Papers › Scale Invariance of Graph Neural Networks

Scale Invariance of Graph Neural Networks

28 Nov 2024arXiv:2411.19392archive 2025-07-28

Qin Jiang, Chengjia Wang, Michael Lones, Wei Pang

We address two fundamental challenges in Graph Neural Networks (GNNs): (1) the lack of theoretical support for invariance learning, a critical property in image processing, and (2) the absence of a unified model capable of excelling on both homophilic and heterophilic graph datasets. To tackle these issues, we establish and prove scale invariance in graphs, extending this key property to graph learning, and validate it through experiments on real-world datasets. Leveraging directed multi-scaled graphs and an adaptive self-loop strategy, we propose ScaleNet, a unified network architecture that achieves state-of-the-art performance across four homophilic and two heterophilic benchmark datasets. Furthermore, we show that through graph transformation based on scale invariance, uniform weights can replace computationally expensive edge weights in digraph inception networks while maintaining or improving performance. For another popular GNN approach to digraphs, we demonstrate the equivalence between Hermitian Laplacian methods and GraphSAGE with incidence normalization. ScaleNet bridges the gap between homophilic and heterophilic graph learning, offering both theoretical insights into scale invariance and practical advancements in unified graph learning. Our implementation is publicly available at https://github.com/Qin87/ScaleNet/tree/Aug23.

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Code

qin87/scalenet officialmentioned in papermentioned on GitHubpytorch report

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Tasks

Graph LearningNode ClassificationNode Classification on Non-Homophilic (Heterophilic) Graphs

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Node Classification Citeseer: fixed 20 node per class ScaleNet Accuracy 68.3±1.5 #2 of 2 Archive leaderboard report
Node Classification Cora: fixed 20 node per class ScaleNet Accuracy 82.3±1.1 #7 of 9 Archive leaderboard report
Node Classification Telegram (Directed Graph label rate 60%) ScaleNet Accuracy 96.8±2.1 #1 of 2 Archive leaderboard report
Node Classification Telegram (Directed Graph label rate 60%) 1iG Accuracy 95.8±3.5 #2 of 2 Archive leaderboard report
Node Classification Wiki-CS ScaleNet Accuracy 79.3±0.6 #6 of 6 Archive leaderboard report
Node Classification on Non-Homophilic (Heterophilic) Graphs Chameleon (48%/32%/20% fixed splits) ScaleNet 1:1 Accuracy 80.1±1.5 #1 of 29 Archive leaderboard report
Node Classification on Non-Homophilic (Heterophilic) Graphs Squirrel (48%/32%/20% fixed splits) ScaleNet 1:1 Accuracy 76.0±2.0 #1 of 29 Archive leaderboard report

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Methods

1x1 ConvolutionAverage PoolingBatch NormalizationBottleneck Residual BlockConvolutionDense ConnectionsGlobal Average PoolingGraphSAGEMax PoolingReLUResidual ConnectionScale Aggregation BlockScaleNetSoftmax

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