Towards Deeper Graph Neural Networks with Differentiable Group Normalization
Abstract
Graph neural networks (GNNs), which learn the representation of a node by aggregating its neighbors, have become an effective computational tool in downstream applications. Over-smoothing is one of the key issues which limit the performance of GNNs as the number of layers increases. It is because the stacked aggregators would make node representations converge to indistinguishable vectors. Several attempts have been made to tackle the issue by bringing linked node pairs close and unlinked pairs distinct. However, they often ignore the intrinsic community structures and would result in sub-optimal performance. The representations of nodes within the same community/class need be similar to facilitate the classification, while different classes are expected to be separated in embedding space. To bridge the gap, we introduce two over-smoothing metrics and a novel technique, i.e., differentiable group normalization (DGN). It normalizes nodes within the same group independently to increase their smoothness, and separates node distributions among different groups to significantly alleviate the over-smoothing issue. Experiments on real-world datasets demonstrate that DGN makes GNN models more robust to over-smoothing and achieves better performance with deeper GNNs.
Benchmark Results
Tested on 4 datasets 9 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
Classic
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GraphSAGE+CNA | 0.9418
±0.0033 | |
| 2 | GCN+CNA | 0.9366
±0.0048 | |
| 3 | TransformerConv | 0.9350
±0.0058 | |
| 21 | GCN | 0.9004 best reported | best at pub: SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels (2017) best today: Understanding Heterophily for Graph Neural Networks (ICML 2024) |
| 39 | SAGE | 0.8911
±0.0012 | |
| 44 | GAT | 0.8897
±0.0014 best reported | best at pub: Topology Adaptive Graph Convolutional Networks (2017) |
| 532 | DGN | 0.8200 | This paper |
| 724 | MLP | 0.7768 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | CNA | 0.9575
±0.0058 | |
| 2 | IS-GIB | 0.9390
±0.0187 | |
| 3 | EERM | 0.9112
±0.0145 | |
| 35 | GAT | 0.8080
±0.0026 best reported | best at pub: Topology Adaptive Graph Convolutional Networks (2017) best today: Feature Expansion for Graph Neural Networks (ICML 2023) |
| 44 | GCN | 0.8033
±0.0088 best reported | best at pub: Graph Neural Ordinary Differential Equations (AAAI 2019) |
| 61 | GraphSAGE | 0.7923
±0.0053 | |
| 96 | SGC | 0.7765
±0.0012 best reported | best at pub: Deep Learning on Graphs: A Survey (2018) |
| 350 | MLP | 0.7289
±0.0010 | |
| 637 | DGN | 0.6950 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | LGTL | 0.9518
±0.0011 | |
| 2 | MixHop (LO) | 0.9513
±0.0038 | |
| 3 | GraphSAGE (LO) | 0.9511
±0.0036 | |
| 18 | GCN | 0.9296
±0.0015 best reported | best at pub: Graph Neural Ordinary Differential Equations (AAAI 2019) |
| 20 | GAT | 0.9233
±0.0018 best reported | |
| 116 | SAGE | 0.8881
±0.0015 | |
| 141 | SGC | 0.8832
±0.0055 best reported | best at pub: Deep Learning on Graphs: A Survey (2018) |
| 210 | MLP | 0.8690
±0.0074 | |
| 507 | DGN | 0.7950 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DoG | 0.9690
±0.0030 | |
| 2 | GWN-fa | 0.9667
±0.0026 | |
| 3 | GWN-sym | 0.9666
±0.0026 | |
| 6 | GraphSAGE | 0.9593
±0.0025 | |
| 12 | GCN | 0.9514
±0.0025 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 21 | GAT | 0.9437
±0.0028 best reported | best at pub: Unifying Graph Convolutional Neural Networks and Label Propagation (2020) best today: Graph Wave Networks (WWW 2025) |
| 88 | MLP | 0.9280
±0.0020 | |
| 96 | SGC | 0.8990 | prev best: Spectral Graph Attention Network with Fast Eigen-approximation (2020) best today: Towards Graph Self-Supervised Learning with Contrastive Adjusted Zooming (2021) |
| 111 | DGN | 0.9230 | This paper |
