Half-Hop: A graph upsampling approach for slowing down message passing

Message passing neural networks have shown a lot of success on graph-structured data. However, there are many instances where message passing can lead to over-smoothing or fail when neighboring nodes belong to different classes. In this work, we introduce a simple yet general framework for improving learning in message passing neural networks. Our approach essentially upsamples edges in the original graph by adding "slow nodes" at each edge that can mediate communication between a source and a target node. Our method only modifies the input graph, making it plug-and-play and easy to use with existing models. To understand the benefits of slowing down message passing, we provide theoretical and empirical analyses. We report results on several supervised and self-supervised benchmarks, and show improvements across the board, notably in heterophilic conditions where adjacent nodes are more likely to have different labels. Finally, we show how our approach can be used to generate augmentations for self-supervised learning, where slow nodes are randomly introduced into different edges in the graph to generate multi-scale views with variable path lengths.

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Results from the Paper


Task Dataset Model Metric Name Metric Value Global Rank Result Benchmark
Node Classification AMZ Comp HH-GraphSAGE Accuracy 86.6% # 4
Node Classification AMZ Comp HH-GCN Accuracy 90.92% # 1
Node Classification AMZ Comp GCN Accuracy 90.22% # 2
Node Classification AMZ Comp GraphSAGE Accuracy 84.79% # 6
Node Classification AMZ Photo GCN Accuracy 93.59% # 7
Node Classification AMZ Photo HH-GraphSAGE Accuracy 94.55% # 4
Node Classification AMZ Photo GraphSAGE Accuracy 95.03% # 3
Node Classification AMZ Photo HH-GCN Accuracy 94.52% # 5
Node Classification Chameleon (60%/20%/20% random splits) HH-GraphSAGE 1:1 Accuracy 62.98 ± 3.35 # 21
Node Classification Chameleon (60%/20%/20% random splits) HH-GAT 1:1 Accuracy 61.12 ± 1.83 # 26
Node Classification Chameleon (60%/20%/20% random splits) HH-GCN 1:1 Accuracy 60.24 ± 1.93 # 30
Node Classification Coauthor CS GraphSAGE Accuracy 95.11% # 7
Node Classification Coauthor CS GCN Accuracy 94.06% # 11
Node Classification Coauthor CS HH-GraphSAGE Accuracy 95.13% # 6
Node Classification Coauthor CS HH-GCN Accuracy 94.71% # 10
Node Classification Cornell (60%/20%/20% random splits) HH-GAT 1:1 Accuracy 72.7 ± 4.26 # 29
Node Classification Cornell (60%/20%/20% random splits) HH-GCN 1:1 Accuracy 63.24 ± 5.43 # 34
Node Classification Cornell (60%/20%/20% random splits) HH-GraphSAGE 1:1 Accuracy 74.6 ± 6.06 # 27
Node Classification Squirrel (60%/20%/20% random splits) HH-GCN 1:1 Accuracy 47.19 ± 1.21 # 18
Node Classification Squirrel (60%/20%/20% random splits) HH-GraphSAGE 1:1 Accuracy 45.25 ± 1.52 # 21
Node Classification Squirrel (60%/20%/20% random splits) HH-GAT 1:1 Accuracy 46.35 ± 1.86 # 20
Node Classification Texas (60%/20%/20% random splits) HH-GCN 1:1 Accuracy 71.89 ± 3.46 # 35
Node Classification Texas (60%/20%/20% random splits) HH-GAT 1:1 Accuracy 80.54 ± 4.80 # 30
Node Classification Texas (60%/20%/20% random splits) HH-GraphSAGE 1:1 Accuracy 85.95 ± 6.42 # 21
Node Classification Wiki-CS HH-GraphSAGE Accuracy 82.81 # 3
Node Classification Wiki-CS HH-GCN Accuracy 82.57 # 4
Node Classification Wiki-CS GCN Accuracy 81.93 # 5
Node Classification Wiki-CS GraphSAGE Accuracy 83.67 # 2
Node Classification Wisconsin (60%/20%/20% random splits) HH-GCN 1:1 Accuracy 79.8 ± 4.30 # 24
Node Classification Wisconsin (60%/20%/20% random splits) HH-GraphSAGE 1:1 Accuracy 85.88 ± 3.99 # 21
Node Classification Wisconsin (60%/20%/20% random splits) HH-GAT 1:1 Accuracy 83.53 ± 3.84 # 22

Methods