How Powerful are Graph Neural Networks?

Graph Neural Networks (GNNs) are an effective framework for representation learning of graphs. GNNs follow a neighborhood aggregation scheme, where the representation vector of a node is computed by recursively aggregating and transforming representation vectors of its neighboring nodes. Many GNN variants have been proposed and have achieved state-of-the-art results on both node and graph classification tasks. However, despite GNNs revolutionizing graph representation learning, there is limited understanding of their representational properties and limitations. Here, we present a theoretical framework for analyzing the expressive power of GNNs to capture different graph structures. Our results characterize the discriminative power of popular GNN variants, such as Graph Convolutional Networks and GraphSAGE, and show that they cannot learn to distinguish certain simple graph structures. We then develop a simple architecture that is provably the most expressive among the class of GNNs and is as powerful as the Weisfeiler-Lehman graph isomorphism test. We empirically validate our theoretical findings on a number of graph classification benchmarks, and demonstrate that our model achieves state-of-the-art performance.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Graph Classification BP-fMRI-97 GIN Accuracy 45.4% # 8
F1 42.3% # 8
Graph Classification CIFAR10 100k GIN Accuracy (%) 53.28 # 10
Graph Classification COLLAB GIN-0 Accuracy 80.2% # 11
Graph Classification HIV-DTI-77 GIN Accuracy 55.1% # 5
F1 53.6% # 6
Graph Classification HIV-fMRI-77 GIN Accuracy 52.5% # 5
F1 35.6% # 5
Graph Classification IMDb-B GIN-0 Accuracy 75.1% # 13
Graph Classification IMDb-M GIN-0 Accuracy 52.3% # 8
Graph Classification MUTAG GIN-0 Accuracy 89.4% # 20
Graph Classification NCI1 GIN-0 Accuracy 82.7% # 18
Graph Property Prediction ogbg-code2 GIN Test F1 score 0.1495 ± 0.0023 # 13
Validation F1 score 0.1376 ± 0.0016 # 13
Number of params 12390715 # 5
Ext. data No # 1
Graph Property Prediction ogbg-code2 GIN+virtual node Test F1 score 0.1581 ± 0.0026 # 8
Validation F1 score 0.1439 ± 0.0020 # 10
Number of params 13841815 # 3
Ext. data No # 1
Graph Property Prediction ogbg-molhiv GIN Test ROC-AUC 0.7558 ± 0.0140 # 35
Validation ROC-AUC 0.8232 ± 0.0090 # 25
Number of params 1885206 # 12
Ext. data No # 1
Graph Property Prediction ogbg-molhiv GIN+virtual node Test ROC-AUC 0.7707 ± 0.0149 # 30
Validation ROC-AUC 0.8479 ± 0.0068 # 3
Number of params 3336306 # 8
Ext. data No # 1
Graph Property Prediction ogbg-molpcba GIN+virtual node Test AP 0.2703 ± 0.0023 # 20
Validation AP 0.2798 ± 0.0025 # 20
Number of params 3374533 # 16
Ext. data No # 1
Graph Property Prediction ogbg-molpcba GIN Test AP 0.2266 ± 0.0028 # 25
Validation AP 0.2305 ± 0.0027 # 25
Number of params 1923433 # 21
Ext. data No # 1
Graph Property Prediction ogbg-ppa GIN+virtual node Test Accuracy 0.7037 ± 0.0107 # 8
Validation Accuracy 0.6678 ± 0.0105 # 8
Number of params 3288042 # 4
Ext. data No # 1
Graph Property Prediction ogbg-ppa GIN Test Accuracy 0.6892 ± 0.0100 # 11
Validation Accuracy 0.6562 ± 0.0107 # 10
Number of params 1836942 # 10
Ext. data No # 1
Node Classification PATTERN 100k GIN Accuracy (%) 85.590 # 5
Graph Classification PROTEINS GIN-0 Accuracy 76,2% # 72
Graph Classification PTC GIN-0 Accuracy 64.40% # 19
Graph Classification REDDIT-B GIN-0 Accuracy 92.4 # 3
Graph Classification RE-M5K GIN-0 Accuracy 57.5% # 1
Graph Regression ZINC-500k GIN MAE 0.526 # 25

Methods