# S4NN: temporal backpropagation for spiking neural networks with one spike per neuron

arXiv: https://arxiv.org/abs/1910.09495 · HTML: https://mlsanity.com/paper/1910.09495/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Oct 2019.

## Built on by (most cited first, 30 of 49)

- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Optimized Potential Initialization for Low-latency Spiking Neural Networks](https://mlsanity.com/paper/2202.01440/) (2022)
- [Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies](https://mlsanity.com/paper/2304.12760/) (2023)
- [Reducing ANN-SNN Conversion Error through Residual Membrane Potential](https://mlsanity.com/paper/2302.02091/) (2023)
- [Bridging the Gap between ANNs and SNNs by Calibrating Offset Spikes](https://mlsanity.com/paper/2302.10685/) (2023)
- [Visual Explanations from Spiking Neural Networks using Interspike Intervals](https://mlsanity.com/paper/2103.14441/) (2021)
- [Training Full Spike Neural Networks via Auxiliary Accumulation Pathway](https://mlsanity.com/paper/2301.11929/) (2023)
- [Signal Propagation: A Framework for Learning and Inference In a Forward Pass](https://mlsanity.com/paper/2204.01723/) (2022)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [An Exact Mapping From ReLU Networks to Spiking Neural Networks](https://mlsanity.com/paper/2212.12522/) (2022)
- [Axonal Delay As a Short-Term Memory for Feed Forward Deep Spiking Neural Networks](https://mlsanity.com/paper/2205.02115/) (2022)
- [LM-HT SNN: Enhancing the Performance of SNN to ANN Counterpart through Learnable Multi-hierarchical Threshold Model](https://mlsanity.com/paper/2402.00411/) (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)
- [Spiking-GAN: A Spiking Generative Adversarial Network Using Time-To-First-Spike Coding](https://mlsanity.com/paper/2106.15420/) (2021)
- [Spike time displacement based error backpropagation in convolutional spiking neural networks](https://mlsanity.com/paper/2108.13621/) (2021)
- [Low Latency Conversion of Artificial Neural Network Models to Rate-encoded Spiking Neural Networks](https://mlsanity.com/paper/2211.08410/) (2022)
- [Paired Competing Neurons Improving STDP Supervised Local Learning In Spiking Neural Networks](https://mlsanity.com/paper/2308.02194/) (2023)
- [Stable Learning Using Spiking Neural Networks Equipped With Affine Encoders and Decoders](https://mlsanity.com/paper/2404.04549/) (2024)
- [Backpropagation-free Spiking Neural Networks with the Forward-Forward Algorithm](https://mlsanity.com/paper/2502.20411/) (2025)
- [Deep Phasor Networks: Connecting Conventional and Spiking Neural Networks](https://mlsanity.com/paper/2106.11908/) (2021)
- [Relational representation learning with spike trains](https://mlsanity.com/paper/2205.09140/) (2022)
- [Addressing the speed-accuracy simulation trade-off for adaptive spiking neurons](https://mlsanity.com/paper/2311.11390/) (2023)
- [Neuronal Competition Groups with Supervised STDP for Spike-Based Classification](https://mlsanity.com/paper/2410.17066/) (2024)
- [Efficient ANN-SNN Conversion with Error Compensation Learning](https://mlsanity.com/paper/2506.01968/) (2025)
- [HYPER-SNN: Towards Energy-efficient Quantized Deep Spiking Neural Networks for Hyperspectral Image Classification](https://mlsanity.com/paper/2107.11979/) (2021)
- [Efficient Training of Spiking Neural Networks with Temporally-Truncated Local Backpropagation through Time](https://mlsanity.com/paper/2201.07210/) (2021)
- [Sparse-firing regularization methods for spiking neural networks with time-to-first spike coding](https://mlsanity.com/paper/2307.13007/) (2023)
- [Recent Advances in Scalable Energy-Efficient and Trustworthy Spiking Neural networks: from Algorithms to Technology](https://mlsanity.com/paper/2312.01213/) (2023)

## Abstract (arXiv)

We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with any number of layers. This approach reaches state-of-the-art performance with supervised multi fully-connected layer SNNs: test accuracy of 97.4% for the MNIST dataset, and 99.2% for the Caltech Face/Motorbike dataset. Yet, the neuron model that we use, non-leaky integrate-and-fire, is much simpler than the one used in all previous works. The source codes of the proposed S4NN are publicly available at https://github.com/SRKH/S4NN.