SlepNet: Spectral Subgraph Representation Learning for Neural Dynamics
🤖 AI Summary
Existing graph neural networks (GNNs) struggle to effectively model graph signals—such as neurophysiological signals—that exhibit strong spatiotemporal locality, high dimensionality, and stringent requirements for physical interpretability. Conventional graph convolutional networks (GCNs) based on graph Fourier transform lack spatial localization, while graph wavelet methods suffer from insufficient normalization and absence of strict subgraph constraints. To address these limitations, this work introduces the Slepian basis into GNNs for the first time, proposing the Subgraph-adaptive Slepian Graph Convolutional Network (SGCN). SGCN employs learnable masks to automatically identify functionally critical subgraphs (e.g., brain regions) and constructs canonical spectral representations that are energy-concentrated, spatially localized, and physically interpretable. Evaluated on three fMRI and two traffic datasets, SGCN significantly outperforms GCN, ChebNet, and classical graph signal processing methods. Moreover, its learned representations demonstrate cross-task transferability, markedly improving pattern discriminability and transient dynamic modeling performance.
Application Category
📝 Abstract
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.
Problem
Research questions and friction points this paper is trying to address.
Representing neural signal patterns on graphs efficiently
Overcoming limitations of graph Fourier transforms in signal localization
Improving resolution in distinguishing similar neural activity patterns
Innovation
Methods, ideas, or system contributions that make the work stand out.
Uses Slepian bases for graph signal representation
Automatically learns relevant subgraphs with mask
Optimally concentrates signal energy on subgraphs
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