Gradual Weisfeiler-Leman: Slow and Steady Wins the Race

Franka Bause, Nils Morten Kriege

Keywords: Weisfeiler-Leman, graphs, color refinement, vertex similarity, graph kernel

Abstract: The classical Weisfeiler-Leman algorithm aka color refinement is fundamental for graph learning with kernels and neural networks. Originally developed for graph isomorphism testing, the algorithm iteratively refines vertex colors. On many datasets, the stable coloring is reached after a few iterations and the optimal number of iterations for machine learning tasks is typically even lower. This suggests that the colors diverge too fast, defining a similarity that is too coarse. We generalize the concept of color refinement and propose a framework for gradual neighborhood refinement, which allows a slower convergence to the stable coloring and thus provides a more fine-grained refinement hierarchy and vertex similarity. We assign new colors by clustering vertex neighborhoods, replacing the original injective color assignment function. Our approach is used to derive new variants of existing graph kernels and to approximate the graph edit distance via optimal assignments regarding vertex similarity. We show that in both tasks, our method outperforms the original color refinement with only a moderate increase in running time advancing the state of the art.

Type Of Submission: Full paper proceedings track submission (max 9 main pages).

Agreement: Check this if you are okay with being contacted to participate in an anonymous survey.

TL;DR: We generalize the Weisfeiler-Leman refinement to generate and include intermediate colorings of nodes improving the derived graph learning methods

Type Of Submission: Full paper proceedings track submission.

Software: https://github.com/frareba/GradualWeisfeilerLeman

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2209.09048/code)