# Timing-Based Backpropagation in Spiking Neural Networks Without Single-Spike Restrictions

arXiv: https://arxiv.org/abs/2211.16113 · HTML: https://mlsanity.com/paper/2211.16113/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 29 Nov 2022.

## Builds on (most cited first, 17 of 17)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Deep Reinforcement Learning for Autonomous Driving: A Survey](https://mlsanity.com/paper/2002.00444/) (2020)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Enabling Spike-based Backpropagation for Training Deep Neural Network Architectures](https://mlsanity.com/paper/1903.06379/) (2019)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)
- [Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks](https://mlsanity.com/paper/2009.08378/) (2020)
- [Fast and energy-efficient neuromorphic deep learning with first-spike times](https://mlsanity.com/paper/1912.11443/) (2019)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [Temporal Coding in Spiking Neural Networks with Alpha Synaptic Function: Learning with Backpropagation](https://mlsanity.com/paper/1907.13223/) (2019)
- [Surrogate gradients for analog neuromorphic computing](https://mlsanity.com/paper/2006.07239/) (2020)
- [Hybrid Macro/Micro Level Backpropagation for Training Deep Spiking Neural Networks](https://mlsanity.com/paper/1805.07866/) (2018)
- [Unifying Activation- and Timing-based Learning Rules for Spiking Neural Networks](https://mlsanity.com/paper/2006.02642/) (2020)
- [Towards Understanding the Effect of Leak in Spiking Neural Networks](https://mlsanity.com/paper/2006.08761/) (2020)
- [A Supervised Learning Algorithm for Multilayer Spiking Neural Networks Based on Temporal Coding Toward Energy-Efficient VLSI Processor Design](https://mlsanity.com/paper/2001.05348/) (2020)

## Built on by (most cited first, 3 of 3)

- [Sparse-firing regularization methods for spiking neural networks with time-to-first spike coding](https://mlsanity.com/paper/2307.13007/) (2023)
- [Towards Efficient Formal Verification of Spiking Neural Network](https://mlsanity.com/paper/2408.10900/) (2024)
- [Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization](https://mlsanity.com/paper/2607.14672/) (2026)

## Abstract (arXiv)

We propose a novel backpropagation algorithm for training spiking neural networks (SNNs) that encodes information in the relative multiple spike timing of individual neurons without single-spike restrictions. The proposed algorithm inherits the advantages of conventional timing-based methods in that it computes accurate gradients with respect to spike timing, which promotes ideal temporal coding. Unlike conventional methods where each neuron fires at most once, the proposed algorithm allows each neuron to fire multiple times. This extension naturally improves the computational capacity of SNNs. Our SNN model outperformed comparable SNN models and achieved as high accuracy as non-convolutional artificial neural networks. The spike count property of our networks was altered depending on the time constant of the postsynaptic current and the membrane potential. Moreover, we found that there existed the optimal time constant with the maximum test accuracy. That was not seen in conventional SNNs with single-spike restrictions on time-to-fast-spike (TTFS) coding. This result demonstrates the computational properties of SNNs that biologically encode information into the multi-spike timing of individual neurons. Our code would be publicly available.