-Layer Customization

Not all layers need the same memory depth. spikeDE allows you to set distinct \(\alpha\) values for each layer or even make \(\alpha\) a learnable parameter, letting the network discover the optimal time-scale spectrum for your specific task.

from spikeDE import SNNWrapper, LIFNeuron

# Make alpha learnable! The network decides how much memory it needs.
net = SNNWrapper(
    base=my_snn_model,
    integrator='fdeint',
    alpha=[0.5, 0.8, 0.9], # Different memory depths per layer
    learn_alpha=True       # Enable gradient updates for alpha
)

Strict Generalization

spikeDE is a strict superset of traditional SNNs. Setting \(\alpha=1.0\) recovers the standard LIF dynamics exactly. This means you can seamlessly migrate existing CNN-to-SNN or direct-training workflows to the fractional domain with minimal code changes.

Early Results: State-of-the-Art Performance

Our experiments, documented in the ICLR 2026 paper, demonstrate that f-SNNs consistently outperform their integer-order counterparts:

  • Neuromorphic Vision: On the HarDVS dataset, our f-SNN achieved 47.66% accuracy, surpassing the best integer-order baseline by +1.55%.
  • Graph Learning: In dynamic graph tasks (e.g., Cora), the fractional Spiking Graph Convolutional Network showed a remarkable +6.2% improvement in node classification, proving the power of long-range temporal aggregation on graph structures.
  • Robustness: Under heavy noise injection and time-jitter attacks, f-SNNs maintained stable performance where traditional SNNs degraded rapidly.

Getting Started

Getting started with spikeDE is easy. Whether you are a neuroscientist modeling biological circuits or a machine learning engineer building low-power AI, our documentation has you covered.

Summary

We believe that Fractional Calculus holds the key to unlocking the next generation of efficient, brain-inspired AI. By open-sourcing spikeDE, we hope to lower the barrier for researchers to explore this fascinating intersection of mathematics and neuroscience.

Full Paper Documentation Source Code

We welcome contributions, issues, and discussions. Let's build the future of memory-rich neural networks together! Happy Spiking!