# SPIDE: A Purely Spike-based Method for Training Feedback Spiking Neural Networks

arXiv: https://arxiv.org/abs/2302.00232 · HTML: https://mlsanity.com/paper/2302.00232/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Builds on 46 of its 81 references that are in the map.
- First posted on arXiv 1 Feb 2023.

## Builds on (most cited first, 30 of 46)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (2018)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (2018)
- [HATS: Histograms of Averaged Time Surfaces for Robust Event-based Object Classification](https://mlsanity.com/paper/1803.07913/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Temporal Efficient Training of Spiking Neural Network via Gradient Re-weighting](https://mlsanity.com/paper/2202.11946/) (2022)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [Multiscale Deep Equilibrium Models](https://mlsanity.com/paper/2006.08656/) (2020)
- [Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagation](https://mlsanity.com/paper/2005.01807/) (2020)
- [Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networks](https://mlsanity.com/paper/2103.00476/) (2021)
- [A Free Lunch From ANN: Towards Efficient, Accurate Spiking Neural Networks Calibration](https://mlsanity.com/paper/2106.06984/) (2021)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Brain-Like Object Recognition with High-Performing Shallow Recurrent ANNs](https://mlsanity.com/paper/1909.06161/) (2019)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Characterizing signal propagation to close the performance gap in unnormalized ResNets](https://mlsanity.com/paper/2101.08692/) (2021)
- [Stabilizing Equilibrium Models by Jacobian Regularization](https://mlsanity.com/paper/2106.14342/) (2021)
- [Towards deep learning with segregated dendrites](https://mlsanity.com/paper/1610.00161/) (2016)
- [Spiking Deep Networks with LIF Neurons](https://mlsanity.com/paper/1510.08829/) (2015)

## Built on by (most cited first, 8 of 8)

- [Towards Memory- and Time-Efficient Backpropagation for Training Spiking Neural Networks](https://mlsanity.com/paper/2302.14311/) (2023)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity](https://mlsanity.com/paper/2506.12087/) (2025)
- [Randomized prior wavelet neural operator for uncertainty quantification](https://mlsanity.com/paper/2302.01051/) (2023)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)
- [Spike Accumulation Forwarding for Effective Training of Spiking Neural Networks](https://mlsanity.com/paper/2310.02772/) (2023)
- [A Self-Ensemble Inspired Approach for Effective Training of Binary-Weight Spiking Neural Networks](https://mlsanity.com/paper/2508.12609/) (2025)
- [NeuroTrain: Surveying Local Learning Rules for Spiking Neural Networks with an Open Benchmarking Framework](https://mlsanity.com/paper/2605.15058/) (2026)

## Abstract (arXiv)

Spiking neural networks (SNNs) with event-based computation are promising brain-inspired models for energy-efficient applications on neuromorphic hardware. However, most supervised SNN training methods, such as conversion from artificial neural networks or direct training with surrogate gradients, require complex computation rather than spike-based operations of spiking neurons during training. In this paper, we study spike-based implicit differentiation on the equilibrium state (SPIDE) that extends the recently proposed training method, implicit differentiation on the equilibrium state (IDE), for supervised learning with purely spike-based computation, which demonstrates the potential for energy-efficient training of SNNs. Specifically, we introduce ternary spiking neuron couples and prove that implicit differentiation can be solved by spikes based on this design, so the whole training procedure, including both forward and backward passes, is made as event-driven spike computation, and weights are updated locally with two-stage average firing rates. Then we propose to modify the reset membrane potential to reduce the approximation error of spikes. With these key components, we can train SNNs with flexible structures in a small number of time steps and with firing sparsity during training, and the theoretical estimation of energy costs demonstrates the potential for high efficiency. Meanwhile, experiments show that even with these constraints, our trained models can still achieve competitive results on MNIST, CIFAR-10, CIFAR-100, and CIFAR10-DVS. Our code is available at https://github.com/pkuxmq/SPIDE-FSNN.