# Improving Spiking Network Training using Dynamical Systems

## Goal
The goal is to overcome a key obstacle in training brain-inspired **Spiking Neural Networks (SNNs)**.  
While SNNs are promising, their all-or-nothing “spikes” are **non-differentiable**, clashing with standard training algorithms.  
The common workaround, **surrogate gradients**, often fails on temporal tasks due to **unstable error signals** that either **explode or vanish**.  

This project reframes the problem using **dynamical systems theory**.  
You will evaluate a novel technique called **surrogate gradient flossing**, which measures the stability of the training process by calculating **surrogate Lyapunov exponents**.  
By actively tuning the network to control these exponents, you will stabilize learning and enable SNNs to tackle challenging **temporal credit assignment** problems.

---

## Project Rationale
The **surrogate gradient flossing** idea has been implemented and showed initial promise, but it requires **rigorous evaluation** and a **deeper theoretical understanding** of its mechanics.  

The central question is whether **explicitly controlling the stability of the gradient flow** is a viable and robust strategy for improving learning in SNNs.  

This project offers a chance to explore the **fundamental link between system dynamics and learning capacity**.

---

## Key Outcomes

- ✅ **Train a simple SNN** with surrogate gradient flossing and perform gradient analysis.  
- 🚀 **(Stretch)**: Compare performance on **benchmark temporal tasks** such as *spiking spoken digits classification* and analyze the resulting network dynamics.  
- 🧠 **(Stretch)**: Implement a **multi-layer SNN** and quantify gradients and performance **with and without** surrogate gradient flossing.  
- 🔧 **(Stretch)**: **Optimize the gradient flossing schedule** to improve stability and convergence.

---

## Project Profile

| Category           | Intensity |
|--------------------|------------|
| Analytical Intensity | ⭐⭐⭐ |
| Coding Intensity      | ⭐⭐⭐ |
| Computational Neuroscience | ⭐⭐⭐ |
| Machine Learning       | ⭐⭐⭐ |

**Starter Toolkit:** Reference example implementations available in **Julia** and **Python**.

---

## Literature

1. **Neftci, E. O., Mostafa, H., & Zenke, F. (2019).**  
   *Surrogate gradient learning in spiking neural networks.*  
   _IEEE Signal Processing Magazine, 36(6), 51–63._

2. **Engelken, R. (2023).**  
   *Gradient Flossing: Improving Gradient Descent through Dynamic Control of Jacobians.*  
   _NeurIPS._  
   [https://doi.org/10.48550/arXiv.2312.17306](https://doi.org/10.48550/arXiv.2312.17306)

3. **Gygax, J., & Zenke, F. (2025).**  
   *Elucidating the theoretical underpinnings of surrogate gradient learning in spiking neural networks.*  
   _Neural Computation, 37(5), 886–925._

4. **Rossbroich, J., Gygax, J., & Zenke, F. (2022).**  
   *Fluctuation-driven initialization for spiking neural network training.*  
   _Neuromorphic Computing and Engineering, 2(4), 044016._

5. **Yik, J., et al. (2025).**  
   *The Neurobench framework for benchmarking neuromorphic computing algorithms and systems.*  
   _Nature Communications, 16(1), 1545._