# Spike time displacement based error backpropagation in convolutional spiking neural networks

arXiv: https://arxiv.org/abs/2108.13621 · HTML: https://mlsanity.com/paper/2108.13621/

## Key facts

- Cited by 6 papers in the map (data through 7 Oct 2026).
- Builds on 26 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2021.

## Builds on (most cited first, 26 of 26)

- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [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)
- [Enabling Spike-based Backpropagation for Training Deep Neural Network Architectures](https://mlsanity.com/paper/1903.06379/) (2019)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)
- [Convolutional Networks for Fast, Energy-Efficient Neuromorphic Computing](https://mlsanity.com/paper/1603.08270/) (2016)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [S4NN: temporal backpropagation for spiking neural networks with one spike per neuron](https://mlsanity.com/paper/1910.09495/) (2019)
- [Temporal-Coded Deep Spiking Neural Network with Easy Training and Robust Performance](https://mlsanity.com/paper/1909.10837/) (2019)
- [Temporal Coding in Spiking Neural Networks with Alpha Synaptic Function: Learning with Backpropagation](https://mlsanity.com/paper/1907.13223/) (2019)
- [Neuromorphic Deep Learning Machines](https://mlsanity.com/paper/1612.05596/) (2016)
- [BS4NN: Binarized Spiking Neural Networks with Temporal Coding and Learning](https://mlsanity.com/paper/2007.04039/) (2020)
- [First-spike based visual categorization using reward-modulated STDP](https://mlsanity.com/paper/1705.09132/) (2017)
- [Training Dynamical Binary Neural Networks with Equilibrium Propagation](https://mlsanity.com/paper/2103.08953/) (2021)
- [Bio-inspired Unsupervised Learning of Visual Features Leads to Robust Invariant Object Recognition](https://mlsanity.com/paper/1504.03871/) (2015)
- [Combining Spiking Neural Network and Artificial Neural Network for Enhanced Image Classification](https://mlsanity.com/paper/2102.10592/) (2021)
- [Optimal localist and distributed coding of spatiotemporal spike patterns through STDP and coincidence detection](https://mlsanity.com/paper/1803.00447/) (2018)

## Built on by (most cited first, 6 of 6)

- [Spike-inspired Rank Coding for Fast and Accurate Recurrent Neural Networks](https://mlsanity.com/paper/2110.02865/) (2021)
- [Paired Competing Neurons Improving STDP Supervised Local Learning In Spiking Neural Networks](https://mlsanity.com/paper/2308.02194/) (2023)
- [An Encoding Framework for Binarized Images using HyperDimensional Computing](https://mlsanity.com/paper/2312.00454/) (2023)
- [Neuronal Competition Groups with Supervised STDP for Spike-Based Classification](https://mlsanity.com/paper/2410.17066/) (2024)
- [Spiking neural networks trained via proxy](https://mlsanity.com/paper/2109.13208/) (2021)
- [Frozen Backpropagation: Relaxing Weight Symmetry in Deep Spiking Neural Networks](https://mlsanity.com/paper/2505.13741/) (2025)

## Abstract (arXiv)

We recently proposed the STiDi-BP algorithm, which avoids backward recursive gradient computation, for training multi-layer spiking neural networks (SNNs) with single-spike-based temporal coding. The algorithm employs a linear approximation to compute the derivative of the spike latency with respect to the membrane potential and it uses spiking neurons with piecewise linear postsynaptic potential to reduce the computational cost and the complexity of neural processing. In this paper, we extend the STiDi-BP algorithm to employ it in deeper and convolutional architectures. The evaluation results on the image classification task based on two popular benchmarks, MNIST and Fashion-MNIST datasets with the accuracies of respectively 99.2% and 92.8%, confirm that this algorithm has been applicable in deep SNNs. Another issue we consider is the reduction of memory storage and computational cost. To do so, we consider a convolutional SNN (CSNN) with two sets of weights: real-valued weights that are updated in the backward pass and their signs, binary weights, that are employed in the feedforward process. We evaluate the binary CSNN on two datasets of MNIST and Fashion-MNIST and obtain acceptable performance with a negligible accuracy drop with respect to real-valued weights (about 0.6% and 0.8% drops, respectively).