A Single Architecture for Representing Invariance Under Any Space Group
This addresses a scalability bottleneck in materials science and condensed matter physics by allowing knowledge transfer across related symmetries, though it is an incremental improvement over existing symmetry-incorporation methods.
The authors tackled the problem of designing separate machine learning architectures for each of the 230 space groups in crystallography by developing a single architecture that automatically adapts to enforce invariance to any input space group, achieving competitive performance on material property prediction tasks and enabling zero-shot learning to generalize to unseen groups.
Incorporating known symmetries in data into machine learning models has consistently improved predictive accuracy, robustness, and generalization. However, achieving exact invariance to specific symmetries typically requires designing bespoke architectures for each group, limiting scalability and preventing knowledge transfer across related symmetries. In the case of the space groups, symmetries critical to modeling crystalline solids in materials science and condensed matter physics, this challenge is particularly salient as there are 230 such groups in three dimensions. In this work we present a new approach to such crystallographic symmetries by developing a single machine learning architecture that is capable of adapting its weights automatically to enforce invariance to any input space group. Our approach is based on constructing symmetry-adapted Fourier bases through an explicit characterization of constraints that group operations impose on Fourier coefficients. Encoding these constraints into a neural network layer enables weight sharing across different space groups, allowing the model to leverage structural similarities between groups and overcome data sparsity when limited measurements are available for specific groups. We demonstrate the effectiveness of this approach in achieving competitive performance on material property prediction tasks and performing zero-shot learning to generalize to unseen groups.