General Framework for Geometric Deep Learning on Tensorial Properties of Molecules and Crystals
The research group led by Prof. Xin Xu developed a general tensor output framework for equivariant graph neural networks, grounded in a fundamental group-theoretical principle: any Cartesian tensor with a given fundamental symmetry corresponds uniquely to a direct sum of irreducible representations of the rotation group. Leveraging this principle, the authors designed a universal output module—referred to as the node-wise self-mix layer—which concentrates symmetry handling at the output stage. This design enables equivariant graph neural networks to predict tensorial properties of arbitrary order and arbitrary fundamental symmetry in an end-to-end manner, and is applicable to atom-wise, molecular, and periodic crystalline systems alike.










