# Hybrid Macro/Micro Level Backpropagation for Training Deep Spiking Neural Networks

arXiv: https://arxiv.org/abs/1805.07866 · HTML: https://mlsanity.com/paper/1805.07866/

## Key facts

- Cited by 30 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 May 2018.

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

- [Event-based Video Reconstruction via Potential-assisted Spiking Neural Network](https://mlsanity.com/paper/2201.10943/) (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)
- [Reducing ANN-SNN Conversion Error through Residual Membrane Potential](https://mlsanity.com/paper/2302.02091/) (2023)
- [TCJA-SNN: Temporal-Channel Joint Attention for Spiking Neural Networks](https://mlsanity.com/paper/2206.10177/) (2022)
- [Spiking Graph Convolutional Networks](https://mlsanity.com/paper/2205.02767/) (2022)
- [Backpropagation with Biologically Plausible Spatio-Temporal Adjustment For Training Deep Spiking Neural Networks](https://mlsanity.com/paper/2110.08858/) (2021)
- [The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware](https://mlsanity.com/paper/2106.07030/) (2021)
- [Spike Calibration: Fast and Accurate Conversion of Spiking Neural Network for Object Detection and Segmentation](https://mlsanity.com/paper/2207.02702/) (2022)
- [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)
- [SNN2ANN: A Fast and Memory-Efficient Training Framework for Spiking Neural Networks](https://mlsanity.com/paper/2206.09449/) (2022)
- [Spiking CapsNet: A Spiking Neural Network With A Biologically Plausible Routing Rule Between Capsules](https://mlsanity.com/paper/2111.07785/) (2021)
- [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)
- [Efficient Training of Spiking Neural Networks with Temporally-Truncated Local Backpropagation through Time](https://mlsanity.com/paper/2201.07210/) (2021)
- [Timing-Based Backpropagation in Spiking Neural Networks Without Single-Spike Restrictions](https://mlsanity.com/paper/2211.16113/) (2022)
- [SIT: A Bionic and Non-Linear Neuron for Spiking Neural Network](https://mlsanity.com/paper/2203.16117/) (2022)
- [Exploiting Heterogeneity in Timescales for Sparse Recurrent Spiking Neural Networks for Energy-Efficient Edge Computing](https://mlsanity.com/paper/2407.06452/) (2024)
- [DPSNN: A Differentially Private Spiking Neural Network with Temporal Enhanced Pooling](https://mlsanity.com/paper/2205.12718/) (2022)
- [Parametric Matrix Models](https://mlsanity.com/paper/2401.11694/) (2024)
- [SpikeX: Exploring Accelerator Architecture and Network-Hardware Co-Optimization for Sparse Spiking Neural Networks](https://mlsanity.com/paper/2505.12292/) (2025)
- [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)
- [Spike-based Neuromorphic Computing for Next-Generation Computer Vision](https://mlsanity.com/paper/2310.09692/) (2023)
- [Forward Direct Feedback Alignment for Online Gradient Estimates of Spiking Neural Networks](https://mlsanity.com/paper/2403.08804/) (2024)
- [IKUN: Initialization to Keep snn training and generalization great with sUrrogate-stable variaNce](https://mlsanity.com/paper/2411.18250/) (2024)
- [HetSyn: Versatile Timescale Integration in Spiking Neural Networks via Heterogeneous Synapses](https://mlsanity.com/paper/2508.11644/) (2025)
- [Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization](https://mlsanity.com/paper/2607.14672/) (2026)

## Abstract (arXiv)

Spiking neural networks (SNNs) are positioned to enable spatio-temporal information processing and ultra-low power event-driven neuromorphic hardware. However, SNNs are yet to reach the same performances of conventional deep artificial neural networks (ANNs), a long-standing challenge due to complex dynamics and non-differentiable spike events encountered in training. The existing SNN error backpropagation (BP) methods are limited in terms of scalability, lack of proper handling of spiking discontinuities, and/or mismatch between the rate-coded loss function and computed gradient. We present a hybrid macro/micro level backpropagation (HM2-BP) algorithm for training multi-layer SNNs. The temporal effects are precisely captured by the proposed spike-train level post-synaptic potential (S-PSP) at the microscopic level. The rate-coded errors are defined at the macroscopic level, computed and back-propagated across both macroscopic and microscopic levels. Different from existing BP methods, HM2-BP directly computes the gradient of the rate-coded loss function w.r.t tunable parameters. We evaluate the proposed HM2-BP algorithm by training deep fully connected and convolutional SNNs based on the static MNIST [14] and dynamic neuromorphic N-MNIST [26]. HM2-BP achieves an accuracy level of 99.49% and 98.88% for MNIST and N-MNIST, respectively, outperforming the best reported performances obtained from the existing SNN BP algorithms. Furthermore, the HM2-BP produces the highest accuracies based on SNNs for the EMNIST [3] dataset, and leads to high recognition accuracy for the 16-speaker spoken English letters of TI46 Corpus [16], a challenging patio-temporal speech recognition benchmark for which no prior success based on SNNs was reported. It also achieves competitive performances surpassing those of conventional deep learning models when dealing with asynchronous spiking streams.