# Estimating Post-Synaptic Effects for Online Training of Feed-Forward SNNs

arXiv: https://arxiv.org/abs/2311.16151 · HTML: https://mlsanity.com/paper/2311.16151/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 31 references that are in the map.
- First posted on arXiv 7 Nov 2023.

## Builds on (most cited first, 18 of 18)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [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)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules](https://mlsanity.com/paper/1801.05219/) (2018)
- [Online Training Through Time for Spiking Neural Networks](https://mlsanity.com/paper/2210.04195/) (2022)
- [Unbiased Online Recurrent Optimization](https://mlsanity.com/paper/1702.05043/) (2017)
- [Online Spatio-Temporal Learning in Deep Neural Networks](https://mlsanity.com/paper/2007.12723/) (2020)
- [Approximating Real-Time Recurrent Learning with Random Kronecker Factors](https://mlsanity.com/paper/1805.10842/) (2018)
- [Optimal Kronecker-Sum Approximation of Real Time Recurrent Learning](https://mlsanity.com/paper/1902.03993/) (2019)
- [Exploring the Promise and Limits of Real-Time Recurrent Learning](https://mlsanity.com/paper/2305.19044/) (2023)
- [A Practical Sparse Approximation for Real Time Recurrent Learning](https://mlsanity.com/paper/2006.07232/) (2020)
- [EXODUS: Stable and Efficient Training of Spiking Neural Networks](https://mlsanity.com/paper/2205.10242/) (2022)

## Built on by (most cited first, 2 of 2)

- [SpikingGamma: Surrogate-Gradient Free and Temporally Precise Online Training of Spiking Neural Networks with Smoothed Delays](https://mlsanity.com/paper/2602.01978/) (2026)
- [NeuroTrain: Surveying Local Learning Rules for Spiking Neural Networks with an Open Benchmarking Framework](https://mlsanity.com/paper/2605.15058/) (2026)

## Abstract (arXiv)

Facilitating online learning in spiking neural networks (SNNs) is a key step in developing event-based models that can adapt to changing environments and learn from continuous data streams in real-time. Although forward-mode differentiation enables online learning, its computational requirements restrict scalability. This is typically addressed through approximations that limit learning in deep models. In this study, we propose Online Training with Postsynaptic Estimates (OTPE) for training feed-forward SNNs, which approximates Real-Time Recurrent Learning (RTRL) by incorporating temporal dynamics not captured by current approximations, such as Online Training Through Time (OTTT) and Online Spatio-Temporal Learning (OSTL). We show improved scaling for multi-layer networks using a novel approximation of temporal effects on the subsequent layer's activity. This approximation incurs minimal overhead in the time and space complexity compared to similar algorithms, and the calculation of temporal effects remains local to each layer. We characterize the learning performance of our proposed algorithms on multiple SNN model configurations for rate-based and time-based encoding. OTPE exhibits the highest directional alignment to exact gradients, calculated with backpropagation through time (BPTT), in deep networks and, on time-based encoding, outperforms other approximate methods. We also observe sizeable gains in average performance over similar algorithms in offline training of Spiking Heidelberg Digits with equivalent hyper-parameters (OTTT/OSTL - 70.5%; OTPE - 75.2%; BPTT - 78.1%).