Papers › E(n) Equivariant Graph Neural Networks
E(n) Equivariant Graph Neural Networks
Victor Garcia Satorras, Emiel Hoogeboom, Max Welling
This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.
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Code
Syntology Ran 15 of 15 code samples harvested from 3 repositories linked to this paper; 0 have no recorded run. Of those that ran: 1 ran · honoured contract; 4 ran · our draft was wrong; 2 ran · fixture could not drive it; 8 ran with no contract checked.
By repository: community (archive-listed): 14 samples from 3 repositories, 14 ran; 1 identical to code first harvested elsewhere. The run record, sample by sample. “Ran” means executed on a synthesized input, not that the code is correct or reproduces the paper.
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
15 samples harvested; 15 ran; 1 honoured the contract we drafted; 0 have no recorded run. Read from Syntology's graph 2026-09-24; that is when this build read the record, not when the samples ran.
Licence: 7 of the 15 samples are pointer only, meaning Syntology does not serve that copy's text. This page shows no code text for any sample; each one links to its file in the repository.
Harvested from 3 repositories linked to this paper, official or community; each sample names its own and says which. Some samples are identical code Syntology first harvested from another repository; for those, this paper's copy is not located and its licence is not recorded. “Ran” means the sample executed on a synthesized input. It does not mean the output is correct, and nothing here reproduces the paper's results. “Honoured” and “violated” refer to a contract Syntology drafted from the code itself; “our draft was wrong” and “fixture could not drive it” are failures of Syntology's instrument, not of the 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 Property Prediction | QM9 | EGNN | Standardized MAE | 1.23 | #10 of 10 | Archive leaderboard | report |
| Graph Property Prediction | QM9 | EGNN | alpha (ma) | 71 | #10 of 10 | Archive leaderboard | report |
| Graph Property Prediction | QM9 | EGNN | gap (meV) | 48 | #10 of 10 | Archive leaderboard | report |
| Graph Property Prediction | QM9 | EGNN | logMAE | -5.43 | #10 of 10 | 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.
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