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e3nn: Euclidean Neural Networks
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e3nn: Euclidean Neural Networks
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We present e3nn, a generalized framework for creating E(3) equivariant trainable functions, also known as Euclidean neural networks. e3nn naturally operates on geometry and geometric tensors that describe systems in 3D and transform predictably under a change of coordinate system. The core of e3nn are equivariant operations such as the TensorProduct class or the spherical harmonics functions that can be composed to create more complex modules such as convolutions and attention mechanisms. These core operations of e3nn can be used to efficiently articulate Tensor Field Networks, 3D Steerable CNNs, Clebsch-Gordan Networks, SE(3) Transformers and other E(3) equivariant networks.
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Cited by 40 Pith papers
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A group-algebraic tensor framework delivers Eckart-Young optimal equivariant approximations and recovers physical selection rules from data alone via a Lean-formalized star_G algebra.
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Fast contracted Clebsch--Gordan tensor products for equivariant graph neural networks
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Symmetry-Protected Basin Localization in Variational Quantum Eigensolvers
A symmetry-constrained preconditioner maps molecular geometry to VQE circuit parameters in the correlated ground-state basin, cutting initialization errors by 38x to 6250x on stretched molecules.
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XANE(3) uses a custom E(3)-equivariant GNN with absorber attention, derivative matching loss, and Gaussian spectral readout to predict XANES spectra from atomic structures at 10^{-3} MSE on iron oxide data.
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Machine Learning Hamiltonians are Accurate Energy-Force Predictors
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Learning Lattice Parameters from Powder X-Ray Diffraction Data Using Invariants
Predicting a symmetry-invariant reciprocal-lattice descriptor (the lattice bispectrum) from powder XRD and then inverting it recovers unit cell parameters more accurately than predicting parameters directly.
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Sobek: Streaming Equivariant Tensor Product Convolutions
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STEP: Spin Tensor Equivariant Potential for Data-Efficient Learning of Magnetic Potential Energy Surfaces
STEP uses a center-environment tensor product in an equivariant neural network to learn magnetic potential energy surfaces data-efficiently, reproducing phonons, magnons, and Curie temperatures for CrI3, Fe, and Fe2Mo3O8.
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Point Group Equivariant Graph Neural Networks for Materials
Partitioning equivariant GNN weights by crystal point-group irreps shows that trivial (A1) blocks carry most predictive signal, letting a lean A1-only model match or beat SO(3)-equivariant baselines on elastic and die...
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Robust and Interpretable Adaptation of Equivariant Materials Foundation Models via Sparsity-promoting Fine-tuning
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Using graph neural networks to predict many-body interactions in amorphous materials
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Multitask learning with semiempirical orbital charges enables sample-efficient MLIPs
Multitask learning on linear-scaling GFN1-xTB orbital charges cuts energy MAE by 46% and data needs by 5x versus energy-only MLIPs while outperforming DFT atomic charge augmentation.
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Exact Symmetry as Algebra: A Machine-Verified Tensor Calculus that Enforces Physical Selection Rules
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Compact SO(3) Equivariant Atomistic Foundation Models via Structural Pruning
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Bayesian E(3)-Equivariant Interatomic Potential with Iterative Restratification of Many-body Message Passing
Bayesian E(3)-equivariant MLPs with joint energy-force NLL loss achieve competitive accuracy while enabling uncertainty-guided active learning, OOD detection, and calibration.
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Adaptive Canonicalization with Application to Invariant Anisotropic Geometric Networks
Adaptive canonicalization selects input canonical forms by maximizing network predictive confidence to yield continuous symmetry-preserving models with universal approximation for equivariant geometric networks.
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A Combined Tight Binding with Machine Learning Potential Model for Magnesium Compounds
A DFTB+MACE model that replaces the pairwise repulsive term with a trained many-body potential improves forces, phonons, and surface energies for MgO and related systems while retaining electronic-structure output.
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Music102 integrates D12-equivariance into a transformer for chord progression accompaniment and shows gains over Music101 on POP909.
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TAGTorch: A PyTorch Library for Geometry, Topology, and Symmetry-Aware Machine Learning
TAGTorch packages geometry, topology, and symmetry-aware deep learning tools into one PyTorch library, with a design built around unified data transforms and group representations.
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