Papers › An end-to-end attention-based approach for learning on graphs

An end-to-end attention-based approach for learning on graphs

16 Feb 2024arXiv:2402.10793archive 2025-07-28

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.

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Tasks

Graph ClassificationGraph RegressionMolecular Property PredictionNode ClassificationTransfer Learning

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
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

AttentionAttention PoolingGraph Self-AttentionSoftmax

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