Papers › Scale Invariance of Graph Neural Networks
Scale Invariance of Graph Neural Networks
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.
Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| 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 |
Ranks are positions in the archive's leaderboards as they stood at the 2025-07-28 snapshot. Results published since then are not among these rows, so a rank here is not a current standing.
Methods
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