# Learning Delays Through Gradients and Structure: Emergence of Spatiotemporal Patterns in Spiking Neural Networks

arXiv: https://arxiv.org/abs/2407.18917 · HTML: https://mlsanity.com/paper/2407.18917/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jul 2024.

## Built on by (most cited first, 3 of 3)

- [A Complete Pipeline for deploying SNNs with Synaptic Delays on Loihi 2](https://mlsanity.com/paper/2510.13757/) (2025)
- [Three factor delay learning rules for spiking neural networks](https://mlsanity.com/paper/2601.00668/) (2026)
- [Delays in Spiking Neural Networks: A State Space Model Approach](https://mlsanity.com/paper/2512.01906/) (2025)

## Abstract (arXiv)

We present a Spiking Neural Network (SNN) model that incorporates learnable synaptic delays through two approaches: per-synapse delay learning via Dilated Convolutions with Learnable Spacings (DCLS) and a dynamic pruning strategy that also serves as a form of delay learning. In the latter approach, the network dynamically selects and prunes connections, optimizing the delays in sparse connectivity settings. We evaluate both approaches on the Raw Heidelberg Digits keyword spotting benchmark using Backpropagation Through Time with surrogate gradients. Our analysis of the spatio-temporal structure of synaptic interactions reveals that, after training, excitation and inhibition group together in space and time. Notably, the dynamic pruning approach, which employs DEEP R for connection removal and RigL for reconnection, not only preserves these spatio-temporal patterns but outperforms per-synapse delay learning in sparse networks. Our results demonstrate the potential of combining delay learning with dynamic pruning to develop efficient SNN models for temporal data processing. Moreover, the preservation of spatio-temporal dynamics throughout pruning and rewiring highlights the robustness of these features, providing a solid foundation for future neuromorphic computing applications.