Revisiting the Canonicalization for Fast and Accurate Crystal Tensor Property Prediction

Predicting the tensor properties of crystalline materials is a fundamental task in materials science. Unlike single-value property prediction, which is inherently invariant, tensor property prediction requires maintaining O(3) group tensor equivariance. Such equivariance constraint often requires specialized architecture designs to achieve effective predictions, inevitably introducing tremendous computational costs. Canonicalization, a classical technique for geometry, has recently been explored for efficient learning with symmetry. In this work, we revisit the problem of crystal tensor property prediction through the lens of canonicalization. Specifically, we demonstrate how polar decomposition, a simple yet efficient algebraic method, can serve as a form of canonicalization and be leveraged to ensure equivariant tensor property prediction. Building upon this insight, we propose a general O(3)-equivariant framework for efficient crystal tensor property prediction, referred to as GoeCTP. By utilizing canonicalization, GoeCTP achieves high efficiency without requiring the explicit incorporation of equivariance constraints into the network architecture. Experimental results indicate that GoeCTP achieves the best prediction performance and runs at most 13 times faster compared to existing state-of-the-art methods in benchmarking datasets, underscoring its effectiveness and efficiency.