Research map / Graph learning / GNN architectures

Equivariant Spherical Transformer for Efficient Molecular Modeling

NeurIPS 2026 · Graph learning › GNN architectures · approach: Equivariant networks for molecules · 1 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes the Equivariant Spherical Transformer (EST), applying attention across Fibonacci-lattice-sampled points on the sphere in the Fourier spatial domain of steerable features, as a plug-and-play equivariant module for molecular GNNs.

Problem

Equivariant GNNs for molecules rely on Clebsch-Gordan tensor products, which have limited non-linearity and expressiveness bounded by maximum degree; point-wise spherical-domain operations ignore cross-orientation interactions.

Approach

Transformer attention is applied across sampled points in the spherical spatial domain, with equivariance preserved by uniform Fibonacci-lattice sampling (plus repulsion-based refinement), a hybrid MoE of steerable and spherical FFN experts, and relative orientation embeddings in Q/K.

Key results

• On OC20 S2EF validation, EST (8 layers, only All, lambda_E=2) reaches 15.0 meV/Å force MAE and 232 meV energy MAE with 45M parameters, beating EquiformerV2 variants on forces.
• On IS2RE, 6-layer EST achieves best ID (501 meV), OOD Ads (652 meV, second), OOD Both (578 meV) energy MAE among compared models, and is second-best on OOD Cat.
• On QM9, EST achieves best on eight of twelve tasks, e.g., Delta-epsilon 28 meV and HOMO 13 meV, while EST shows equivariance error of about 1.8e-5 on trained 6-layer models.

Surprising findings

• e3nn grid sampling yields large equivariance errors (e.g., 0.1006 at 2 layers) in untrained networks, showing sampling uniformity matters.
• EST distinguishes 100-fold symmetric structures with a single 1-degree layer, exceeding the tensor-product bound of distinguishing n-fold symmetry only when n ≤ L.

Limitations

• Slight equivariance loss due to practical spherical sampling, acknowledged in the conclusion.
• Message module replaced by EquiformerV2/Equiformer attention in experiments, so gains are partly from the update block design.
• Equivariance on QM9 is not perfect; the authors note minor deviations may cause overfitting.

Experimental setup

Datasets: OC20 S2EF-All OC20 MD OC20 IS2RE QM9

Benchmarks: OC20 S2EF validation OC20 IS2RE QM9

Metrics: energy MAE force MAE energy within threshold (EwT) QM9 MAE per property equivariance error n-fold symmetry discrimination accuracy

Baselines: SchNet PaiNN SEGNN TFN DimeNet++ Equiformer EquiformerV2 EScAIP SpinConv GemNet SphereNet SCN

Builds on: Equiformer EquiformerV2 SCN e3nn GotenNet

Closest papers by meaning

• E2Former: An Efficient and Equivariant Transformer with Linear-Scaling Tensor Products (NeurIPS 2025 · similarity 0.92)
• Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning (ICML 2024 · similarity 0.89)
• GeoMFormer: A General Architecture for Geometric Molecular Representation Learning (ICML 2024 · similarity 0.88)
• Scalable Non-Equivariant 3D Molecule Generation via Rotational Alignment (ICML 2025 · similarity 0.87)
• Equivariant Graph Neural Operator for Modeling 3D Dynamics (ICML 2024 · similarity 0.87)
• DualEqui: A Dual-Space Hierarchical Equivariant Network for Large Biomolecules (NeurIPS 2025 · similarity 0.87)