RandAlign: A Parameter-Free Method for Regularizing Graph Convolutional Networks
Abstract
Studies continually find that message-passing graph convolutional networks suffer from the over-smoothing issue. Basically, the issue of over-smoothing refers to the phenomenon that the learned embeddings for all nodes can become very similar to one another and therefore are uninformative after repeatedly applying message passing iterations. Intuitively, we can expect the generated embeddings become smooth asymptotically layerwisely, that is each layer of graph convolution generates a smoothed version of embeddings as compared to that generated by the previous layer. Based on this intuition, we propose RandAlign, a stochastic regularization method for graph convolutional networks. The idea of RandAlign is to randomly align the learned embedding for each node with that of the previous layer using randomly interpolation in each graph convolution layer. Through alignment, the smoothness of the generated embeddings is explicitly reduced. To better maintain the benefit yielded by the graph convolution, in the alignment step we introduce to first scale the embedding of the previous layer to the same norm as the generated embedding and then perform random interpolation for aligning the generated embedding. RandAlign is a parameter-free method and can be directly applied without introducing additional trainable weights or hyper-parameters. We experimentally evaluate RandAlign on different graph domain tasks on seven benchmark datasets. The experimental results show that RandAlign is a general method that improves the generalization performance of various graph convolutional network models and also improves the numerical stability of optimization, advancing the state of the art performance for graph representation learning.
Benchmark Results
Tested on 7 datasets 19 baseline values reported too low
Tables show presented results in global context (best 3 papers + GCN + MLP).
OGB
| # | Model | ROC-AUC ↑ | Paper |
|---|---|---|---|
| 1 | Multi-RF Fusion with Multi-GNN Blending | 0.8476
±0.0002 | |
| 2 | HyperFusion | 0.8475
±0.0003 | |
| 3 | PAS+FPs | 0.8420
±0.0015 | |
| 9 | GatedGCN | 0.8090
±0.0160 | |
| 22 | GPS + RandAlign | 0.8021
±0.0305 | This paper |
| 37 | DGN | 0.7970
±0.0097 | This paper |
| 38 | GIN-AK+ | 0.7961
±0.0119 | This paper |
| 62 | PNA | 0.7905
±0.0132 | This paper |
| 69 | GPS | 0.7880
±0.0101 | This paper |
| 78 | DeeperGCN | 0.7860
±0.0120 best reported | best at pub: Wasserstein Embedding for Graph Learning (ICLR 2020) best today: Graph convolutions that can finally model local structure (2020) Difference within reported uncertainty; not counted as underperformance. |
| 102 | ExpC | 0.7799
±0.0082 | This paper |
| 106 | SAN | 0.7785
±0.2470 | This paper |
| 109 | GIN | 0.7780
±0.0182 best reported | best at pub: GRPE: Relative Positional Encoding for Graph Transformer (2022) Difference within reported uncertainty; not counted as underperformance. |
| 160 | GraphSAGE | 0.7690
±0.0136 | |
| 184 | GCN | 0.7630
±0.0030 best reported | best at pub: Motif-based Graph Representation Learning with Application to Chemical Molecules (2022) Difference within reported uncertainty; not counted as underperformance. |
LRGB
| # | Model | AP ↑ | Paper |
|---|---|---|---|
| 1 | S^2GCN | 0.7311
±0.0066 | |
| 2 | S4G | 0.7293
±0.0004 | |
| 3 | BuNN | 0.7276
±0.0065 | |
| 4 | GCN | 0.7261
±0.0011 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: From Message-Passing to Linearized Graph Sequence Models (2026) |
| 26 | GIN | 0.7059
±0.0089 | |
| 34 | GatedGCN | 0.7006
±0.0033 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: From Message-Passing to Linearized Graph Sequence Models (2026) |
| 73 | GatedGCN+RWSE | 0.6685
±0.0062 best reported | best at pub: On the Connection Between MPNN and Graph Transformer (ICML 2023) |
| 76 | GPS + RandAlign | 0.6630
±0.0005 | This paper |
| 78 | GINE | 0.6621
±0.0067 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: From Message-Passing to Linearized Graph Sequence Models (2026) |
