Simple and Deep Graph Convolutional Networks

Graph convolutional networks (GCNs) are a powerful deep learning approach for graph-structured data. Recently, GCNs and subsequent variants have shown superior performance in various application areas on real-world datasets. Despite their success, most of the current GCN models are shallow, due to the {\em over-smoothing} problem. In this paper, we study the problem of designing and analyzing deep graph convolutional networks. We propose the GCNII, an extension of the vanilla GCN model with two simple yet effective techniques: {\em Initial residual} and {\em Identity mapping}. We provide theoretical and empirical evidence that the two techniques effectively relieves the problem of over-smoothing. Our experiments show that the deep GCNII model outperforms the state-of-the-art methods on various semi- and full-supervised tasks. Code is available at https://github.com/chennnM/GCNII .

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Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification Actor GCNII Accuracy 37.44 ± 1.30 # 14
Node Classification Chameleon GCNII Accuracy 63.86 ± 3.04 # 42
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 63.86 ± 3.04  # 21
Node Classification Chameleon (60%/20%/20% random splits) GCNII 1:1 Accuracy 60.35 ± 2.7 # 29
Node Classification Chameleon (60%/20%/20% random splits) GCNII* 1:1 Accuracy 62.8 ± 2.87 # 22
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon(60%/20%/20% random splits) GCNII 1:1 Accuracy 60.35 ± 2.7 # 26
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon(60%/20%/20% random splits) GCNII* 1:1 Accuracy 62.8 ± 2.87 # 20
Node Classification Citeseer (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 77.33 ± 1.48 # 5
Node Classification CiteSeer (60%/20%/20% random splits) GCNII* 1:1 Accuracy 81.83 ± 1.78 # 5
Node Classification CiteSeer (60%/20%/20% random splits) GCNII 1:1 Accuracy 81.58 ± 1.3 # 11
Node Classification Citeseer Full-supervised GCNII* Accuracy 77.13% # 4
Node Classification CiteSeer with Public Split: fixed 20 nodes per class GCNII Accuracy 73.4% # 14
Node Classification COCO-SP GCNII macro F1 0.1404±0.0011 # 11
Node Classification Cora (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 88.37 ± 1.25 # 2
Node Classification Cora (60%/20%/20% random splits) GCNII* 1:1 Accuracy 88.93 ± 1.37 # 14
Node Classification Cora (60%/20%/20% random splits) GCNII 1:1 Accuracy 88.98 ± 1.33 # 12
Node Classification Cora Full-supervised GCNII Accuracy 88.49% # 1
Node Classification Cora with Public Split: fixed 20 nodes per class GCNII Accuracy 85.5% # 2
Node Classification Cornell GCNII Accuracy 77.86 ± 3.79 # 40
Node Classification on Non-Homophilic (Heterophilic) Graphs Cornell (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 77.86 ± 3.79  # 21
Node Classification on Non-Homophilic (Heterophilic) Graphs Cornell (60%/20%/20% random splits) GCNII 1:1 Accuracy 89.18 ± 3.96 # 20
Node Classification on Non-Homophilic (Heterophilic) Graphs Cornell (60%/20%/20% random splits) GCNII* 1:1 Accuracy 90.49 ± 4.45 # 19
Node Classification Cornell (60%/20%/20% random splits) GCNII* 1:1 Accuracy 90.49 ± 4.45 # 19
Node Classification Cornell (60%/20%/20% random splits) GCNII 1:1 Accuracy 89.18 ± 3.96 # 20
Node Classification on Non-Homophilic (Heterophilic) Graphs Deezer-Europe GCNII* 1:1 Accuracy 66.42±0.56 # 16
Node Classification on Non-Homophilic (Heterophilic) Graphs Deezer-Europe GCNII 1:1 Accuracy 66.38±0.45 # 18
