# The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware

arXiv: https://arxiv.org/abs/2106.07030 · HTML: https://mlsanity.com/paper/2106.07030/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 41 of its 137 references that are in the map.
- First posted on arXiv 13 Jun 2021.

## Builds on (most cited first, 30 of 41)

- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Estimating or Propagating Gradients Through Stochastic Neurons for Conditional Computation](https://mlsanity.com/paper/1308.3432/) (2013)
- [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)
- [Deep Learning in Spiking Neural Networks](https://mlsanity.com/paper/1804.08150/) (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)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (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)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [Fast and energy-efficient neuromorphic deep learning with first-spike times](https://mlsanity.com/paper/1912.11443/) (2019)
- [Gradient Descent for Spiking Neural Networks](https://mlsanity.com/paper/1706.04698/) (2017)
- [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)
- [Hybrid Macro/Micro Level Backpropagation for Training Deep Spiking Neural Networks](https://mlsanity.com/paper/1805.07866/) (2018)
- [BP-STDP: Approximating Backpropagation using Spike Timing Dependent Plasticity](https://mlsanity.com/paper/1711.04214/) (2017)
- [Recurrent Network Models Of Sequence Generation And Memory](https://mlsanity.com/paper/1603.04687/) (2016)
- [Rapid online learning and robust recall in a neuromorphic olfactory circuit](https://mlsanity.com/paper/1906.07067/) (2019)
- [Nengo and low-power AI hardware for robust, embedded neurorobotics](https://mlsanity.com/paper/2007.10227/) (2020)
- [Whetstone: A Method for Training Deep Artificial Neural Networks for Binary Communication](https://mlsanity.com/paper/1810.11521/) (2018)
- [NengoDL: Combining deep learning and neuromorphic modelling methods](https://mlsanity.com/paper/1805.11144/) (2018)
- [In-Hardware Learning of Multilayer Spiking Neural Networks on a Neuromorphic Processor](https://mlsanity.com/paper/2105.03649/) (2021)
- [A 28-nm Convolutional Neuromorphic Processor Enabling Online Learning with Spike-Based Retinas](https://mlsanity.com/paper/2005.06318/) (2020)

## Built on by (most cited first, 19 of 19)

- [Spiking Neural Networks for Frame-based and Event-based Single Object Localization](https://mlsanity.com/paper/2206.06506/) (2022)
- [Spiking Neural Networks for Visual Place Recognition via Weighted Neuronal Assignments](https://mlsanity.com/paper/2109.06452/) (2021)
- [Applications of Spiking Neural Networks in Visual Place Recognition](https://mlsanity.com/paper/2311.13186/) (2023)
- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [Ensembles of Compact, Region-specific & Regularized Spiking Neural Networks for Scalable Place Recognition](https://mlsanity.com/paper/2209.08723/) (2022)
- [Visual Odometry with Neuromorphic Resonator Networks](https://mlsanity.com/paper/2209.02000/) (2022)
- [Intelligence Processing Units Accelerate Neuromorphic Learning](https://mlsanity.com/paper/2211.10725/) (2022)
- [Edge Intelligence with Spiking Neural Networks](https://mlsanity.com/paper/2507.14069/) (2025)
- [Neuromorphic on-chip reservoir computing with spiking neural network architectures](https://mlsanity.com/paper/2407.20547/) (2024)
- [Training Multi-Layer Binary Neural Networks With Local Binary Error Signals](https://mlsanity.com/paper/2412.00119/) (2024)
- [Threshold Adaptation in Spiking Networks Enables Shortest Path Finding and Place Disambiguation](https://mlsanity.com/paper/2503.21795/) (2025)
- [SPACE: SPike-Aware Consistency Enhancement for Test-Time Adaptation in Spiking Neural Networks](https://mlsanity.com/paper/2504.02298/) (2025)
- [Guiding Sparse Neural Networks with Neurobiological Principles to Elicit Biologically Plausible Representations](https://mlsanity.com/paper/2603.03234/) (2026)
- [A method for the ethical analysis of brain-inspired AI](https://mlsanity.com/paper/2305.10938/) (2023)
- [Frozen Backpropagation: Relaxing Weight Symmetry in Deep Spiking Neural Networks](https://mlsanity.com/paper/2505.13741/) (2025)
- [Predictive Spike Timing Enables Distributed Shortest Path Computation in Spiking Neural Networks](https://mlsanity.com/paper/2509.10077/) (2025)
- [Governance at the Edge of Architecture: Regulating NeuroAI and Neuromorphic Systems](https://mlsanity.com/paper/2602.01503/) (2026)
- [Adaptive Speech-to-Spike Encoding for Spiking Neural Networks](https://mlsanity.com/paper/2606.19039/) (2026)
- [All On-Board: Fully On-Chip Neuromorphic Q-Learning with Embedded CartPole Simulation](https://mlsanity.com/paper/2609.32317/) (2026)

## Abstract (arXiv)

The capabilities of natural neural systems have inspired new generations of machine learning algorithms as well as neuromorphic very large-scale integrated (VLSI) circuits capable of fast, low-power information processing. However, it has been argued that most modern machine learning algorithms are not neurophysiologically plausible. In particular, the workhorse of modern deep learning, the backpropagation algorithm, has proven difficult to translate to neuromorphic hardware. In this study, we present a neuromorphic, spiking backpropagation algorithm based on synfire-gated dynamical information coordination and processing, implemented on Intel's Loihi neuromorphic research processor. We demonstrate a proof-of-principle three-layer circuit that learns to classify digits from the MNIST dataset. To our knowledge, this is the first work to show a Spiking Neural Network (SNN) implementation of the backpropagation algorithm that is fully on-chip, without a computer in the loop. It is competitive in accuracy with off-chip trained SNNs and achieves an energy-delay product suitable for edge computing. This implementation shows a path for using in-memory, massively parallel neuromorphic processors for low-power, low-latency implementation of modern deep learning applications.