# SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics

arXiv: https://arxiv.org/abs/2506.16602 · HTML: https://mlsanity.com/paper/2506.16602/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 52 references that are in the map.
- First posted on arXiv 19 Jun 2025.

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

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [How Powerful are Graph Neural Networks?](https://mlsanity.com/paper/1810.00826/) (2018)
- [Neural Message Passing for Quantum Chemistry](https://mlsanity.com/paper/1704.01212/) (2017)
- [Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering](https://mlsanity.com/paper/1606.09375/) (2016)
- [Spectral Networks and Locally Connected Networks on Graphs](https://mlsanity.com/paper/1312.6203/) (2013)
- [Graph Wavelet Neural Network](https://mlsanity.com/paper/1904.07785/) (2019)
- [SpectralNet: Spectral Clustering using Deep Neural Networks](https://mlsanity.com/paper/1801.01587/) (2018)
- [Subgraph Neural Networks](https://mlsanity.com/paper/2006.10538/) (2020)
- [Spatio-Temporal Graph Convolution for Resting-State fMRI Analysis](https://mlsanity.com/paper/2003.10613/) (2020)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Fine-grain atlases of functional modes for fMRI analysis](https://mlsanity.com/paper/2003.05405/) (2020)
- [Diffusion Nets](https://mlsanity.com/paper/1506.07840/) (2015)
- [Geometric Scattering on Measure Spaces](https://mlsanity.com/paper/2208.08561/) (2022)
- [Graph Neural Networks for Brain Graph Learning: A Survey](https://mlsanity.com/paper/2406.02594/) (2024)
- [Graph Signal Processing and Deep Learning: Convolution, Pooling, and Topology](https://mlsanity.com/paper/2008.01247/) (2020)
- [Learnable Filters for Geometric Scattering Modules](https://mlsanity.com/paper/2208.07458/) (2022)
- [SHINE: SubHypergraph Inductive Neural nEtwork](https://mlsanity.com/paper/2210.07309/) (2022)
- [Graph Neural Networks With Lifting-based Adaptive Graph Wavelets](https://mlsanity.com/paper/2108.01660/) (2021)
- [Improving Subgraph Representation Learning via Multi-View Augmentation](https://mlsanity.com/paper/2205.13038/) (2022)
- [When Slepian Meets Fiedler: Putting a Focus on the Graph Spectrum](https://mlsanity.com/paper/1701.08401/) (2017)
- [Guiding Network Analysis using Graph Slepians: An Illustration for the C. Elegans Connectome](https://mlsanity.com/paper/1708.04657/) (2017)
- [Guided Graph Spectral Embedding: Application to the C. elegans Connectome](https://mlsanity.com/paper/1812.03684/) (2018)
- [Generalizing Weisfeiler-Lehman Kernels to Subgraphs](https://mlsanity.com/paper/2412.02181/) (2024)

## Abstract (arXiv)

Graph neural networks have been useful in machine learning on graph-structured data, particularly for node classification and some types of graph classification tasks. However, they have had limited use in representing patterning of signals over graphs. Patterning of signals over graphs and in subgraphs carries important information in many domains including neuroscience. Neural signals are spatiotemporally patterned, high dimensional and difficult to decode. Graph signal processing and associated GCN models utilize the graph Fourier transform and are unable to efficiently represent spatially or spectrally localized signal patterning on graphs. Wavelet transforms have shown promise here, but offer non-canonical representations and cannot be tightly confined to subgraphs. Here we propose SlepNet, a novel GCN architecture that uses Slepian bases rather than graph Fourier harmonics. In SlepNet, the Slepian harmonics optimally concentrate signal energy on specifically relevant subgraphs that are automatically learned with a mask. Thus, they can produce canonical and highly resolved representations of neural activity, focusing energy of harmonics on areas of the brain which are activated. We evaluated SlepNet across three fMRI datasets, spanning cognitive and visual tasks, and two traffic dynamics datasets, comparing its performance against conventional GNNs and graph signal processing constructs. SlepNet outperforms the baselines in all datasets. Moreover, the extracted representations of signal patterns from SlepNet offers more resolution in distinguishing between similar patterns, and thus represent brain signaling transients as informative trajectories. Here we have shown that these extracted trajectory representations can be used for other downstream untrained tasks. Thus we establish that SlepNet is useful both for prediction and representation learning in spatiotemporal data.