Node Classification on Non-Homophilic (Heterophilic) Graphs Film(48%/32%/20% fixed splits) GCNII 1:1 Accuracy 37.44 ± 1.30 # 7
Node Classification Film (60%/20%/20% random splits) GCNII* 1:1 Accuracy 41.54 ± 0.99 # 8
Node Classification Film (60%/20%/20% random splits) GCNII 1:1 Accuracy 40.82 ± 1.79 # 15
Node Classification genius GCNII Accuracy 90.24 ± 0.09 # 11
Node Classification on Non-Homophilic (Heterophilic) Graphs genius GCNII 1:1 Accuracy 90.24 ± 0.09 # 13
Node Property Prediction ogbn-arxiv GCNII Test Accuracy 0.7274 ± 0.0016 # 54
Validation Accuracy Please tell us # 77
Number of params 2148648 # 16
Ext. data No # 1
Node Classification PascalVOC-SP GCNII macro F1 0.1698±0.0080 # 14
Link Prediction PCQM-Contact GCNII Hits@1 0.1325±0.0009 # 5
Hits@3 0.3607±0.0003 # 10
Hits@10 0.8116±0.0009 # 10
MRR 0.3161±0.0004 # 17
Node Classification on Non-Homophilic (Heterophilic) Graphs Penn94 GCNII 1:1 Accuracy 82.92 ± 0.59 # 9
Node Classification Penn94 GCNII Accuracy 82.92 ± 0.59 # 11
Graph Classification Peptides-func GCNII AP 0.5543±0.0078 # 25
Graph Regression Peptides-struct GCNII MAE 0.3471±0.0010 # 24
Node Classification PPI GCNII* F1 99.56 # 2
Node Classification PubMed (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 90.15 ± 0.43 # 1
Node Classification PubMed (60%/20%/20% random splits) GCNII 1:1 Accuracy 89.8 ± 0.3 # 19
Node Classification PubMed (60%/20%/20% random splits) GCNII* 1:1 Accuracy 89.98 ± 0.52 # 16
Node Classification Pubmed Full-supervised GCNII* Accuracy 90.30% # 4
Node Classification PubMed with Public Split: fixed 20 nodes per class GCNII Accuracy 80.2% # 14
Node Classification Squirrel GCNII Accuracy 38.47 ± 1.58 # 43
Node Classification on Non-Homophilic (Heterophilic) Graphs Squirrel (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 38.47 ± 1.58 # 24
Node Classification Squirrel (60%/20%/20% random splits) GCNII 1:1 Accuracy 38.81 ± 1.97 # 29
Node Classification Squirrel (60%/20%/20% random splits) GCNII* 1:1 Accuracy 38.31 ± 1.3 # 31
Node Classification Texas GCNII Accuracy 77.57 ± 3.83 # 45
Node Classification on Non-Homophilic (Heterophilic) Graphs Texas (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 77.57 ± 3.83 # 21
Node Classification Texas (60%/20%/20% random splits) GCNII 1:1 Accuracy 82.46 ± 4.58 # 27
Node Classification Texas (60%/20%/20% random splits) GCNII* 1:1 Accuracy 88.52 ± 3.02 # 20
Node Classification on Non-Homophilic (Heterophilic) Graphs Texas(60%/20%/20% random splits) GCNII 1:1 Accuracy 82.46 ± 4.58 # 25
Node Classification on Non-Homophilic (Heterophilic) Graphs Texas(60%/20%/20% random splits) GCNII* 1:1 Accuracy 88.52 ± 3.02 # 19
Node Classification on Non-Homophilic (Heterophilic) Graphs twitch-gamers GCNII 1:1 Accuracy 63.39 ± 0.61 # 18
Node Classification Wisconsin GCNII Accuracy 80.39 ± 3.40 # 43
Node Classification on Non-Homophilic (Heterophilic) Graphs Wisconsin (48%/32%/20% fixed splits) GCNII 1:1 Accuracy 80.39 ± 3.40 # 20
Node Classification Wisconsin (60%/20%/20% random splits) GCNII* 1:1 Accuracy 89.12 ± 3.06 # 19
Node Classification Wisconsin (60%/20%/20% random splits) GCNII 1:1 Accuracy 83.25 ± 2.69 # 23
Node Classification on Non-Homophilic (Heterophilic) Graphs Wisconsin(60%/20%/20% random splits) GCNII 1:1 Accuracy 83.25 ± 2.69 # 21
Node Classification on Non-Homophilic (Heterophilic) Graphs Wisconsin(60%/20%/20% random splits) GCNII* 1:1 Accuracy 89.12 ± 3.06 # 19

Methods