Welcome to spikeDE's documentation
spikeDE is a powerful, PyTorch-native library designed to build, train, and deploy Fractional-Order Spiking Neural Networks (f-SNNs).
While traditional Spiking Neural Networks (SNNs) rely on integer-order differential equations (e.g., standard Leaky Integrate-and-Fire models) that assume Markovian dynamics—where the current state depends solely on the immediate past—spikeDE introduces a generalized fractional calculus framework. By utilizing Caputo fractional derivatives (\(D^\alpha\)), our library enables neural units with inherent long-term memory and non-Markovian properties, closely mimicking the complex temporal dynamics and fractal structures observed in biological neurons.
Why Fractional?
The core innovation of spikeDE lies in its ability to treat fractional order as a strict generalization of integer order. It is not merely an alternative model; it is a comprehensive superset framework.
| Feature | Traditional Integer-Order SNNs (\(\alpha = 1\)) | spikeDE Fractional-Order SNNs (\(0 < \alpha \le 1\)) |
|---|---|---|
| Dynamics | Forgets history rapidly; strictly Markovian. | Integrates history over long time horizons with heavy-tailed memory. |
| Memory Mechanism | Short-term memory with a fixed time constant. Simulating long dependencies requires large, deep networks. | A single fractional neuron naturally captures multi-scale temporal correlations without extra depth. |
| Expressivity | Limited by fixed decay rates and finite timescales. | Theoretical analysis proves that one fractional neuron cannot be equated to any finite ensemble of integer-order neurons. |
| Robustness | Often sensitive to input noise and parameter perturbations. | Fractional dynamics provide enhanced robustness against disturbances and noise. |
In spikeDE, setting the fractional order \(\alpha = 1\) seamlessly recovers standard SNN behavior, ensuring backward compatibility. Conversely, setting \(0 < \alpha < 1\) unlocks the power of fractional dynamics, offering superior performance in tasks requiring complex temporal processing, such as neuromorphic vision, speech recognition, and event-based graph learning.
Documentation Overview
Navigate through our comprehensive guides to get started, master the core concepts, or dive into advanced API usage.
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Getting Started
New to spikeDE? Start here to install the package and launch your first fractional spiking network with our step-by-step quickstart guide.
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Tutorials
From core concepts to advanced mastery. Deepen your understanding of the mathematical foundations and learn how to optimize your spikeDE workflows.
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API Reference
Comprehensive documentation for spikeDE's core modules. Build custom architectures with full control.
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Blog & Updates
Stay updated with the latest posts on new features, performance benchmarks, and insights from the community.
Happy spiking with fractional dynamics!