# Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity

arXiv: https://arxiv.org/abs/2506.12087 · HTML: https://mlsanity.com/paper/2506.12087/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 44 references that are in the map.
- First posted on arXiv 10 Jun 2025.

## Builds on (most cited first, 25 of 25)

- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [Going Deeper With Directly-Trained Larger Spiking Neural Networks](https://mlsanity.com/paper/2011.05280/) (2020)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Training High-Performance Low-Latency Spiking Neural Networks by Differentiation on Spike Representation](https://mlsanity.com/paper/2205.00459/) (2022)
- [HARDVS: Revisiting Human Activity Recognition with Dynamic Vision Sensors](https://mlsanity.com/paper/2211.09648/) (2022)
- [Parallelizing non-linear sequential models over the sequence length](https://mlsanity.com/paper/2309.12252/) (2023)
- [SEENN: Towards Temporal Spiking Early-Exit Neural Networks](https://mlsanity.com/paper/2304.01230/) (2023)
- [Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies](https://mlsanity.com/paper/2304.12760/) (2023)
- [Training Feedback Spiking Neural Networks by Implicit Differentiation on the Equilibrium State](https://mlsanity.com/paper/2109.14247/) (2021)
- [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)
- [Exploring Temporal Information Dynamics in Spiking Neural Networks](https://mlsanity.com/paper/2211.14406/) (2022)
- [Learning Long Sequences in Spiking Neural Networks](https://mlsanity.com/paper/2401.00955/) (2023)
- [Shrinking Your TimeStep: Towards Low-Latency Neuromorphic Object Recognition with Spiking Neural Network](https://mlsanity.com/paper/2401.01912/) (2024)
- [Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networks](https://mlsanity.com/paper/2305.16044/) (2023)
- [Unleashing the Potential of Spiking Neural Networks by Dynamic Confidence](https://mlsanity.com/paper/2303.10276/) (2023)
- [Towards Lossless ANN-SNN Conversion under Ultra-Low Latency with Dual-Phase Optimization](https://mlsanity.com/paper/2205.07473/) (2022)
- [High-Performance Temporal Reversible Spiking Neural Networks with O(L) Training Memory and O(1) Inference Cost](https://mlsanity.com/paper/2405.16466/) (2024)
- [Inherent Redundancy in Spiking Neural Networks](https://mlsanity.com/paper/2308.08227/) (2023)
- [SPIDE: A Purely Spike-based Method for Training Feedback Spiking Neural Networks](https://mlsanity.com/paper/2302.00232/) (2023)
- [Sharing Leaky-Integrate-and-Fire Neurons for Memory-Efficient Spiking Neural Networks](https://mlsanity.com/paper/2305.18360/) (2023)
- [Accelerating SNN Training with Stochastic Parallelizable Spiking Neurons](https://mlsanity.com/paper/2306.12666/) (2023)
- [Addressing the speed-accuracy simulation trade-off for adaptive spiking neurons](https://mlsanity.com/paper/2311.11390/) (2023)
- [Approximate Fixed-Points in Recurrent Neural Networks](https://mlsanity.com/paper/2106.02417/) (2021)
- [Learning fixed points of recurrent neural networks by reparameterizing the network model](https://mlsanity.com/paper/2307.06732/) (2023)

## Built on by (most cited first, 5 of 5)

- [AR-LIF: Adaptive reset leaky integrate-and-fire neuron for spiking neural networks](https://mlsanity.com/paper/2507.20746/) (2025)
- [Learning from Dense Events: Towards Fast Spiking Neural Networks Training via Event Dataset Distillation](https://mlsanity.com/paper/2511.12095/) (2025)
- [Bullet Trains: Parallelizing Training of Temporally Precise Spiking Neural Networks](https://mlsanity.com/paper/2603.13283/) (2026)
- [ParaRevSNN: A Parallel Reversible Spiking Neural Network for Efficient Training and Inference](https://mlsanity.com/paper/2508.01223/) (2025)
- [ADPTNet: Adaptive with Prescriptive Timescales Non-Linear SSM for Sequence Modelling](https://mlsanity.com/paper/2609.34034/) (2026)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) often suffer from high time complexity O(T) due to the sequential processing of T spikes, making training computationally expensive. In this paper, we propose a novel Fixed-point Parallel Training (FPT) method to accelerate SNN training without modifying the network architecture or introducing additional assumptions. FPT reduces the time complexity to O(K), where K is a small constant (usually K=3), by using a fixed-point iteration form of Leaky Integrate-and-Fire (LIF) neurons for all T timesteps. We provide a theoretical convergence analysis of FPT and demonstrate that existing parallel spiking neurons can be viewed as special cases of our proposed method. Experimental results show that FPT effectively simulates the dynamics of original LIF neurons, significantly reducing computational time without sacrificing accuracy. This makes FPT a scalable and efficient solution for real-world applications, particularly for long-term tasks. Our code will be released at hrefhttps://github.com/WanjinVon/FPTtexttthttps://github.com/WanjinVon/FPT.