Papers › An end-to-end attention-based approach for learning on graphs
An end-to-end attention-based approach for learning on graphs
David Buterez, Jon Paul Janet, Dino Oglic, Pietro Lio
There has been a recent surge in transformer-based architectures for learning on graphs, mainly motivated by attention as an effective learning mechanism and the desire to supersede handcrafted operators characteristic of message passing schemes. However, concerns over their empirical effectiveness, scalability, and complexity of the pre-processing steps have been raised, especially in relation to much simpler graph neural networks that typically perform on par with them across a wide range of benchmarks. To tackle these shortcomings, we consider graphs as sets of edges and propose a purely attention-based approach consisting of an encoder and an attention pooling mechanism. The encoder vertically interleaves masked and vanilla self-attention modules to learn an effective representations of edges, while allowing for tackling possible misspecifications in input graphs. Despite its simplicity, the approach outperforms fine-tuned message passing baselines and recently proposed transformer-based methods on more than 70 node and graph-level tasks, including challenging long-range benchmarks. Moreover, we demonstrate state-of-the-art performance across different tasks, ranging from molecular to vision graphs, and heterophilous node classification. The approach also outperforms graph neural networks and transformers in transfer learning settings, and scales much better than alternatives with a similar performance level or expressive power.
Code
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Tasks
Results from the paper archive 2025-07-28
| Task | Dataset | Model | Metric | Value | Rank at snapshot | Leaderboard | Report |
|---|---|---|---|---|---|---|---|
| Graph Classification | CIFAR10 100k | ESA (Edge set attention, no positional encodings) | Accuracy (%) | 75.413±0.248 | #6 of 20 | Archive leaderboard | report |
| Graph Classification | D&D | ESA (Edge set attention, no positional encodings) | Accuracy | 83.529±1.743 | #3 of 53 | Archive leaderboard | report |
| Graph Classification | ENZYMES | ESA (Edge set attention, no positional encodings) | Accuracy | 79.423±1.658 | #1 of 54 | Archive leaderboard | report |
| Graph Classification | IMDb-B | ESA (Edge set attention, no positional encodings) | Accuracy | 86.250±0.957 | #2 of 51 | Archive leaderboard | report |
| Graph Classification | MNIST | ESA (Edge set attention, no positional encodings, tuned) | Accuracy | 98.917±0.020 | #1 of 13 | Archive leaderboard | report |
| Graph Classification | MNIST | ESA (Edge set attention, no positional encodings) | Accuracy | 98.753±0.041 | #3 of 13 | Archive leaderboard | report |
| Graph Classification | MalNet-Tiny | ESA (Edge set attention, no positional encodings) | Accuracy | 94.800±0.424 | #1 of 4 | Archive leaderboard | report |
| Graph Classification | MalNet-Tiny | ESA (Edge set attention, no positional encodings) | MCC | 0.935±0.005 | #1 of 4 | Archive leaderboard | report |
| Graph Classification | NCI1 | ESA (Edge set attention, no positional encodings) | Accuracy | 87.835±0.644 | #2 of 69 | Archive leaderboard | report |
| Graph Classification | NCI109 | ESA (Edge set attention, no positional encodings) | Accuracy | 84.976±0.551 | #3 of 38 | Archive leaderboard | report |
| Graph Classification | PROTEINS | ESA (Edge set attention, no positional encodings) | Accuracy | 82.679±0.799 | #4 of 103 | Archive leaderboard | report |
| Graph Classification | Peptides-func | ESA + RWSE (Edge set attention, Random Walk Structural Encoding, + validation set) | AP | 0.7479 | #1 of 44 | Archive leaderboard | report |
| Graph Classification | Peptides-func | ESA + RWSE (Edge set attention, Random Walk Structural Encoding, tuned) | AP | 0.7357±0.0036 | #3 of 44 | Archive leaderboard | report |
| Graph Classification | Peptides-func | ESA (Edge set attention, no positional encodings, tuned) | AP | 0.7071±0.0015 | #13 of 44 | Archive leaderboard | report |
