Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings

Published: 18 Apr 2023, Last Modified: 18 Apr 2023Accepted by TMLREveryoneRevisionsBibTeX
Abstract: The limit in the expressivity of Message Passing Graph Neural Networks (MPGNNs) has recently led to the development of end-to-end learning GNN architectures. These advanced GNNs usually generalize existing notions in the GNN architecture or suggest new ones that break the limit of the existing, relatively simple MPGNNs. In this paper, we focus on a different solution, the two-phase approach (or pre-coloring), which enables to use of the same simple MPGNNs while improving their expressivity. We prove that using pre-colorings could strictly increase the expressivity of MPGNNs ad infinitum. We also suggest new pre-coloring based on the spectral decomposition of the graph Laplacian and prove that it strictly improves the expressivity of standard MPGNNs. An extensive evaluation of the proposed method with different MPGNN models on various graph classification and node property prediction datasets consistently outperforms previous pre-coloring strategies. The code to reproduce our experiments is available at \url{https://github.com/TPFI22/Spectral-and-Combinatorial}.
License: Creative Commons Attribution 4.0 International (CC BY 4.0)
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: 1. We added the relevant explicit statement in section 3. 2. We added a paragraph in section 4 regarding the known comparison between spectral based approaches and 2-WL. 3. We removed closely located repeated references. 4. We fixed the types in the citation formatting. 5. We fixed the styling of k. 6. We fixed the styling of \Delta{k-WL}. 7. We fixed the styling of t. 8. We fixed the styling of i. 9. We removed the redundant space in page 5. 10. We fixed the misplaced . in pages 5 and 6. 11. We added references in the text for tables 1,2 and 3. 12. We added an acknowledgment section. 13. We removed duplicated references. 14. In the reference section, we fixed preprinted referenced works to their published version. 15. We set all of the tables to have the same font size. 16. We fixed the typography where necessary.
Supplementary Material: pdf
Assigned Action Editor: ~Guido_Montufar1
Submission Number: 584