# Fractional-order spike-timing-dependent gradient descent for multi-layer spiking neural networks

arXiv: https://arxiv.org/abs/2410.15293 · HTML: https://mlsanity.com/paper/2410.15293/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 62 references that are in the map.
- First posted on arXiv 20 Oct 2024.

## Builds on (most cited first, 16 of 16)

- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (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)
- [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)
- [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)
- [Fast and energy-efficient neuromorphic deep learning with first-spike times](https://mlsanity.com/paper/1912.11443/) (2019)
- [Temporal Coding in Spiking Neural Networks with Alpha Synaptic Function: Learning with Backpropagation](https://mlsanity.com/paper/1907.13223/) (2019)
- [STDP-based spiking deep convolutional neural networks for object recognition](https://mlsanity.com/paper/1611.01421/) (2016)
- [BP-STDP: Approximating Backpropagation using Spike Timing Dependent Plasticity](https://mlsanity.com/paper/1711.04214/) (2017)
- [Bio-Inspired Spiking Convolutional Neural Network using Layer-wise Sparse Coding and STDP Learning](https://mlsanity.com/paper/1611.03000/) (2016)
- [Convolutional neural networks with fractional order gradient method](https://mlsanity.com/paper/1905.05336/) (2019)

## Built on by (most cited first, 1 of 1)

- [Theoretical Framework for Tempered Fractional Gradient Descent: Application to Breast Cancer Classification](https://mlsanity.com/paper/2504.18849/) (2025)

## Abstract (arXiv)

Accumulated detailed knowledge about the neuronal activities in human brains has brought more attention to bio-inspired spiking neural networks (SNNs). In contrast to non-spiking deep neural networks (DNNs), SNNs can encode and transmit spatiotemporal information more efficiently by exploiting biologically realistic and low-power event-driven neuromorphic architectures. However, the supervised learning of SNNs still remains a challenge because the spike-timing-dependent plasticity (STDP) of connected spiking neurons is difficult to implement and interpret in existing backpropagation learning schemes. This paper proposes a fractional-order spike-timing-dependent gradient descent (FO-STDGD) learning model by considering a derived nonlinear activation function that describes the relationship between the quasi-instantaneous firing rate and the temporal membrane potentials of nonleaky integrate-and-fire neurons. The training strategy can be generalized to any fractional orders between 0 and 2 since the FO-STDGD incorporates the fractional gradient descent method into the calculation of spike-timing-dependent loss gradients. The proposed FO-STDGD model is tested on the MNIST and DVS128 Gesture datasets and its accuracy under different network structure and fractional orders is analyzed. It can be found that the classification accuracy increases as the fractional order increases, and specifically, the case of fractional order 1.9 improves by 155% relative to the case of fractional order 1 (traditional gradient descent). In addition, our scheme demonstrates the state-of-the-art computational efficacy for the same SNN structure and training epochs.