# Bullet Trains: Parallelizing Training of Temporally Precise Spiking Neural Networks

arXiv: https://arxiv.org/abs/2603.13283 · HTML: https://mlsanity.com/paper/2603.13283/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 45 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 22 of 22)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Supervised learning based on temporal coding in spiking neural networks](https://mlsanity.com/paper/1606.08165/) (2016)
- [Event-Based Backpropagation can compute Exact Gradients for Spiking Neural Networks](https://mlsanity.com/paper/2009.08378/) (2020)
- [Fast and energy-efficient neuromorphic deep learning with first-spike times](https://mlsanity.com/paper/1912.11443/) (2019)
- [Speck: A Smart event-based Vision Sensor with a low latency 327K Neuron Convolutional Neuronal Network Processing Pipeline](https://mlsanity.com/paper/2304.06793/) (2023)
- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Parallel Spiking Neurons with High Efficiency and Ability to Learn Long-term Dependencies](https://mlsanity.com/paper/2304.12760/) (2023)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [DYNAP-SE2: a scalable multi-core dynamic neuromorphic asynchronous spiking neural network processor](https://mlsanity.com/paper/2310.00564/) (2023)
- [Loss shaping enhances exact gradient learning with Eventprop in spiking neural networks](https://mlsanity.com/paper/2212.01232/) (2022)
- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [SPikE-SSM: A Sparse, Precise, and Efficient Spiking State Space Model for Long Sequences Learning](https://mlsanity.com/paper/2410.17268/) (2024)
- [Efficient Event-based Delay Learning in Spiking Neural Networks](https://mlsanity.com/paper/2501.07331/) (2025)
- [SparseProp: Efficient Event-Based Simulation and Training of Sparse Recurrent Spiking Neural Networks](https://mlsanity.com/paper/2312.17216/) (2023)
- [Spiking Neural Networks for Temporal Processing: Status Quo and Future Prospects](https://mlsanity.com/paper/2502.09449/) (2025)
- [jaxsnn: Event-driven Gradient Estimation for Analog Neuromorphic Hardware](https://mlsanity.com/paper/2401.16841/) (2024)
- [Efficient Parallel Training Methods for Spiking Neural Networks with Constant Time Complexity](https://mlsanity.com/paper/2506.12087/) (2025)
- [EXODUS: Stable and Efficient Training of Spiking Neural Networks](https://mlsanity.com/paper/2205.10242/) (2022)
- [Parallel Spiking Unit for Efficient Training of Spiking Neural Networks](https://mlsanity.com/paper/2402.00449/) (2024)
- [ADSEQ: A delay-aware autograd-compatible framework for spike-event delivery in SNNs](https://mlsanity.com/paper/2512.05906/) (2025)

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

- [Scalable Training of Continuous-Time Spiking Neural Networks with Differentiable Spike-Time Discretization](https://mlsanity.com/paper/2607.14672/) (2026)
- [ADPTNet: Adaptive with Prescriptive Timescales Non-Linear SSM for Sequence Modelling](https://mlsanity.com/paper/2609.34034/) (2026)

## Abstract (arXiv)

Continuous-time, event-native spiking neural networks (SNNs) operate strictly on spike events, treating spike timing and ordering as the representation rather than an artifact of time discretization. This viewpoint aligns with biological computation and with the native resolution of event sensors and neuromorphic processors, while enabling compute and memory that scale with the number of events. However, two challenges hinder practical, end-to-end trainable event-based SNN systems: 1) exact charge--fire--reset dynamics impose inherently sequential processing of input spikes, and 2) precise spike times must be solved without time bins. We address both. First, we use parallel associative scans to consume multiple input spikes at once, yielding up to 44x speedups over sequential simulation while retaining exact hard-reset dynamics. Second, we implement differentiable spike time solvers that compute spike times to machine-precision without discrete-time approximations or restrictive analytic assumptions. We demonstrate the viability of training SNNs using our solutions on four event-based datasets on GPUs.