# Delays in Spiking Neural Networks: A State Space Model Approach

arXiv: https://arxiv.org/abs/2512.01906 · HTML: https://mlsanity.com/paper/2512.01906/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 28 of 28)

- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Efficiently Modeling Long Sequences with Structured State Spaces](https://mlsanity.com/paper/2111.00396/) (2021)
- [Event-based Vision: A Survey](https://mlsanity.com/paper/1904.08405/) (2019)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Hungry Hungry Hippos: Towards Language Modeling with State Space Models](https://mlsanity.com/paper/2212.14052/) (2022)
- [Diagonal State Spaces are as Effective as Structured State Spaces](https://mlsanity.com/paper/2203.14343/) (2022)
- [SLAYER: Spike Layer Error Reassignment in Time](https://mlsanity.com/paper/1810.08646/) (2018)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Effectively Modeling Time Series with Simple Discrete State Spaces](https://mlsanity.com/paper/2303.09489/) (2023)
- [Learning Delays in Spiking Neural Networks using Dilated Convolutions with Learnable Spacings](https://mlsanity.com/paper/2306.17670/) (2023)
- [Scalable Event-by-event Processing of Neuromorphic Sensory Signals With Deep State-Space Models](https://mlsanity.com/paper/2404.18508/) (2024)
- [Spiking Structured State Space Model for Monaural Speech Enhancement](https://mlsanity.com/paper/2309.03641/) (2023)
- [DenRAM: Neuromorphic Dendritic Architecture with RRAM for Efficient Temporal Processing with Delays](https://mlsanity.com/paper/2312.08960/) (2023)
- [Co-learning synaptic delays, weights and adaptation in spiking neural networks](https://mlsanity.com/paper/2311.16112/) (2023)
- [DelGrad: Exact event-based gradients for training delays and weights on spiking neuromorphic hardware](https://mlsanity.com/paper/2404.19165/) (2024)
- [Efficient Event-based Delay Learning in Spiking Neural Networks](https://mlsanity.com/paper/2501.07331/) (2025)
- [Braille Letter Reading: A Benchmark for Spatio-Temporal Pattern Recognition on Neuromorphic Hardware](https://mlsanity.com/paper/2205.15864/) (2022)
- [Zero-Shot Temporal Resolution Domain Adaptation for Spiking Neural Networks](https://mlsanity.com/paper/2411.04760/) (2024)
- [DelRec: learning delays in recurrent spiking neural networks](https://mlsanity.com/paper/2509.24852/) (2025)
- [Beyond Weights: Deep learning in Spiking Neural Networks with pure synaptic-delay training](https://mlsanity.com/paper/2306.06237/) (2023)
- [Adapting to time: Why nature may have evolved a diverse set of neurons](https://mlsanity.com/paper/2404.14325/) (2024)
- [State-Space Model Inspired Multiple-Input Multiple-Output Spiking Neurons](https://mlsanity.com/paper/2504.02591/) (2025)
- [Learning Delays Through Gradients and Structure: Emergence of Spatiotemporal Patterns in Spiking Neural Networks](https://mlsanity.com/paper/2407.18917/) (2024)
- [Accurate Mapping of RNNs on Neuromorphic Hardware with Adaptive Spiking Neurons](https://mlsanity.com/paper/2407.13534/) (2024)
- [Efficient Synaptic Delay Implementation in Digital Event-Driven AI Accelerators](https://mlsanity.com/paper/2501.13610/) (2025)
- [Extending Spike-Timing Dependent Plasticity to Learning Synaptic Delays](https://mlsanity.com/paper/2506.14984/) (2025)
- [Exploiting heterogeneous delays for efficient computation in low-bit neural networks](https://mlsanity.com/paper/2510.27434/) (2025)
- [Low-Bit Data Processing Using Multiple-Output Spiking Neurons with Non-linear Reset Feedback](https://mlsanity.com/paper/2508.06292/) (2025)

## Abstract (arXiv)

Spiking neural networks (SNNs) are biologically inspired, event-driven models suited for temporal data processing and energy-efficient neuromorphic computing. In SNNs, richer neuronal dynamic allows capturing more complex temporal dependencies, with delays playing a crucial role by allowing past inputs to directly influence present spiking behavior. We propose a general framework for incorporating delays into SNNs through additional state variables. The proposed mechanism enables each neuron to access a finite temporal input history. The framework is agnostic to neuron models and hence can be seamlessly integrated into standard spiking neuron models such as Leaky Integrate-and-Fire (LIF) and Adaptive LIF (adLIF). We analyze how the duration of the delays and the learnable parameters associated with them affect the performance. We investigate the trade-offs in the network architecture due to additional state variables introduced by the delay mechanism. Experiments on the Spiking Heidelberg Digits (SHD) dataset show that the proposed mechanism matches existing delay-based SNNs in performance while remaining computationally efficient, with particular gains in smaller networks.