# Elucidating the theoretical underpinnings of surrogate gradient learning in spiking neural networks

arXiv: https://arxiv.org/abs/2404.14964 · HTML: https://mlsanity.com/paper/2404.14964/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Apr 2024.

## Built on by (most cited first, 11 of 11)

- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals](https://mlsanity.com/paper/2405.13587/) (2024)
- [Enforcing convex constraints in Graph Neural Networks](https://mlsanity.com/paper/2510.11227/) (2025)
- [Quadratic integrate-and-fire neurons exhibit less fragmented loss landscapes and outperform leaky integrate-and-fire neurons in spike-based gradient descent](https://mlsanity.com/paper/2606.03935/) (2026)
- [Harnessing Nonidealities in Analog In-Memory Computing Circuits: A Physical Modeling Approach for Neuromorphic Systems](https://mlsanity.com/paper/2412.09010/) (2024)
- [Adaptive Surrogate Gradients for Sequential Reinforcement Learning in Spiking Neural Networks](https://mlsanity.com/paper/2510.24461/) (2025)
- [PTS-SNN: A Prompt-Tuned Temporal Shift Spiking Neural Networks for Efficient Speech Emotion Recognition](https://mlsanity.com/paper/2602.08240/) (2026)
- [IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce](https://mlsanity.com/paper/2411.18250/) (2024)
- [A Principled Bayesian Framework for Training Binary and Spiking Neural Networks](https://mlsanity.com/paper/2505.17962/) (2025)
- [Random Feature Spiking Neural Networks](https://mlsanity.com/paper/2510.01012/) (2025)
- [Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization](https://mlsanity.com/paper/2607.14672/) (2026)

## Abstract (arXiv)

Training spiking neural networks to approximate universal functions is essential for studying information processing in the brain and for neuromorphic computing. Yet the binary nature of spikes poses a challenge for direct gradient-based training. Surrogate gradients have been empirically successful in circumventing this problem, but their theoretical foundation remains elusive. Here, we investigate the relation of surrogate gradients to two theoretically well-founded approaches. On the one hand, we consider smoothed probabilistic models, which, due to the lack of support for automatic differentiation, are impractical for training multi-layer spiking neural networks but provide derivatives equivalent to surrogate gradients for single neurons. On the other hand, we investigate stochastic automatic differentiation, which is compatible with discrete randomness but has not yet been used to train spiking neural networks. We find that the latter gives surrogate gradients a theoretical basis in stochastic spiking neural networks, where the surrogate derivative matches the derivative of the neuronal escape noise function. This finding supports the effectiveness of surrogate gradients in practice and suggests their suitability for stochastic spiking neural networks. However, surrogate gradients are generally not gradients of a surrogate loss despite their relation to stochastic automatic differentiation. Nevertheless, we empirically confirm the effectiveness of surrogate gradients in stochastic multi-layer spiking neural networks and discuss their relation to deterministic networks as a special case. Our work gives theoretical support to surrogate gradients and the choice of a suitable surrogate derivative in stochastic spiking neural networks.