# Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks

arXiv: https://arxiv.org/abs/2009.08378 · HTML: https://mlsanity.com/paper/2009.08378/

## Key facts

- Cited by 59 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Sep 2020.

## Built on by (most cited first, 30 of 59)

- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Beyond Classification: Directly Training Spiking Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/2110.07742/) (2021)
- [Sparse Spiking Gradient Descent](https://mlsanity.com/paper/2105.08810/) (2021)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Efficient recurrent architectures through activity sparsity and sparse back-propagation through time](https://mlsanity.com/paper/2206.06178/) (2022)
- [SpiNNaker2: A Large-Scale Neuromorphic System for Event-Based and Asynchronous Machine Learning](https://mlsanity.com/paper/2401.04491/) (2024)
- [High-performance deep spiking neural networks with 0.3 spikes per neuron](https://mlsanity.com/paper/2306.08744/) (2023)
- [Spike Calibration: Fast and Accurate Conversion of Spiking Neural Network for Object Detection and Segmentation](https://mlsanity.com/paper/2207.02702/) (2022)
- [Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks](https://mlsanity.com/paper/2212.01232/) (2022)
- [The Yin-Yang dataset](https://mlsanity.com/paper/2102.08211/) (2021)
- [Neuromorphic Computing and Sensing in Space](https://mlsanity.com/paper/2212.05236/) (2022)
- [Backpropagation through space, time, and the brain](https://mlsanity.com/paper/2403.16933/) (2024)
- [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)
- [Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation](https://mlsanity.com/paper/2410.11488/) (2024)
- [Supervised training of spiking neural networks for robust deployment on mixed-signal neuromorphic processors](https://mlsanity.com/paper/2102.06408/) (2021)
- [Learning through structure: towards deep neuromorphic knowledge graph embeddings](https://mlsanity.com/paper/2109.10376/) (2021)
- [SpikeCV: Open a Continuous Computer Vision Era](https://mlsanity.com/paper/2303.11684/) (2023)
- [Persistent learning signals and working memory without continuous attractors](https://mlsanity.com/paper/2308.12585/) (2023)
- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)
- [A Review of Neuroscience-Inspired Machine Learning](https://mlsanity.com/paper/2403.18929/) (2024)
- [Adaptive Intelligence: leveraging insights from adaptive behavior in animals to build flexible AI systems](https://mlsanity.com/paper/2411.15234/) (2024)
- [Relational representation learning with spike trains](https://mlsanity.com/paper/2205.09140/) (2022)
- [EXODUS: Stable and Efficient Training of Spiking Neural Networks](https://mlsanity.com/paper/2205.10242/) (2022)
- [Romanian Multiword Expression Detection Using Multilingual Adversarial Training and Lateral Inhibition](https://mlsanity.com/paper/2304.11350/) (2023)
- [Timing-Based Backpropagation in Spiking Neural Networks Without Single-Spike Restrictions](https://mlsanity.com/paper/2211.16113/) (2022)
- [Sparse-firing regularization methods for spiking neural networks with time-to-first spike coding](https://mlsanity.com/paper/2307.13007/) (2023)
- [Exploring the Limitations of Layer Synchronization in Spiking Neural Networks](https://mlsanity.com/paper/2408.05098/) (2024)

## Abstract (arXiv)

Spiking neural networks combine analog computation with event-based communication using discrete spikes. While the impressive advances of deep learning are enabled by training non-spiking artificial neural networks using the backpropagation algorithm, applying this algorithm to spiking networks was previously hindered by the existence of discrete spike events and discontinuities. For the first time, this work derives the backpropagation algorithm for a continuous-time spiking neural network and a general loss function by applying the adjoint method together with the proper partial derivative jumps, allowing for backpropagation through discrete spike events without approximations. This algorithm, EventProp, backpropagates errors at spike times in order to compute the exact gradient in an event-based, temporally and spatially sparse fashion. We use gradients computed via EventProp to train networks on the Yin-Yang and MNIST datasets using either a spike time or voltage based loss function and report competitive performance. Our work supports the rigorous study of gradient-based learning algorithms in spiking neural networks and provides insights toward their implementation in novel brain-inspired hardware.