| 89 | SAN+RWSE | 0.6562
±0.0075 best reported | best at pub: Multiresolution Graph Transformers and Wavelet Positional Encoding for Learning Hierarchical Structures (2023) Difference within reported uncertainty; not counted as underperformance. |
| 87 | GPS | 0.6562
±0.0115 best reported | best at pub: A Generalization of ViT/MLP-Mixer to Graphs (ICML 2022) Difference within reported uncertainty; not counted as underperformance. |
| 116 | SAN+LapPE | 0.6384
±0.0121 | This paper |
| 118 | Transformer+LapPE | 0.6326
±0.0126 | This paper |
| 181 | MLP | 0.4060
±0.0021 |
| # | Model | F1 ↑ | Paper |
|---|---|---|---|
| 1 | NeuralWalker | 0.4912
±0.0042 | |
| 2 | PPGT | 0.4641
±0.0033 | |
| 3 | CRaWl | 0.4588
±0.0079 | |
| 14 | GPS | 0.4440
±0.0065 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: Plain Transformers Can be Powerful Graph Learners (2025) |
| 18 | GPS + RandAlign | 0.4288
±0.0062 | This paper |
| 40 | GatedGCN+RWSE | 0.3882
±0.0041 best reported | best today: Benchmarking Positional Encodings for GNNs and Graph Transformers (KDD 2024) |
| 41 | GatedGCN | 0.3880
±0.0040 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: Plain Transformers Can be Powerful Graph Learners (2025) |
| 42 | Gated-GCN | 0.3880
±0.0040 | |
| 67 | SAN+LapPE | 0.3230
±0.0039 | This paper |
| 68 | SAN+RWSE | 0.3216
±0.0027 | This paper |
| 75 | GINE | 0.2718
±0.0054 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: Chimera: State Space Models Beyond Sequences (TMLR 2025) |
| 76 | Transformer+LapPE | 0.2694
±0.0098 | This paper |
| 81 | GCN | 0.2380
±0.0160 best reported | best at pub: Where Did the Gap Go? Reassessing the Long-Range Graph Benchmark (TMLR 2023) best today: When Graph Neural Networks Meet Dynamic Mode Decomposition (ICLR 2024) |
| 93 | MLP | 0.1140
±0.0230 |
GNNBenchmark
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | Schrödinger | 0.9913
±0.0004 | |
| 2 | CNN | 0.9907
±0.0007 | |
| 3 | MPNN | 0.9895
±0.0006 | |
| 12 | GatedGCN + RandAlign | 0.9855
±0.0002 | This paper |
| 11 | GatedGCN | 0.9855
±0.0002 | prev best: Formatting Instructions for ICLR 2021 Conference Submissions (2020) |
| 15 | RandAlign | 0.9851
±0.0005 | This paper |
| 32 | GIN | 0.9833
±0.0011 best reported | best at pub: Graph-Coupled Oscillator Networks (ICML 2022) |
| 47 | EGT | 0.9817
±0.0009 | This paper |
| 59 | GPS | 0.9808
±0.0011 best reported | best at pub: Recipe for a General, Powerful, Scalable Graph Transformer (NeurIPS 2022) Difference within reported uncertainty; not counted as underperformance. |
| 70 | GatedGCN + SSFG | 0.9798
±0.0003 | This paper |
| 73 | CRaWl | 0.9794
±0.0005 | This paper |
| 75 | PNA | 0.9794
±0.0012 | This paper |
| 87 | GAT + RandAlign | 0.9755
±0.0003 | This paper |
| 86 | GAT | 0.9755
±0.0003 | prev best: Formatting Instructions for ICLR 2021 Conference Submissions (2020) |
| 92 | GatedGCN-16 | 0.9734
±0.0014 | This paper |
| 95 | GraphSAGE | 0.9731
±0.0010 | This paper |
| 97 | SAGE | 0.9731
±0.0010 | |
| 123 | GAT-16 | 0.9554
±0.0021 | This paper |
| 126 | MLP | 0.9534
±0.0014 | |
| 129 | 3WLGNN | 0.9507
±0.0096 | This paper |
| 136 | GCN + RandAlign | 0.9405
±0.0005 | This paper |
| 135 | GCN | 0.9405
±0.0005 | prev best: A Generalization of ViT/MLP-Mixer to Graphs (ICML 2022) |
| 137 | MoNet | 0.9111 best reported | best at pub: Graph-Coupled Oscillator Networks (ICML 2022) |
| 141 | GCNII | 0.9067
±0.0014 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | RandAlign | 0.7942
±0.0007 | This paper |
| 2 | differential encoding | 0.7907
±0.0027 | |
| 3 | PPGT | 0.7856
±0.0070 | |
| 9 | GatedGCN + RandAlign | 0.7640
±0.0019 | This paper |
| 10 | GatedGCN-16 + RandAlign | 0.7640
±0.0019 | This paper |
| 38 | PNA | 0.7311
±0.0011 best reported | best at pub: From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness (ICLR 2021) |
| 40 | DGN | 0.7284
±0.0042 best reported | best at pub: From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness (ICLR 2021) Difference within reported uncertainty; not counted as underperformance. |
