Papers › Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs

Equiformer: Equivariant Graph Attention Transformer for 3D Atomistic Graphs

23 Jun 2022arXiv:2206.11990archive 2025-07-28

Yi-Lun Liao, Tess Smidt

Despite their widespread success in various domains, Transformer networks have yet to perform well across datasets in the domain of 3D atomistic graphs such as molecules even when 3D-related inductive biases like translational invariance and rotational equivariance are considered. In this paper, we demonstrate that Transformers can generalize well to 3D atomistic graphs and present Equiformer, a graph neural network leveraging the strength of Transformer architectures and incorporating SE(3)/E(3)-equivariant features based on irreducible representations (irreps). First, we propose a simple and effective architecture by only replacing original operations in Transformers with their equivariant counterparts and including tensor products. Using equivariant operations enables encoding equivariant information in channels of irreps features without complicating graph structures. With minimal modifications to Transformers, this architecture has already achieved strong empirical results. Second, we propose a novel attention mechanism called equivariant graph attention, which improves upon typical attention in Transformers through replacing dot product attention with multi-layer perceptron attention and including non-linear message passing. With these two innovations, Equiformer achieves competitive results to previous models on QM9, MD17 and OC20 datasets.

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atomicarchitects/equiformer officialmentioned in papermentioned on GitHubpytorch report
atomicarchitects/dens mentioned on GitHubpytorchMIT report
atomicarchitects/equiformer_v2 mentioned on GitHubpytorchMIT report
lucidrains/equiformer-pytorch mentioned on GitHubpytorch report

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get_mul_0 atomicarchitects/equiformer/nets/graph_attention_transformer.py official repository ran · honoured contract MIT (permissive) · fd4284f5532a264d · report
get_norm_layer atomicarchitects/equiformer/nets/graph_attention_transformer.py official repository unverified MIT (permissive) · 22ae6ca5b382e2d0 · report
pack_one lucidrains/equiformer-pytorch/equiformer_pytorch/equiformer_pytorch.py community (archive-listed) ran · our draft was wrong MIT (permissive) · 122e87ee0b05894f · report
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Tasks

Graph AttentionGraph Neural NetworkGraph Property PredictionInitial Structure to Relaxed Energy (IS2RE), DirectMolecular Property Prediction

Results from the paper archive 2025-07-28

TaskDatasetModelMetricValueRank at snapshotLeaderboardReport
Graph Property Prediction QM9 Equiformer Standardized MAE 0.70 #5 of 10 Archive leaderboard report
Graph Property Prediction QM9 Equiformer alpha (ma) 46 #5 of 10 Archive leaderboard report
Graph Property Prediction QM9 Equiformer gap (meV) 30 #5 of 10 Archive leaderboard report
Graph Property Prediction QM9 Equiformer logMAE -5.82 #5 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.

Methods

Absolute Position EncodingsAdamAttentionBPEDense ConnectionsDropoutGraph Neural NetworkLabel SmoothingLayer NormalizationLinear LayerMulti-Head AttentionPosition-Wise Feed-Forward LayerResidual ConnectionSoftmaxTransformer

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