# ADMM-Based Training for Spiking Neural Networks

arXiv: https://arxiv.org/abs/2505.05527 · HTML: https://mlsanity.com/paper/2505.05527/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 17 references that are in the map.
- First posted on arXiv 8 May 2025.

## Builds on (most cited first, 11 of 11)

- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [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)
- [Training Neural Networks Without Gradients: A Scalable ADMM Approach](https://mlsanity.com/paper/1605.02026/) (2016)
- [Signal Propagation: A Framework for Learning and Inference In a Forward Pass](https://mlsanity.com/paper/2204.01723/) (2022)
- [ADMM for Efficient Deep Learning with Global Convergence](https://mlsanity.com/paper/1905.13611/) (2019)
- [Fusing Event-based Camera and Radar for SLAM Using Spiking Neural Networks with Continual STDP Learning](https://mlsanity.com/paper/2210.04236/) (2022)
- [Toward Model Parallelism for Deep Neural Network based on Gradient-free ADMM Framework](https://mlsanity.com/paper/2009.02868/) (2020)
- [Training Recurrent Neural Networks by Sequential Least Squares and the Alternating Direction Method of Multipliers](https://mlsanity.com/paper/2112.15348/) (2021)

## Abstract (arXiv)

In recent years, spiking neural networks (SNNs) have gained momentum due to their high potential in time-series processing combined with minimal energy consumption. However, they still lack a dedicated and efficient training algorithm. The popular backpropagation with surrogate gradients, adapted from stochastic gradient descent (SGD)-derived algorithms, has several drawbacks when used as an optimizer for SNNs. Specifically, the approximation introduced by the use of surrogate gradients leads to numerical imprecision, poor tracking of SNN firing times at training time, and, in turn, poor scalability. In this paper, we propose a novel SNN training method based on the alternating direction method of multipliers (ADMM). Our ADMM-based training aims to solve the problem of the SNN step function's non-differentiability by taking an entirely new approach with respect to gradient backpropagation. For the first time, we formulate the SNN training problem as an ADMM-based iterative optimization, derive closed-form updates, and empirically show the optimizer's convergence, its great potential, and discuss future and promising research directions to improve the method to different layer types and deeper architectures.