# Spike-Train Level Backpropagation for Training Deep Recurrent Spiking Neural Networks

arXiv: https://arxiv.org/abs/1908.06378 · HTML: https://mlsanity.com/paper/1908.06378/

## Key facts

- Cited by 32 papers in the map (data through 7 Oct 2026).
- First posted on arXiv 18 Aug 2019.

## Built on by (most cited first, 30 of 32)

- [Neural Architecture Search for Spiking Neural Networks](https://mlsanity.com/paper/2201.10355/) (2022)
- [Online Training Through Time for Spiking Neural Networks](https://mlsanity.com/paper/2210.04195/) (2022)
- [Training Feedback Spiking Neural Networks by Implicit Differentiation on the Equilibrium State](https://mlsanity.com/paper/2109.14247/) (2021)
- [TCJA-SNN: Temporal-Channel Joint Attention for Spiking Neural Networks](https://mlsanity.com/paper/2206.10177/) (2022)
- [Backpropagation with Biologically Plausible Spatio-Temporal Adjustment For Training Deep Spiking Neural Networks](https://mlsanity.com/paper/2110.08858/) (2021)
- [STSC-SNN: Spatio-Temporal Synaptic Connection with Temporal Convolution and Attention for Spiking Neural Networks](https://mlsanity.com/paper/2210.05241/) (2022)
- [Axonal Delay As a Short-Term Memory for Feed Forward Deep Spiking Neural Networks](https://mlsanity.com/paper/2205.02115/) (2022)
- [Fully Spiking Actor Network with Intra-layer Connections for Reinforcement Learning](https://mlsanity.com/paper/2401.05444/) (2024)
- [A Synapse-Threshold Synergistic Learning Approach for Spiking Neural Networks](https://mlsanity.com/paper/2206.06129/) (2022)
- [SPIDE: A Purely Spike-based Method for Training Feedback Spiking Neural Networks](https://mlsanity.com/paper/2302.00232/) (2023)
- [Tensor Decomposition Based Attention Module for Spiking Neural Networks](https://mlsanity.com/paper/2310.14576/) (2023)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [Spiking CapsNet: A Spiking Neural Network With A Biologically Plausible Routing Rule Between Capsules](https://mlsanity.com/paper/2111.07785/) (2021)
- [KLIF: An optimized spiking neuron unit for tuning surrogate gradient slope and membrane potential](https://mlsanity.com/paper/2302.09238/) (2023)
- [Ultra-low Latency Spiking Neural Networks with Spatio-Temporal Compression and Synaptic Convolutional Block](https://mlsanity.com/paper/2203.10006/) (2022)
- [Direct Training via Backpropagation for Ultra-low Latency Spiking Neural Networks with Multi-threshold](https://mlsanity.com/paper/2112.07426/) (2021)
- [SIT: A Bionic and Non-Linear Neuron for Spiking Neural Network](https://mlsanity.com/paper/2203.16117/) (2022)
- [Learning in Feedback-driven Recurrent Spiking Neural Networks using full-FORCE Training](https://mlsanity.com/paper/2205.13585/) (2022)
- [Models Developed for Spiking Neural Networks](https://mlsanity.com/paper/2212.04377/) (2022)
- [Fully Spiking Denoising Diffusion Implicit Models](https://mlsanity.com/paper/2312.01742/) (2023)
- [Edge Intelligence with Spiking Neural Networks](https://mlsanity.com/paper/2507.14069/) (2025)
- [S3NN: Time Step Reduction of Spiking Surrogate Gradients for Training Energy Efficient Single-Step Spiking Neural Networks](https://mlsanity.com/paper/2201.10879/) (2022)
- [SpikeX: Exploring Accelerator Architecture and Network-Hardware Co-Optimization for Sparse Spiking Neural Networks](https://mlsanity.com/paper/2505.12292/) (2025)
- [Front Contribution instead of Back Propagation](https://mlsanity.com/paper/2106.05569/) (2021)
- [The Spike Gating Flow: A Hierarchical Structure Based Spiking Neural Network for Online Gesture Recognition](https://mlsanity.com/paper/2206.01910/) (2022)
- [A temporally and spatially local spike-based backpropagation algorithm to enable training in hardware](https://mlsanity.com/paper/2207.09755/) (2022)
- [Exploring Tradeoffs in Spiking Neural Networks](https://mlsanity.com/paper/2212.09500/) (2022)
- [Membrane Potential Distribution Adjustment and Parametric Surrogate Gradient in Spiking Neural Networks](https://mlsanity.com/paper/2304.13289/) (2023)
- [SPENSER: Towards a NeuroEvolutionary Approach for Convolutional Spiking Neural Networks](https://mlsanity.com/paper/2305.10987/) (2023)
- [ParaRevSNN: A Parallel Reversible Spiking Neural Network for Efficient Training and Inference](https://mlsanity.com/paper/2508.01223/) (2025)

## Abstract (arXiv)

Spiking neural networks (SNNs) well support spatiotemporal learning and energy-efficient event-driven hardware neuromorphic processors. As an important class of SNNs, recurrent spiking neural networks (RSNNs) possess great computational power. However, the practical application of RSNNs is severely limited by challenges in training. Biologically-inspired unsupervised learning has limited capability in boosting the performance of RSNNs. On the other hand, existing backpropagation (BP) methods suffer from high complexity of unrolling in time, vanishing and exploding gradients, and approximate differentiation of discontinuous spiking activities when applied to RSNNs. To enable supervised training of RSNNs under a well-defined loss function, we present a novel Spike-Train level RSNNs Backpropagation (ST-RSBP) algorithm for training deep RSNNs. The proposed ST-RSBP directly computes the gradient of a rated-coded loss function defined at the output layer of the network w.r.t tunable parameters. The scalability of ST-RSBP is achieved by the proposed spike-train level computation during which temporal effects of the SNN is captured in both the forward and backward pass of BP. Our ST-RSBP algorithm can be broadly applied to RSNNs with a single recurrent layer or deep RSNNs with multiple feed-forward and recurrent layers. Based upon challenging speech and image datasets including TI46, N-TIDIGITS, Fashion-MNIST and MNIST, ST-RSBP is able to train RSNNs with an accuracy surpassing that of the current state-of-art SNN BP algorithms and conventional non-spiking deep learning models.