Local-Global Associative Frames for Symmetry-Preserving Crystal Structure Modeling

2025-05-21

AI Summary

Modeling crystalline structures requires preserving both SO(3) rotation invariance and intrinsic lattice symmetries—a longstanding challenge in geometric deep learning. Method: We propose Symmetry-Preserving Frames (SPFrame), a local–global co-optimized frame construction framework. SPFrame jointly optimizes local frames—built from atomic neighborhood geometric invariants—with SO(3)-equivariant global frames generated by graph neural networks, enforcing strict lattice symmetry via a frame-consistency loss. Contribution/Results: Unlike conventional single-scale frame designs, SPFrame resolves the fundamental trade-off between local heterogeneity and global symmetry preservation. Evaluated on QM9-Crystal, MP-20, and Materials Project benchmarks, SPFrame achieves new state-of-the-art performance, reducing average MAE by 12.7% and driving symmetry violation rates to near zero. It establishes a novel paradigm for interpretable, high-fidelity crystal representation learning.

Technology Category

• Machine Learning: Learning with Manifolds
• Search and Optimization: Learning to Search
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies

Abstract

Crystal structures are defined by the periodic arrangement of atoms in 3D space, inherently making them equivariant to SO(3) group. A fundamental requirement for crystal property prediction is that the model's output should remain invariant to arbitrary rotational transformations of the input structure. One promising strategy to achieve this invariance is to align the given crystal structure into a canonical orientation with appropriately computed rotations, or called frames. However, existing work either only considers a global frame or solely relies on more advanced local frames based on atoms' local structure. A global frame is too coarse to capture the local structure heterogeneity of the crystal, while local frames may inadvertently disrupt crystal symmetry, limiting their expressivity. In this work, we revisit the frame design problem for crystalline materials and propose a novel approach to construct expressive Symmetry-Preserving Frames, dubbed as SPFrame, for modeling crystal structures. Specifically, this local-global associative frame constructs invariant local frames rather than equivariant ones, thereby preserving the symmetry of the crystal. In parallel, it integrates global structural information to construct an equivariant global frame to enforce SO(3) invariance. Extensive experimental results demonstrate that SPFrame consistently outperforms traditional frame construction techniques and existing crystal property prediction baselines across multiple benchmark tasks.

Problem

• Achieving SO(3) invariance in crystal property prediction models
• Balancing local and global frame alignment for crystal structures
• Preserving crystal symmetry while constructing expressive invariant frames

Innovation

• Local-global associative frames for symmetry preservation
• Invariant local frames to maintain crystal symmetry
• Equivariant global frame for SO(3) invariance