# Frozen Backpropagation: Relaxing Weight Symmetry in Deep Spiking Neural Networks

arXiv: https://arxiv.org/abs/2505.13741 · HTML: https://mlsanity.com/paper/2505.13741/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 37 of its 57 references that are in the map.
- First posted on arXiv 19 May 2025.

## Builds on (most cited first, 30 of 37)

- [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)
- [Delving Deep into Rectifiers: Surpassing Human-Level Performance on ImageNet Classification](https://mlsanity.com/paper/1502.01852/) (2015)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Assessing the Scalability of Biologically-Motivated Deep Learning Algorithms and Architectures](https://mlsanity.com/paper/1807.04587/) (2018)
- [Asynchronous Stochastic Gradient Descent with Delay Compensation](https://mlsanity.com/paper/1609.08326/) (2016)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [A Survey of Neuromorphic Computing and Neural Networks in Hardware](https://mlsanity.com/paper/1705.06963/) (2017)
- [Advancing Spiking Neural Networks towards Deep Residual Learning](https://mlsanity.com/paper/2112.08954/) (2021)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [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)
- [T2FSNN: Deep Spiking Neural Networks with Time-to-first-spike Coding](https://mlsanity.com/paper/2003.11741/) (2020)
- [SEENN: Towards Temporal Spiking Early-Exit Neural Networks](https://mlsanity.com/paper/2304.01230/) (2023)
- [Neuromorphic Deep Learning Machines](https://mlsanity.com/paper/1612.05596/) (2016)
- [Biologically-plausible learning algorithms can scale to large datasets](https://mlsanity.com/paper/1811.03567/) (2018)
- [Benchmarking Keyword Spotting Efficiency on Neuromorphic Hardware](https://mlsanity.com/paper/1812.01739/) (2018)
- [Brain-Inspired Learning on Neuromorphic Substrates](https://mlsanity.com/paper/2010.11931/) (2020)
- [Feedback alignment in deep convolutional networks](https://mlsanity.com/paper/1812.06488/) (2018)
- [Bio-inspired digit recognition using reward-modulated spike-timing-dependent plasticity in deep convolutional networks](https://mlsanity.com/paper/1804.00227/) (2018)
- [High-performance deep spiking neural networks with 0.3 spikes per neuron](https://mlsanity.com/paper/2306.08744/) (2023)
- [Two Routes to Scalable Credit Assignment without Weight Symmetry](https://mlsanity.com/paper/2003.01513/) (2020)
- [The Backpropagation Algorithm Implemented on Spiking Neuromorphic Hardware](https://mlsanity.com/paper/2106.07030/) (2021)
- [Tuning Convolutional Spiking Neural Network with Biologically-plausible Reward Propagation](https://mlsanity.com/paper/2010.04434/) (2020)
- [Fully Decoupled Neural Network Learning Using Delayed Gradients](https://mlsanity.com/paper/1906.09108/) (2019)
- [In-Hardware Learning of Multilayer Spiking Neural Networks on a Neuromorphic Processor](https://mlsanity.com/paper/2105.03649/) (2021)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)

## Abstract (arXiv)

Direct training of Spiking Neural Networks (SNNs) on neuromorphic hardware can greatly reduce energy costs compared to GPU-based training. However, implementing Backpropagation (BP) on such hardware is challenging because forward and backward passes are typically performed by separate networks with distinct weights. To compute correct gradients, forward and feedback weights must remain symmetric during training, necessitating weight transport between the two networks. This symmetry requirement imposes hardware overhead and increases energy costs. To address this issue, we introduce Frozen Backpropagation (textscfBP), a BP-based training algorithm relaxing weight symmetry in settings with separate networks. fBP updates forward weights by computing gradients with periodically frozen feedback weights, reducing weight transports during training and minimizing synchronization overhead. To further improve transport efficiency, we propose three partial weight transport schemes of varying computational complexity, where only a subset of weights is transported at a time. We evaluate our methods on image recognition tasks using both temporally and rate-coded SNNs, and compare them to existing approaches addressing the weight symmetry requirement. Our results show that fBP outperforms these methods and achieves accuracy comparable to BP while significantly lowering transport costs. With partial weight transport, fBP can further lower those costs by up to 10,000x at the expense of moderate accuracy loss. This work provides insights for guiding the design of neuromorphic hardware incorporating BP-based on-chip learning.