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

TL;DR

This paper introduces SPFrame, a novel local-global associative frame approach that preserves crystal symmetry and improves property prediction accuracy by combining invariant local frames with an equivariant global frame.

Contribution

The paper proposes a new symmetry-preserving frame construction method, SPFrame, that effectively combines local and global structural information for crystal modeling.

Findings

SPFrame outperforms existing methods on multiple benchmarks.

It effectively preserves crystal symmetry while capturing local heterogeneity.

Experimental results show improved prediction accuracy.

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.