E(n) Equivariant Graph Neural Networks

By Victor Garcia Satorras, Emiel Hoogeboom, Max Welling. International Conference on Machine Learning, 2021

1,567 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Materials Chemistry, Molecular Biology, Representation & Self-Supervised Learning, Graph Learning

View Paper: https://arxiv.org/abs/2102.09844

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In Materials Chemistry

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In Graph Learning

Citations in the corpus

State-specific protein–ligand complex structure prediction with a multiscale deep generative model (2022, positive): “2e and Supplementary Information Section E) is inspired by previous works on 3D graph and attentional neural networks for point clouds 61,62 , rigid-body simulations 63 and biopolymer representation learning 1,64–66 .”
EquiBind: Geometric Deep Learning for Drug Binding Structure Prediction (2022, methodology): “…Euclidean symmetries into GNNs. Injecting Euclidean 3D transformations into geometric DL models has become possible using equivariant message passing layers (Cohen & Welling, 2016; Thomas et al., 2018; Fuchs et al., 2020; Satorras et al., 2021; Brandstetter et al., 2021; Batzner et al., 2021).”
Inductive biases for deep learning of higher-level cognition (2020, background): “, 2020), invariance or equivariance to known transformations (Bruna et al., 2013; Defferrard et al., 2016; Ravanbakhsh et al., 2017; Thomas et al., 2018; Finzi et al., 2020; Satorras et al., 2021) or choices of prior distributions in a Bayesian model (Jeffreys, 1946; Berger and Bernardo,”
Diffusion probabilistic modeling of protein backbones in 3D for the motif-scaffolding problem (2022, positive): “ProtDiff , based on EGNN, is reflection equivariant since it only sees pairwise distances between 3D C-α coordinates.”
Torsional Diffusion for Molecular Conformer Generation (2022, background): “While there exist several GNN architectures which are SE (3) -equivariant [Jing et al., 2021, Satorras et al., 2021], their SE (3) -invariant outputs are also parity invariant and, therefore, cannot satisfy the desired symmetry.”
Learning Gradient Fields for Molecular Conformation Generation (2021, positive): “, 2017) or using equivariant networks (Fuchs et al., 2020; Satorras et al., 2021).”
Independent SE(3)-Equivariant Models for End-to-End Rigid Protein Docking (2021, methodology): “Motivated by symmetries naturally occurring in different data types, architectures are tailored to explicitly incorporate such properties (Cohen and Welling, 2016a;b; Thomas et al., 2018; Fuchs et al., 2020; Finzi et al., 2020; Eismann et al., 2020; Satorras et al., 2021).”
Protein Representation Learning by Geometric Structure Pretraining (2022, methodology): “To verify the effectiveness of our proposed methods, we choose another common backbone model, equivariant graph neural network (EGNN) (Satorras et al., 2021), for pretraining.”
A Survey on Vision--Language--Action Models for Embodied AI (2024, neutral): “Equivariant message passing networks are recently introduced to handle 3D graphs, including E(n)- and SE(3)- Equivariant GNN [325], [326].”
QMugs, quantum mechanical properties of drug-like molecules (2022, neutral): “…several options, such as the QM9 18 , ANI-1 19 , or PubChemQC 20 datasets have paved the way for the development of current-generation QML methods 5–8, There has been a recent surge in interest in the delta-learning ( Δ -learning) of chemical properties, which aims to use a machine learning…”
Geometric and Physical Quantities improve E(3) Equivariant Message Passing (2021, methodology): “…results in an input (Thomas et al., 2018) .0155 .0182 NMP (Gilmer et al., 2017) .0107 .0017 Radial Field (K¨ohler et al., 2019) .0104 .0019 EGNN (Satorras et al., 2021) .0070 ± .00022 .0029 SE linear ( l f = 2 ,l a = 2 ) .0116 ± .00021 .0640 SE non-linear ( l f = 1 ,l a = 1 ) .0060 ± .00019…”
Equivariant Graph Neural Networks for 3D Macromolecular Structure (2021, neutral): “Equivariant message-passing, proposed by Jing et al. (2021) and more recently Satorras et al. (2021) and Sch ¨ utt et al. (2021), seeks to instead incorporate the equivariant representations of ENNs within the message-passing framework of GNNs.”
MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design (2022, methodology): “E-NFs [52] also respects the symmetry via integrating an equivariant graph neural network in a normalizing ﬂow-based generative model.”
Message Passing Neural PDE Solvers (2022, background): “For the former, simply position updates need to be included in the processor, similar to Satorras et al. (2021).”
Predicting Molecular Conformation via Dynamic Graph Score Matching (2021, background): “Directly parameterizing score networks on absolute Cartesian coordinates with Graph Neural Networks (GNNs) [11, 13, 19, 29] relies on the arbitrary choice of rotation and translation [36, 43], which are non-essential degrees of freedom for effecting conformational changes in molecular systems.”
The design space of E(3)-equivariant atom-centred interatomic potentials (2022, neutral): “We denote the set of neighbors of an atom i , i.e., atoms with the cutoﬀ distance, by N ( i ).”