# Online Training Through Time for Spiking Neural Networks

arXiv: https://arxiv.org/abs/2210.04195 · HTML: https://mlsanity.com/paper/2210.04195/

## Key facts

- Cited by 49 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 79 references that are in the map.
- First posted on arXiv 9 Oct 2022.

## Builds on (most cited first, 30 of 40)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Identity Mappings in Deep Residual Networks](https://mlsanity.com/paper/1603.05027/) (2016)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Spatio-Temporal Backpropagation for Training High-performance Spiking Neural Networks](https://mlsanity.com/paper/1706.02609/) (2017)
- [High-Performance Large-Scale Image Recognition Without Normalization](https://mlsanity.com/paper/2102.06171/) (2021)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Deep Residual Learning in Spiking Neural Networks](https://mlsanity.com/paper/2102.04159/) (2021)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [Going Deeper in Spiking Neural Networks: VGG and Residual Architectures](https://mlsanity.com/paper/1802.02627/) (2018)
- [Direct Feedback Alignment Provides Learning in Deep Neural Networks](https://mlsanity.com/paper/1609.01596/) (2016)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (2018)
- [Training Deep Spiking Neural Networks using Backpropagation](https://mlsanity.com/paper/1608.08782/) (2016)
- [Temporal Efficient Training of Spiking Neural Network via Gradient Re-weighting](https://mlsanity.com/paper/2202.11946/) (2022)
- [SuperSpike: Supervised learning in multi-layer spiking neural networks](https://mlsanity.com/paper/1705.11146/) (2017)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Enabling Deep Spiking Neural Networks with Hybrid Conversion and Spike Timing Dependent Backpropagation](https://mlsanity.com/paper/2005.01807/) (2020)
- [Optimal Conversion of Conventional Artificial Neural Networks to Spiking Neural Networks](https://mlsanity.com/paper/2103.00476/) (2021)
- [A Free Lunch From ANN: Towards Efficient, Accurate Spiking Neural Networks Calibration](https://mlsanity.com/paper/2106.06984/) (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)
- [JFB: Jacobian-Free Backpropagation for Implicit Networks](https://mlsanity.com/paper/2103.12803/) (2021)
- [On Training Implicit Models](https://mlsanity.com/paper/2111.05177/) (2021)
- [Spiking Deep Networks with LIF Neurons](https://mlsanity.com/paper/1510.08829/) (2015)
- [Neural Architecture Search for Spiking Neural Networks](https://mlsanity.com/paper/2201.10355/) (2022)
- [Unbiased Online Recurrent Optimization](https://mlsanity.com/paper/1702.05043/) (2017)

