# Three factor delay learning rules for spiking neural networks

arXiv: https://arxiv.org/abs/2601.00668 · HTML: https://mlsanity.com/paper/2601.00668/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 2 Jan 2026.

## Builds on (most cited first, 29 of 29)

- [Speech Commands: A Dataset for Limited-Vocabulary Speech Recognition](https://mlsanity.com/paper/1804.03209/) (2018)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [SpikingJelly: An open-source machine learning infrastructure platform for spike-based intelligence](https://mlsanity.com/paper/2310.16620/) (2023)
- [Decoupled Neural Interfaces using Synthetic Gradients](https://mlsanity.com/paper/1608.05343/) (2016)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks](https://mlsanity.com/paper/2009.08378/) (2020)
- [How Important is Weight Symmetry in Backpropagation?](https://mlsanity.com/paper/1510.05067/) (2015)
- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Unbiased Online Recurrent Optimization](https://mlsanity.com/paper/1702.05043/) (2017)
- [A Unified Framework of Online Learning Algorithms for Training Recurrent Neural Networks](https://mlsanity.com/paper/1907.02649/) (2019)
- [ReckOn: A 28nm Sub-mm2 Task-Agnostic Spiking Recurrent Neural Network Processor Enabling On-Chip Learning over Second-Long Timescales](https://mlsanity.com/paper/2208.09759/) (2022)
- [Online Spatio-Temporal Learning in Deep Neural Networks](https://mlsanity.com/paper/2007.12723/) (2020)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Optimal Kronecker-Sum Approximation of Real Time Recurrent Learning](https://mlsanity.com/paper/1902.03993/) (2019)
- [Dilated convolution with learnable spacings](https://mlsanity.com/paper/2112.03740/) (2021)
- [S7: Selective and Simplified State Space Layers for Sequence Modeling](https://mlsanity.com/paper/2410.03464/) (2024)
- [Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks](https://mlsanity.com/paper/2212.01232/) (2022)
- [Co-learning synaptic delays, weights and adaptation in spiking neural networks](https://mlsanity.com/paper/2311.16112/) (2023)
- [Advancing Spatio-Temporal Processing in Spiking Neural Networks through Adaptation](https://mlsanity.com/paper/2408.07517/) (2024)
- [Axonal Delay As a Short-Term Memory for Feed Forward Deep Spiking Neural Networks](https://mlsanity.com/paper/2205.02115/) (2022)
- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [Efficient Event-based Delay Learning in Spiking Neural Networks](https://mlsanity.com/paper/2501.07331/) (2025)
- [Learning Delays Through Gradients and Structure: Emergence of Spatiotemporal Patterns in Spiking Neural Networks](https://mlsanity.com/paper/2407.18917/) (2024)
- [Event-based backpropagation on the neuromorphic platform SpiNNaker2](https://mlsanity.com/paper/2412.15021/) (2024)
- [Exploiting heterogeneous delays for efficient computation in low-bit neural networks](https://mlsanity.com/paper/2510.27434/) (2025)

## Built on by (most cited first, 1 of 1)

- [Congestion-Aware Dynamic Axonal Delay for Spiking Neural Networks](https://mlsanity.com/paper/2605.01291/) (2026)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) are dynamical systems that operate on spatiotemporal data, yet their learnable parameters are often limited to synaptic weights, contributing little to temporal pattern recognition. Learnable parameters that delay spike times can improve classification performance in temporal tasks, but existing methods rely on large networks and offline learning, making them unsuitable for real-time operation in resource-constrained environments. In this paper, we introduce synaptic and axonal delays to leaky integrate and fire (LIF)-based feedforward and recurrent SNNs, and propose three-factor learning rules to simultaneously learn delay parameters online. We employ a smooth Gaussian surrogate to approximate spike derivatives exclusively for the eligibility trace calculation, and together with a top-down error signal determine parameter updates. Our experiments show that incorporating delays improves accuracy by up to 20% over a weights-only baseline, and for networks with similar parameter counts, jointly learning weights and delays yields up to 14% higher accuracy. On the SHD speech recognition dataset, our method achieves similar accuracy to offline backpropagation-based approaches. Compared to state-of-the-art methods, it reduces model size by 6.6x and inference latency by 67%, with only a 2.4% drop in classification accuracy. Our findings benefit the design of power and area-constrained neuromorphic processors by enabling on-device learning and lowering memory requirements.