# Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks

arXiv: https://arxiv.org/abs/2407.12516 · HTML: https://mlsanity.com/paper/2407.12516/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 44 of its 79 references that are in the map.
- First posted on arXiv 17 Jul 2024.

## Builds on (most cited first, 30 of 44)

- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [ZOO: Zeroth Order Optimization based Black-box Attacks to Deep Neural Networks without Training Substitute Models](https://mlsanity.com/paper/1708.03999/) (2017)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Fine-Tuning Language Models with Just Forward Passes](https://mlsanity.com/paper/2305.17333/) (2023)
- [Converting Static Image Datasets to Spiking Neuromorphic Datasets Using Saccades](https://mlsanity.com/paper/1507.07629/) (2015)
- [Spikformer: When Spiking Neural Network Meets Transformer](https://mlsanity.com/paper/2209.15425/) (2022)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [The Forward-Forward Algorithm: Some Preliminary Investigations](https://mlsanity.com/paper/2212.13345/) (2022)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Difference Target Propagation](https://mlsanity.com/paper/1412.7525/) (2014)
- [Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networks](https://mlsanity.com/paper/2103.00476/) (2021)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [Characterizing signal propagation to close the performance gap in unnormalized ResNets](https://mlsanity.com/paper/2101.08692/) (2021)
- [Deep Learning without Weight Transport](https://mlsanity.com/paper/1904.05391/) (2019)
- [DeepZero: Scaling up Zeroth-Order Optimization for Deep Model Training](https://mlsanity.com/paper/2310.02025/) (2023)
- [Gradients without Backpropagation](https://mlsanity.com/paper/2202.08587/) (2022)
- [Scaling Forward Gradient With Local Losses](https://mlsanity.com/paper/2210.03310/) (2022)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [Direct Feedback Alignment Scales to Modern Deep Learning Tasks and Architectures](https://mlsanity.com/paper/2006.12878/) (2020)
- [Temporal-Coded Deep Spiking Neural Network with Easy Training and Robust Performance](https://mlsanity.com/paper/1909.10837/) (2019)
- [SEENN: Towards Temporal Spiking Early-Exit Neural Networks](https://mlsanity.com/paper/2304.01230/) (2023)
- [Training Feedback Spiking Neural Networks by Implicit Differentiation on the Equilibrium State](https://mlsanity.com/paper/2109.14247/) (2021)
- [Neuromorphic Deep Learning Machines](https://mlsanity.com/paper/1612.05596/) (2016)
- [Surrogate gradients for analog neuromorphic computing](https://mlsanity.com/paper/2006.07239/) (2020)

## Built on by (most cited first, 3 of 3)

- [Training Non-Differentiable Networks via Optimal Transport](https://mlsanity.com/paper/2605.01928/) (2026)
- [Position: Zeroth-Order Optimization in Deep Learning Is Underexplored, Not Underpowered](https://mlsanity.com/paper/2605.15622/) (2026)
- [Scaling of hardware-compatible perturbative training algorithms](https://mlsanity.com/paper/2501.15403/) (2025)

## Abstract (arXiv)

Brain-inspired neuromorphic computing with spiking neural networks (SNNs) is a promising energy-efficient computational approach. However, successfully training SNNs in a more biologically plausible and neuromorphic-hardware-friendly way is still challenging. Most recent methods leverage spatial and temporal backpropagation (BP), not adhering to neuromorphic properties. Despite the efforts of some online training methods, tackling spatial credit assignments by alternatives with comparable performance as spatial BP remains a significant problem. In this work, we propose a novel method, online pseudo-zeroth-order (OPZO) training. Our method only requires a single forward propagation with noise injection and direct top-down signals for spatial credit assignment, avoiding spatial BP's problem of symmetric weights and separate phases for layer-by-layer forward-backward propagation. OPZO solves the large variance problem of zeroth-order methods by the pseudo-zeroth-order formulation and momentum feedback connections, while having more guarantees than random feedback. Combining online training, OPZO can pave paths to on-chip SNN training. Experiments on neuromorphic and static datasets with fully connected and convolutional networks demonstrate the effectiveness of OPZO with similar performance compared with spatial BP, as well as estimated low training costs.