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On the Stability of Expressive Positional Encodings for Graphs
April 16, 2024, 4:44 a.m. | Yinan Huang, William Lu, Joshua Robinson, Yu Yang, Muhan Zhang, Stefanie Jegelka, Pan Li
cs.LG updates on arXiv.org arxiv.org
Abstract: Designing effective positional encodings for graphs is key to building powerful graph transformers and enhancing message-passing graph neural networks. Although widespread, using Laplacian eigenvectors as positional encodings faces two fundamental challenges: (1) \emph{Non-uniqueness}: there are many different eigendecompositions of the same Laplacian, and (2) \emph{Instability}: small perturbations to the Laplacian could result in completely different eigenspaces, leading to unpredictable changes in positional encoding. Despite many attempts to address non-uniqueness, most methods overlook stability, leading to …
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