Provably Powerful Graph Networks

Recently, the Weisfeiler-Lehman (WL) graph isomorphism test was used to measure the expressive power of graph neural networks (GNN). It was shown that the popular message passing GNN cannot distinguish between graphs that are indistinguishable by the 1-WL test (Morris et al. 2018; Xu et al. 2019). Unfortunately, many simple instances of graphs are indistinguishable by the 1-WL test. In search for more expressive graph learning models we build upon the recent k-order invariant and equivariant graph neural networks (Maron et al. 2019a,b) and present two results: First, we show that such k-order networks can distinguish between non-isomorphic graphs as good as the k-WL tests, which are provably stronger than the 1-WL test for k>2. This makes these models strictly stronger than message passing models. Unfortunately, the higher expressiveness of these models comes with a computational cost of processing high order tensors. Second, setting our goal at building a provably stronger, simple and scalable model we show that a reduced 2-order network containing just scaled identity operator, augmented with a single quadratic operation (matrix multiplication) has a provable 3-WL expressive power. Differently put, we suggest a simple model that interleaves applications of standard Multilayer-Perceptron (MLP) applied to the feature dimension and matrix multiplication. We validate this model by presenting state of the art results on popular graph classification and regression tasks. To the best of our knowledge, this is the first practical invariant/equivariant model with guaranteed 3-WL expressiveness, strictly stronger than message passing models.

PDF Abstract NeurIPS 2019 PDF NeurIPS 2019 Abstract

Results from the Paper

Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification COLLAB PPGN Accuracy 81.38% # 6
Graph Classification IMDb-B PPGN Accuracy 72.6% # 29
Graph Classification IMDb-M PPGN Accuracy 50% # 24
Graph Classification MUTAG PPGN Accuracy 90.55% # 19
Graph Classification NCI1 PPGN Accuracy 83.19% # 21
Graph Classification NCI109 PPGN Accuracy 82.23 # 10
Graph Classification PROTEINS PPGN Accuracy 77.20% # 29
Graph Classification PTC PPGN Accuracy 66.17% # 20
Graph Regression ZINC-500k 3WLGNN MAE 0.303 # 28


No methods listed for this paper. Add relevant methods here