## Built on by (most cited first, 30 of 49)

- [Scaling Spike-driven Transformer with Efficient Spike Firing Approximation Training](https://mlsanity.com/paper/2411.16061/) (2024)
- [Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies](https://mlsanity.com/paper/2304.12760/) (2023)
- [Towards Memory- and Time-Efficient Backpropagation for Training Spiking Neural Networks](https://mlsanity.com/paper/2302.14311/) (2023)
- [Membrane Potential Batch Normalization for Spiking Neural Networks](https://mlsanity.com/paper/2308.08359/) (2023)
- [Spiking PointNet: Spiking Neural Networks for Point Clouds](https://mlsanity.com/paper/2310.06232/) (2023)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Training Full Spike Neural Networks via Auxiliary Accumulation Pathway](https://mlsanity.com/paper/2301.11929/) (2023)
- [Kolmogorov-Arnold Convolutions: Design Principles and Empirical Studies](https://mlsanity.com/paper/2407.01092/) (2024)
- [Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks](https://mlsanity.com/paper/2305.16044/) (2023)
- [Take A Shortcut Back: Mitigating the Gradient Vanishing for Training Spiking Neural Networks](https://mlsanity.com/paper/2401.04486/) (2024)
- [Quantized Spike-driven Transformer](https://mlsanity.com/paper/2501.13492/) (2025)
- [Exact Gradients for Stochastic Spiking Neural Networks Driven by Rough Signals](https://mlsanity.com/paper/2405.13587/) (2024)
- [SPIDE: A Purely Spike-based Method for Training Feedback Spiking Neural Networks](https://mlsanity.com/paper/2302.00232/) (2023)
- [A Comprehensive Review of Spiking Neural Networks: Interpretation, Optimization, Efficiency, and Best Practices](https://mlsanity.com/paper/2303.10780/) (2023)
- [Hebbian Learning based Orthogonal Projection for Continual Learning of Spiking Neural Networks](https://mlsanity.com/paper/2402.11984/) (2024)
- [Brain-Inspired Online Adaptation for Remote Sensing with Spiking Neural Network](https://mlsanity.com/paper/2409.02146/) (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)
- [Efficient ANN-Guided Distillation: Aligning Rate-based Features of Spiking Neural Networks through Hybrid Block-wise Replacement](https://mlsanity.com/paper/2503.16572/) (2025)
- [CADE: Cosine Annealing Differential Evolution for Spiking Neural Network](https://mlsanity.com/paper/2406.02349/) (2024)
- [TESS: A Scalable Temporally and Spatially Local Learning Rule for Spiking Neural Networks](https://mlsanity.com/paper/2502.01837/) (2025)
- [A differentiable brain simulator bridging brain simulation and brain-inspired computing](https://mlsanity.com/paper/2311.05106/) (2023)
- [Estimating Post-Synaptic Effects for Online Training of Feed-Forward SNNs](https://mlsanity.com/paper/2311.16151/) (2023)
- [Faster and Stronger: When ANN-SNN Conversion Meets Parallel Spiking Calculation](https://mlsanity.com/paper/2412.13610/) (2024)
- [Temporal Flexibility in Spiking Neural Networks: Towards Generalization Across Time Steps and Deployment Friendliness](https://mlsanity.com/paper/2503.17394/) (2025)
- [Brain-inspired Evolutionary Architectures for Spiking Neural Networks](https://mlsanity.com/paper/2309.05263/) (2023)
- [Spike Accumulation Forwarding for Effective Training of Spiking Neural Networks](https://mlsanity.com/paper/2310.02772/) (2023)
- [FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning](https://mlsanity.com/paper/2504.01257/) (2025)
- [Spike-TBR: a Noise Resilient Neuromorphic Event Representation](https://mlsanity.com/paper/2506.04817/) (2025)
- [IML-Spikeformer: Input-aware Multi-Level Spiking Transformer for Speech Processing](https://mlsanity.com/paper/2507.07396/) (2025)

## Abstract (arXiv)

Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Recent progress in training methods has enabled successful deep SNNs on large-scale tasks with low latency. Particularly, backpropagation through time (BPTT) with surrogate gradients (SG) is popularly used to achieve high performance in a very small number of time steps. However, it is at the cost of large memory consumption for training, lack of theoretical clarity for optimization, and inconsistency with the online property of biological learning and rules on neuromorphic hardware. Other works connect spike representations of SNNs with equivalent artificial neural network formulation and train SNNs by gradients from equivalent mappings to ensure descent directions. But they fail to achieve low latency and are also not online. In this work, we propose online training through time (OTTT) for SNNs, which is derived from BPTT to enable forward-in-time learning by tracking presynaptic activities and leveraging instantaneous loss and gradients. Meanwhile, we theoretically analyze and prove that gradients of OTTT can provide a similar descent direction for optimization as gradients based on spike representations under both feedforward and recurrent conditions. OTTT only requires constant training memory costs agnostic to time steps, avoiding the significant memory costs of BPTT for GPU training. Furthermore, the update rule of OTTT is in the form of three-factor Hebbian learning, which could pave a path for online on-chip learning. With OTTT, it is the first time that two mainstream supervised SNN training methods, BPTT with SG and spike representation-based training, are connected, and meanwhile in a biologically plausible form. Experiments on CIFAR-10, CIFAR-100, ImageNet, and CIFAR10-DVS demonstrate the superior performance of our method on large-scale static and neuromorphic datasets in small time steps.