| 44 | GIN-AK+ | 0.7239
±0.0038 best reported | best at pub: Improving Subgraph-GNNs via Edge-Level Ego-Network Encodings (TMLR 2023) Difference within reported uncertainty; not counted as underperformance. |
| 46 | GPS | 0.7236
±0.0032 best reported | best at pub: Recipe for a General, Powerful, Scalable Graph Transformer (NeurIPS 2022) Difference within reported uncertainty; not counted as underperformance. |
| 56 | GatedGCN + SSFG | 0.7194
±0.0019 | This paper |
| 62 | GatedGCN | 0.7133
±0.0039 | |
| 69 | GAT + RandAlign | 0.6992
±0.0008 | This paper |
| 70 | GAT-16 + RandAlign | 0.6992
±0.0008 | This paper |
| 80 | CRaWl | 0.6901
±0.0026 | This paper |
| 82 | EGT | 0.6870
±0.0041 | This paper |
| 91 | GatedGCN-16 | 0.6731
±0.0031 | This paper |
| 92 | GraphSAGE | 0.6690
±0.0020 best reported | best at pub: Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering (2021) |
| 103 | MoNet | 0.6591
±0.0251 best reported | best at pub: SoGCN: Second-Order Graph Convolutional Networks (2021) |
| 104 | SAGE | 0.6577
±0.0031 | |
| 109 | GIN | 0.6510
±0.0050 best reported | best at pub: Beyond Low-pass Filtering: Graph Convolutional Networks with Automatic Filtering (2021) |
| 114 | GAT-16 | 0.6422
±0.0046 | This paper |
| 123 | 3WLGNN | 0.5917
±0.0159 | This paper |
| 124 | GCN | 0.5839
±0.0073 best reported | best at pub: From Stars to Subgraphs: Uplifting Any GNN with Local Structure Awareness (ICLR 2021) |
| 125 | GCN + RandAlign | 0.5774
±0.0016 | This paper |
| 126 | MLP | 0.5634
±0.0018 | |
| 128 | GCNII | 0.5608
±0.0020 | This paper |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | GRPE-Small | 0.8159
±0.0019 | |
| 2 | TANGO-GPS | 0.8011
±0.0014 | |
| 3 | GRIT | 0.8003
±0.0028 | |
| 10 | GPS + RandAlign | 0.7859
±0.0005 | This paper |
| 22 | GPS | 0.7802
±0.0018 | This paper |
| 23 | K-Subgraph SAT | 0.7786
±0.0010 | This paper |
| 26 | SAN + RandAlign | 0.7785
±0.0007 | This paper |
| 50 | SAN | 0.7669
±0.0065 | This paper |
| 54 | GatedGCN | 0.7608
±0.0020 best reported | best at pub: GRPE: Relative Positional Encoding for Graph Transformer (2022) |
| 57 | GatedGCN + SSFG | 0.7596
±0.0002 | This paper |
| 67 | GAT | 0.7059
±0.0045 | This paper |
| 70 | GCN | 0.6903
±0.0137 best reported | best at pub: Recurrent Distance Filtering for Graph Representation Learning (ICML 2023) Difference within reported uncertainty; not counted as underperformance. |
| 76 | MoNet | 0.6641
±0.0054 | prev best: SoGCN: Second-Order Graph Convolutional Networks (2021) |
| 79 | GIN | 0.6472
±0.0155 | This paper |
| 80 | GraphSAGE | 0.6388
±0.0011 best reported | best at pub: IJCAI--23 Formatting Instructions (IJCAI 2023) Difference within reported uncertainty; not counted as underperformance. |
| 104 | RingGNN | 0.4242
±0.2006 | This paper |
| 114 | MLP | 0.2097
±0.0000 |
| # | Model | Accuracy ↑ | Paper |
|---|---|---|---|
| 1 | DeepGraph (48) | 0.9066
±0.0006 | |
| 2 | GRIT (our run) | 0.9041
±0.0023 | |
| 3 | GRIT 2-QiQRW | 0.9016
±0.0045 | |
| 18 | GPS + RandAlign | 0.8686
±0.0001 | This paper |
| 21 | K-Subgraph SAT | 0.8685
±0.0004 | This paper |
| 31 | SAN + RandAlign | 0.8677
±0.0007 | This paper |
| 50 | GPS | 0.8669
±0.0006 | This paper |
| 58 | SAN | 0.8658
±0.0004 | This paper |
| 66 | GatedGCN | 0.8651
±0.0008 best reported | best at pub: IJCAI--23 Formatting Instructions (IJCAI 2023) |
| 88 | GCN | 0.8561
±0.0003 best reported | best at pub: Recurrent Distance Filtering for Graph Representation Learning (ICML 2023) |
| 89 | GIN | 0.8559
±0.0001 best reported | best at pub: Factorizable Graph Convolutional Networks (NeurIPS 2020) best today: GNNBenchmark (JMLR 2023) Difference within reported uncertainty; not counted as underperformance. |
| 91 | MoNet | 0.8558
±0.0004 | prev best: SoGCN: Second-Order Graph Convolutional Networks (2021) |
| 107 | GAT | 0.7827
±0.0019 | This paper |
| 123 | MLP | 0.5052 | |
| 124 | GraphSAGE | 0.5052
±0.0000 best reported | best at pub: SoGCN: Second-Order Graph Convolutional Networks (2021) best today: GNNBenchmark (JMLR 2023) |
