WEISFEILER AND LEMAN GO INFINITE: SPECTRAL AND COMBINATORIAL PRE-COLORINGSDownload PDF

02 Mar 2022, 12:21 (edited 04 Apr 2022)GTRL 2022 PosterReaders: Everyone
  • Keywords: Graph Neural Networks, Message Passing Architectures, Graph Isomorphim, WL test
  • TL;DR: We propose an efficient pre-coloring based on spectral features that provably increases the expressive power of the vanilla WL test
  • Abstract: Two popular alternatives for graph isomorphism testing that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the Weisfeiler-Leman (WL) test) and spectral invariants. While the exact power of the latter is still an open question, the former is regularly criticized for its limited power, when a standard configuration of uniform pre-coloring is used. This drawback hinders the applicability of Message Passing Graph Neural Networks (MPGNNs), whose expressive power is upper bounded by the WL test. Relaxing the assumption of uniform pre-coloring, we show that one can increase the expressive power of the WL test ad infinitum. Following that, we propose an efficient pre-coloring based on spectral features that provably increase the expressive power of the vanilla WL test. The code to reproduce our experiments is available at \url{https://github.com/TPFI22/Spectral-and-Combinatorial}
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