# Accurate online training of dynamical spiking neural networks through Forward Propagation Through Time

arXiv: https://arxiv.org/abs/2112.11231 · HTML: https://mlsanity.com/paper/2112.11231/

## Key facts

- Cited by 34 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 58 references that are in the map.
- First posted on arXiv 20 Dec 2021.

## Builds on (most cited first, 21 of 21)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [YOLOv4: Optimal Speed and Accuracy of Object Detection](https://mlsanity.com/paper/2004.10934/) (2020)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Federated Learning Based on Dynamic Regularization](https://mlsanity.com/paper/2111.04263/) (2021)
- [Incorporating Learnable Membrane Time Constant to Enhance Learning of Spiking Neural Networks](https://mlsanity.com/paper/2007.05785/) (2020)
- [Equilibrium Propagation: Bridging the Gap Between Energy-Based Models and Backpropagation](https://mlsanity.com/paper/1602.05179/) (2016)
- [Direct Training for Spiking Neural Networks: Faster, Larger, Better](https://mlsanity.com/paper/1809.05793/) (2018)
- [Efficient Neural Audio Synthesis](https://mlsanity.com/paper/1802.08435/) (2018)
- [Long short-term memory and learning-to-learn in networks of spiking neurons](https://mlsanity.com/paper/1803.09574/) (2018)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [Liquid Time-constant Networks](https://mlsanity.com/paper/2006.04439/) (2020)
- [Accurate and efficient time-domain classification with adaptive spiking recurrent neural networks](https://mlsanity.com/paper/2103.12593/) (2021)
- [Dendritic cortical microcircuits approximate the backpropagation algorithm](https://mlsanity.com/paper/1810.11393/) (2018)
- [Brain-inspired computing: We need a master plan](https://mlsanity.com/paper/2104.14517/) (2021)
- [Effective and Efficient Computation with Multiple-timescale Spiking Recurrent Neural Networks](https://mlsanity.com/paper/2005.11633/) (2020)
- [Online Spatio-Temporal Learning in Deep Neural Networks](https://mlsanity.com/paper/2007.12723/) (2020)
- [A Fully Spiking Hybrid Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/2104.10719/) (2021)
- [Deep SCNN-based Real-time Object Detection for Self-driving Vehicles Using LiDAR Temporal Data](https://mlsanity.com/paper/1912.07906/) (2019)
- [Real-time object detection method based on improved YOLOv4-tiny](https://mlsanity.com/paper/2011.04244/) (2020)
- [RetinaNet Object Detector based on Analog-to-Spiking Neural Network Conversion](https://mlsanity.com/paper/2106.05624/) (2021)

## Built on by (most cited first, 30 of 34)

- [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)
- [SpikingSSMs: Learning Long Sequences with Sparse and Parallel Spiking State Space Models](https://mlsanity.com/paper/2408.14909/) (2024)
- [Advancing Training Efficiency of Deep Spiking Neural Networks through Rate-based Backpropagation](https://mlsanity.com/paper/2410.11488/) (2024)
- [SpikeMOT: Event-based Multi-Object Tracking with Sparse Motion Features](https://mlsanity.com/paper/2309.16987/) (2023)
- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)
- [Efficient Uncertainty Estimation in Spiking Neural Networks via MC-dropout](https://mlsanity.com/paper/2304.10191/) (2023)
- [A Sparse Quantized Hopfield Network for Online-Continual Memory](https://mlsanity.com/paper/2307.15040/) (2023)
- [Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity](https://mlsanity.com/paper/2506.12087/) (2025)
- [Addressing the speed-accuracy simulation trade-off for adaptive spiking neurons](https://mlsanity.com/paper/2311.11390/) (2023)
- [The Role of Temporal Hierarchy in Spiking Neural Networks](https://mlsanity.com/paper/2407.18838/) (2024)
- [Online Pseudo-Zeroth-Order Training of Neuromorphic Spiking Neural Networks](https://mlsanity.com/paper/2407.12516/) (2024)
- [GazeSCRNN: Event-based Near-eye Gaze Tracking using a Spiking Neural Network](https://mlsanity.com/paper/2503.16012/) (2025)
- [Exploiting Heterogeneity in Timescales for Sparse Recurrent Spiking Neural Networks for Energy-Efficient Edge Computing](https://mlsanity.com/paper/2407.06452/) (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)
- [Energy-Efficient Spiking Recurrent Neural Network for Gesture Recognition on Embedded GPUs](https://mlsanity.com/paper/2408.12978/) (2024)
- [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)
- [Current Opinions on Memristor-Accelerated Machine Learning Hardware](https://mlsanity.com/paper/2501.12644/) (2025)
- [FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning](https://mlsanity.com/paper/2504.01257/) (2025)
- [Signal-Adaptive Trust Regions for Gradient-Free Optimization of Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2601.21572/) (2026)
- [Quantized Context Based LIF Neurons for Recurrent Spiking Neural Networks in 45nm](https://mlsanity.com/paper/2404.18066/) (2024)
- [Topology Optimization of Random Memristors for Input-Aware Dynamic SNN](https://mlsanity.com/paper/2407.18625/) (2024)
- [Rethinking SNN Online Training and Deployment: Gradient-Coherent Learning via Hybrid-Driven LIF Model](https://mlsanity.com/paper/2410.07547/) (2024)
- [A Self-Ensemble Inspired Approach for Effective Training of Binary-Weight Spiking Neural Networks](https://mlsanity.com/paper/2508.12609/) (2025)
- [Complementary Learning System Empowers Online Continual Learning of Vehicle Motion Forecasting in Smart Cities](https://mlsanity.com/paper/2508.19597/) (2025)
- [Spiking Neural Networks for Continuous Control via End-to-End Model-Based Learning](https://mlsanity.com/paper/2509.05356/) (2025)
- [Enhanced Self-Distillation Framework for Efficient Spiking Neural Network Training](https://mlsanity.com/paper/2510.06254/) (2025)
- [Reliable Brain Tumor Segmentation Based on Spiking Neural Networks with Efficient Training](https://mlsanity.com/paper/2601.16652/) (2026)

## Abstract (arXiv)

The event-driven and sparse nature of communication between spiking neurons in the brain holds great promise for flexible and energy-efficient AI. Recent advances in learning algorithms have demonstrated that recurrent networks of spiking neurons can be effectively trained to achieve competitive performance compared to standard recurrent neural networks. Still, as these learning algorithms use error-backpropagation through time (BPTT), they suffer from high memory requirements, are slow to train, and are incompatible with online learning. This limits the application of these learning algorithms to relatively small networks and to limited temporal sequence lengths. Online approximations to BPTT with lower computational and memory complexity have been proposed (e-prop, OSTL), but in practice also suffer from memory limitations and, as approximations, do not outperform standard BPTT training. Here, we show how a recently developed alternative to BPTT, Forward Propagation Through Time (FPTT) can be applied in spiking neural networks. Different from BPTT, FPTT attempts to minimize an ongoing dynamically regularized risk on the loss. As a result, FPTT can be computed in an online fashion and has fixed complexity with respect to the sequence length. When combined with a novel dynamic spiking neuron model, the Liquid-Time-Constant neuron, we show that SNNs trained with FPTT outperform online BPTT approximations, and approach or exceed offline BPTT accuracy on temporal classification tasks. This approach thus makes it feasible to train SNNs in a memory-friendly online fashion on long sequences and scale up SNNs to novel and complex neural architectures.