Laplace-Transform-Filters render spectral Graph Neural Networks transferable

ICLR 2025 Conference Submission279 Authors

Keywords: Graph Neural Networks, Spectral Graph Theory, Transferability

TL;DR: We develop a novel approach to GNN transferability based on information diffusion on graphs. We find that spectral graph neural networks are transferable from this new point of view if their filters arise as Laplace transforms of certain functions.

Abstract: We introduce a new point of view on transferability of graph neural networks based on the intrinsic notion of information diffusion within graphs. This notion is adapted to considering graphs to be similar if their overall rough structures are similar, while their fine-print articulation may differ. Transferability of graph neural networks is then considered between graphs that are similar from this novel perspective on transferability. After carefully analysing transferability of single filters, the transferability properties of entire networks are relegated to the transferability characteristics of the filters employed inside their convolutional blocks. A rigorous analysis establishes our main theoretical finding: Spectral convolutional networks are transferable between graphs whose overall rough structures align, if their filters arise as Laplace transforms of certain generalized functions. Numerical experiments illustrate and validate the theoretical findings in practice.

Primary Area: learning on graphs and other geometries & topologies

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Submission Number: 279