Towards better evaluation of gnn expressiveness with brec dataset

Y Wang, M Zhang - arXiv preprint arXiv:2304.07702, 2023 - arxiv.org
arXiv preprint arXiv:2304.07702, 2023arxiv.org
Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has
developed rapidly, and many methods have been proposed to enhance the expressiveness.
However, most methods do not have a uniform expressiveness measure except for a few
that strictly follow the $ k $-dimensional Weisfeiler-Lehman ($ k $-WL) test hierarchy. Their
theoretical analyses are often limited to distinguishing certain families of non-isomorphic
graphs, leading to difficulties in quantitatively comparing their expressiveness. In contrast to …
Research on the theoretical expressiveness of Graph Neural Networks (GNNs) has developed rapidly, and many methods have been proposed to enhance the expressiveness. However, most methods do not have a uniform expressiveness measure except for a few that strictly follow the -dimensional Weisfeiler-Lehman (-WL) test hierarchy. Their theoretical analyses are often limited to distinguishing certain families of non-isomorphic graphs, leading to difficulties in quantitatively comparing their expressiveness. In contrast to theoretical analysis, another way to measure expressiveness is by evaluating model performance on certain datasets containing 1-WL-indistinguishable graphs. Previous datasets specifically designed for this purpose, however, face problems with difficulty (any model surpassing 1-WL has nearly 100% accuracy), granularity (models tend to be either 100% correct or near random guess), and scale (only a few essentially different graphs in each dataset). To address these limitations, we propose a new expressiveness dataset, , which includes 400 pairs of non-isomorphic graphs carefully selected from four primary categories (Basic, Regular, Extension, and CFI). These graphs have higher difficulty (up to 4-WL-indistinguishable), finer granularity (able to compare models between 1-WL and 3-WL), and a larger scale (400 pairs). Further, we synthetically test 23 models with higher-than-1-WL expressiveness on our BREC dataset. Our experiment gives the first thorough comparison of the expressiveness of those state-of-the-art beyond-1-WL GNN models. We expect this dataset to serve as a benchmark for testing the expressiveness of future GNNs. Our dataset and evaluation code are released at: https://github.com/GraphPKU/BREC.
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