# Online Spatio-Temporal Learning in Deep Neural Networks

arXiv: https://arxiv.org/abs/2007.12723 · HTML: https://mlsanity.com/paper/2007.12723/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2020.

## Built on by (most cited first, 30 of 32)

- [Training Spiking Neural Networks Using Lessons From Deep Learning](https://mlsanity.com/paper/2109.12894/) (2021)
- [Online Training Through Time for Spiking Neural Networks](https://mlsanity.com/paper/2210.04195/) (2022)
- [Towards Memory- and Time-Efficient Backpropagation for Training Spiking Neural Networks](https://mlsanity.com/paper/2302.14311/) (2023)
- [Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time](https://mlsanity.com/paper/2112.11231/) (2021)
- [Bottom-up and top-down approaches for the design of neuromorphic processing systems: Tradeoffs and synergies between natural and artificial intelligence](https://mlsanity.com/paper/2106.01288/) (2021)
- [Differential Coding for Training-Free ANN-to-SNN Conversion](https://mlsanity.com/paper/2503.00301/) (2025)
- [Online Spatio-Temporal Learning with Target Projection](https://mlsanity.com/paper/2304.05124/) (2023)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation](https://mlsanity.com/paper/2410.11488/) (2024)
- [S-TLLR: STDP-inspired Temporal Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2306.15220/) (2023)
- [Advection Augmented Convolutional Neural Networks](https://mlsanity.com/paper/2406.19253/) (2024)
- [Prediction of the Position of External Markers Using a Recurrent Neural Network Trained With Unbiased Online Recurrent Optimization for Safe Lung Cancer Radiotherapy](https://mlsanity.com/paper/2106.01100/) (2021)
- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)
- [ReverB-SNN: Reversing Bit of the Weight and Activation for Spiking Neural Networks](https://mlsanity.com/paper/2506.07720/) (2025)
- [Estimating Post-Synaptic Effects for Online Training of Feed-Forward SNNs](https://mlsanity.com/paper/2311.16151/) (2023)
- [EchoSpike Predictive Plasticity: An Online Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2405.13976/) (2024)
- [Incremental Online Learning of Randomized Neural Network with Forward Regularization](https://mlsanity.com/paper/2412.13096/) (2024)
- [Efficient Logit-based Knowledge Distillation of Deep Spiking Neural Networks for Full-Range Timestep Deployment](https://mlsanity.com/paper/2501.15925/) (2025)
- [BSO: Binary Spiking Online Optimization Algorithm](https://mlsanity.com/paper/2511.12502/) (2025)
- [Intrinsic Biologically Plausible Adversarial Robustness](https://mlsanity.com/paper/2309.17348/) (2023)
- [STOP: Spatiotemporal Orthogonal Propagation for Weight-Threshold-Leakage Synergistic Training of Deep Spiking Neural Networks](https://mlsanity.com/paper/2411.11082/) (2024)
- [A Truly Sparse and General Implementation of Gradient-Based Synaptic Plasticity](https://mlsanity.com/paper/2501.11407/) (2025)
- [Traces Propagation: Memory-Efficient and Scalable Forward-Only Learning in Spiking Neural Networks](https://mlsanity.com/paper/2509.13053/) (2025)
- [Three factor delay learning rules for spiking neural networks](https://mlsanity.com/paper/2601.00668/) (2026)
- [A method for the ethical analysis of brain-inspired AI](https://mlsanity.com/paper/2305.10938/) (2023)
- [Bruno: Backpropagation Running Undersampled for Novel device Optimization](https://mlsanity.com/paper/2505.17791/) (2025)
- [A Self-Ensemble Inspired Approach for Effective Training of Binary-Weight Spiking Neural Networks](https://mlsanity.com/paper/2508.12609/) (2025)
- [Enhanced Self-Distillation Framework for Efficient Spiking Neural Network Training](https://mlsanity.com/paper/2510.06254/) (2025)
- [SpikingGamma: Surrogate-Gradient Free and Temporally Precise Online Training of Spiking Neural Networks with Smoothed Delays](https://mlsanity.com/paper/2602.01978/) (2026)

## Abstract (arXiv)

Biological neural networks are equipped with an inherent capability to continuously adapt through online learning. This aspect remains in stark contrast to learning with error backpropagation through time (BPTT) applied to recurrent neural networks (RNNs), or recently to biologically-inspired spiking neural networks (SNNs). BPTT involves offline computation of the gradients due to the requirement to unroll the network through time. Online learning has recently regained the attention of the research community, focusing either on approaches that approximate BPTT or on biologically-plausible schemes applied to SNNs. Here we present an alternative perspective that is based on a clear separation of spatial and temporal gradient components. Combined with insights from biology, we derive from first principles a novel online learning algorithm for deep SNNs, called online spatio-temporal learning (OSTL). For shallow networks, OSTL is gradient-equivalent to BPTT enabling for the first time online training of SNNs with BPTT-equivalent gradients. In addition, the proposed formulation unveils a class of SNN architectures trainable online at low time complexity. Moreover, we extend OSTL to a generic form, applicable to a wide range of network architectures, including networks comprising long short-term memory (LSTM) and gated recurrent units (GRU). We demonstrate the operation of our algorithm on various tasks from language modelling to speech recognition and obtain results on par with the BPTT baselines. The proposed algorithm provides a framework for developing succinct and efficient online training approaches for SNNs and in general deep RNNs.