| Graph Classification | Peptides-func | ESA (Edge set attention, no positional encodings, not tuned) | AP | 0.6863±0.0044 | #19 of 44 | Archive leaderboard | report |
| Graph Regression | ESR2 | ESA (Edge set attention, no positional encodings) | R2 | 0.697±0.000 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | ESR2 | ESA (Edge set attention, no positional encodings) | RMSE | 0.486±0.697 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | F2 | ESA (Edge set attention, no positional encodings) | R2 | 0.891±0.000 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | F2 | ESA (Edge set attention, no positional encodings) | RMSE | 0.335±0.891 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | KIT | ESA (Edge set attention, no positional encodings) | R2 | 0.841±0.000 | #2 of 9 | Archive leaderboard | report |
| Graph Regression | KIT | ESA (Edge set attention, no positional encodings) | RMSE | 0.433±0.841 | #2 of 9 | Archive leaderboard | report |
| Graph Regression | Lipophilicity | ESA (Edge set attention, no positional encodings) | R2 | 0.809±0.008 | #5 of 23 | Archive leaderboard | report |
| Graph Regression | Lipophilicity | ESA (Edge set attention, no positional encodings) | RMSE | 0.552±0.012 | #5 of 23 | Archive leaderboard | report |
| Graph Regression | PARP1 | ESA (Edge set attention, no positional encodings) | R2 | 0.925±0.000 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | PARP1 | ESA (Edge set attention, no positional encodings) | RMSE | 0.343±0.925 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | PCQM4Mv2-LSC | ESA (Edge set attention, no positional encodings) | Test MAE | N/A | #1 of 20 | Archive leaderboard | report |
| Graph Regression | PCQM4Mv2-LSC | ESA (Edge set attention, no positional encodings) | Validation MAE | 0.0235 | #1 of 20 | Archive leaderboard | report |
| Graph Regression | PGR | ESA (Edge set attention, no positional encodings) | R2 | 0.725±0.000 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | PGR | ESA (Edge set attention, no positional encodings) | RMSE | 0.507±0.725 | #1 of 9 | Archive leaderboard | report |
| Graph Regression | Peptides-struct | ESA + RWSE (Edge set attention, Random Walk Structural Encoding, tuned) | MAE | 0.2393±0.0004 | #1 of 39 | Archive leaderboard | report |
| Graph Regression | Peptides-struct | ESA (Edge set attention, no positional encodings, not tuned) | MAE | 0.2453±0.0003 | #8 of 39 | Archive leaderboard | report |
| Graph Regression | ZINC | ESA + rings + NodeRWSE + EdgeRWSE | MAE | 0.051 | #1 of 27 | Archive leaderboard | report |
| Graph Regression | ZINC-500k | ESA + rings + NodeRWSE + EdgeRWSE | MAE | 0.051 | #1 of 36 | Archive leaderboard | report |
| Graph Regression | ZINC-full | ESA + rings + NodeRWSE + EdgeRWSE | Test MAE | 0.0109±0.0002 | #1 of 19 | Archive leaderboard | report |
| Graph Regression | ZINC-full | ESA + RWSE + CY2C (Edge set attention, Random Walk Structural Encoding, clique adjacency, tuned) | Test MAE | 0.0122±0.0004 | #2 of 19 | Archive leaderboard | report |
| Graph Regression | ZINC-full | ESA + RWSE (Edge set attention, Random Walk Structural Encoding, tuned) | Test MAE | 0.0154±0.0001 | #4 of 19 | Archive leaderboard | report |
| Graph Regression | ZINC-full | ESA + RWSE (Edge set attention, Random Walk Structural Encoding) | Test MAE | 0.017±0.001 | #5 of 19 | Archive leaderboard | report |
| Graph Regression | ZINC-full | ESA (Edge set attention, no positional encodings) | Test MAE | 0.027±0.001 | #9 of 19 | Archive leaderboard | report |
| Molecular Property Prediction | ESOL | ESA (Edge set attention, no positional encodings) | R2 | 0.944±0.002 | #1 of 20 | Archive leaderboard | report |
| Molecular Property Prediction | ESOL | ESA (Edge set attention, no positional encodings) | RMSE | 0.485±0.009 | #1 of 20 | Archive leaderboard | report |
| Molecular Property Prediction | FreeSolv | ESA (Edge set attention, no positional encodings) | R2 | 0.977±0.001 | #1 of 22 | Archive leaderboard | report |
| Molecular Property Prediction | FreeSolv | ESA (Edge set attention, no positional encodings) | RMSE | 0.595±0.013 | #1 of 22 | 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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