# Topological Representations of Heterogeneous Learning Dynamics of Recurrent Spiking Neural Networks

arXiv: https://arxiv.org/abs/2403.12462 · HTML: https://mlsanity.com/paper/2403.12462/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 19 Mar 2024.

## Builds on (most cited first, 18 of 18)

- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [Do Vision Transformers See Like Convolutional Neural Networks?](https://mlsanity.com/paper/2108.08810/) (2021)
- [Surrogate Gradient Learning in Spiking Neural Networks](https://mlsanity.com/paper/1901.09948/) (2019)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [Insights on representational similarity in neural networks with canonical correlation](https://mlsanity.com/paper/1806.05759/) (2018)
- [On the Expressive Power of Deep Neural Networks](https://mlsanity.com/paper/1606.05336/) (2016)
- [Do Wide and Deep Networks Learn the Same Things? Uncovering How Neural Network Representations Vary with Width and Depth](https://mlsanity.com/paper/2010.15327/) (2020)
- [Spiking-YOLO: Spiking Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/1903.06530/) (2019)
- [The Heidelberg spiking datasets for the systematic evaluation of spiking neural networks](https://mlsanity.com/paper/1910.07407/) (2019)
- [Temporal Spike Sequence Learning via Backpropagation for Deep Spiking Neural Networks](https://mlsanity.com/paper/2002.10085/) (2020)
- [Representation Topology Divergence: A Method for Comparing Neural Network Representations](https://mlsanity.com/paper/2201.00058/) (2021)
- [A Fully Spiking Hybrid Neural Network for Energy-Efficient Object Detection](https://mlsanity.com/paper/2104.10719/) (2021)
- [Heterogeneous Recurrent Spiking Neural Network for Spatio-Temporal Classification](https://mlsanity.com/paper/2211.04297/) (2022)
- [Uncovering the Representation of Spiking Neural Networks Trained with Surrogate Gradient](https://mlsanity.com/paper/2304.13098/) (2023)
- [Sparse Spiking Neural Network: Exploiting Heterogeneity in Timescales for Pruning Recurrent SNN](https://mlsanity.com/paper/2403.03409/) (2024)
- [Characterization of Generalizability of Spike Timing Dependent Plasticity trained Spiking Neural Networks](https://mlsanity.com/paper/2105.14677/) (2021)
- [Heterogeneous Neuronal and Synaptic Dynamics for Spike-Efficient Unsupervised Learning: Theory and Design Principles](https://mlsanity.com/paper/2302.11618/) (2023)
- [Brain-Inspired Spiking Neural Network for Online Unsupervised Time Series Prediction](https://mlsanity.com/paper/2304.04697/) (2023)

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

- [Exploiting Heterogeneity in Timescales for Sparse Recurrent Spiking Neural Networks for Energy-Efficient Edge Computing](https://mlsanity.com/paper/2407.06452/) (2024)
- [A Dynamical Systems-Inspired Pruning Strategy for Addressing Oversmoothing in Graph Neural Networks](https://mlsanity.com/paper/2412.07243/) (2024)
- [FLAMES: A Hybrid Spiking-State Space Model for Adaptive Memory Retention in Event-Based Learning](https://mlsanity.com/paper/2504.01257/) (2025)

## Abstract (arXiv)

Spiking Neural Networks (SNNs) have become an essential paradigm in neuroscience and artificial intelligence, providing brain-inspired computation. Recent advances in literature have studied the network representations of deep neural networks. However, there has been little work that studies representations learned by SNNs, especially using unsupervised local learning methods like spike-timing dependent plasticity (STDP). Recent work by citebarannikov2021representation has introduced a novel method to compare topological mappings of learned representations called Representation Topology Divergence (RTD). Though useful, this method is engineered particularly for feedforward deep neural networks and cannot be used for recurrent networks like Recurrent SNNs (RSNNs). This paper introduces a novel methodology to use RTD to measure the difference between distributed representations of RSNN models with different learning methods. We propose a novel reformulation of RSNNs using feedforward autoencoder networks with skip connections to help us compute the RTD for recurrent networks. Thus, we investigate the learning capabilities of RSNN trained using STDP and the role of heterogeneity in the synaptic dynamics in learning such representations. We demonstrate that heterogeneous STDP in RSNNs yield distinct representations than their homogeneous and surrogate gradient-based supervised learning counterparts. Our results provide insights into the potential of heterogeneous SNN models, aiding the development of more efficient and biologically plausible hybrid artificial intelligence systems.