# Temporal Coding in Spiking Neural Networks with Alpha Synaptic Function: Learning with Backpropagation

arXiv: https://arxiv.org/abs/1907.13223 · HTML: https://mlsanity.com/paper/1907.13223/

## Key facts

- Cited by 45 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2019.

## Built on by (most cited first, 30 of 45)

- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Attention Spiking Neural Networks](https://mlsanity.com/paper/2209.13929/) (2022)
- [Beyond Classification: Directly Training Spiking Neural Networks for Semantic Segmentation](https://mlsanity.com/paper/2110.07742/) (2021)
- [Neural Architecture Search for Spiking Neural Networks](https://mlsanity.com/paper/2201.10355/) (2022)
- [Visual Explanations from Spiking Neural Networks using Interspike Intervals](https://mlsanity.com/paper/2103.14441/) (2021)
- [Exploring Lottery Ticket Hypothesis in Spiking Neural Networks](https://mlsanity.com/paper/2207.01382/) (2022)
- [Training Full Spike Neural Networks via Auxiliary Accumulation Pathway](https://mlsanity.com/paper/2301.11929/) (2023)
- [Rate Coding or Direct Coding: Which One is Better for Accurate, Robust, and Energy-efficient Spiking Neural Networks?](https://mlsanity.com/paper/2202.03133/) (2022)
- [Exploring Temporal Information Dynamics in Spiking Neural Networks](https://mlsanity.com/paper/2211.14406/) (2022)
- [High-performance deep spiking neural networks with 0.3 spikes per neuron](https://mlsanity.com/paper/2306.08744/) (2023)
- [The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware](https://mlsanity.com/paper/2106.07030/) (2021)
- [One Timestep is All You Need: Training Spiking Neural Networks with Ultra Low Latency](https://mlsanity.com/paper/2110.05929/) (2021)
- [Neuromorphic Visual Scene Understanding with Resonator Networks](https://mlsanity.com/paper/2208.12880/) (2022)
- [Efficient Federated Learning with Spike Neural Networks for Traffic Sign Recognition](https://mlsanity.com/paper/2205.14315/) (2022)
- [An Exact Mapping From ReLU Networks to Spiking Neural Networks](https://mlsanity.com/paper/2212.12522/) (2022)
- [Mamba-Spike: Enhancing the Mamba Architecture with a Spiking Front-End for Efficient Temporal Data Processing](https://mlsanity.com/paper/2408.11823/) (2024)
- [Neuromorphic Computing and Sensing in Space](https://mlsanity.com/paper/2212.05236/) (2022)
- [SpikE: spike-based embeddings for multi-relational graph data](https://mlsanity.com/paper/2104.13398/) (2021)
- [Can Deep Neural Networks be Converted to Ultra Low-Latency Spiking Neural Networks?](https://mlsanity.com/paper/2112.12133/) (2021)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [LoAS: Fully Temporal-Parallel Dataflow for Dual-Sparse Spiking Neural Networks](https://mlsanity.com/paper/2407.14073/) (2024)
- [Spike time displacement based error backpropagation in convolutional spiking neural networks](https://mlsanity.com/paper/2108.13621/) (2021)
- [Rethinking the role of normalization and residual blocks for spiking neural networks](https://mlsanity.com/paper/2203.01544/) (2022)
- [In-Sensor & Neuromorphic Computing are all you need for Energy Efficient Computer Vision](https://mlsanity.com/paper/2212.10881/) (2022)
- [Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders](https://mlsanity.com/paper/2404.04549/) (2024)
- [Temporal Spiking Neural Networks with Synaptic Delay for Graph Reasoning](https://mlsanity.com/paper/2405.16851/) (2024)
- [Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithm](https://mlsanity.com/paper/2502.20411/) (2025)
- [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)
- [Hoyer regularizer is all you need for ultra low-latency spiking neural networks](https://mlsanity.com/paper/2212.10170/) (2022)

## Abstract (arXiv)

The timing of individual neuronal spikes is essential for biological brains to make fast responses to sensory stimuli. However, conventional artificial neural networks lack the intrinsic temporal coding ability present in biological networks. We propose a spiking neural network model that encodes information in the relative timing of individual neuron spikes. In classification tasks, the output of the network is indicated by the first neuron to spike in the output layer. This temporal coding scheme allows the supervised training of the network with backpropagation, using locally exact derivatives of the postsynaptic spike times with respect to presynaptic spike times. The network operates using a biologically-plausible alpha synaptic transfer function. Additionally, we use trainable synchronisation pulses that provide bias, add flexibility during training and exploit the decay part of the alpha function. We show that such networks can be trained successfully on noisy Boolean logic tasks and on the MNIST dataset encoded in time. The results show that the spiking neural network outperforms comparable spiking models on MNIST and achieves similar quality to fully connected conventional networks with the same architecture. We also find that the spiking network spontaneously discovers two operating regimes, mirroring the accuracy-speed trade-off observed in human decision-making: a slow regime, where a decision is taken after all hidden neurons have spiked and the accuracy is very high, and a fast regime, where a decision is taken very fast but the accuracy is lower. These results demonstrate the computational power of spiking networks with biological characteristics that encode information in the timing of individual neurons. By studying temporal coding in spiking networks, we aim to create building blocks towards energy-efficient and more complex biologically-inspired neural architectures.