<ul><li>Irreducible Cartesian tensors (ICTs) are important in the design of equivariant graph neural networks and theoretical chemistry.</li><li>The ICT decomposition and basis for equivariant spaces are challenging to obtain for high-order tensors.</li><li>Researchers have achieved an explicit ICT decomposition for $n=5$ with factorial complexity and obtained decomposition matrices for ICTs up to rank $n=9$ with reduced complexity.</li><li>They used path matrices obtained through chain-like contraction with Clebsch-Gordan matrices to establish an orthonormal change-of-basis matrix and a complete orthogonal basis for the equivariant space.</li></ul>

Free the Design Space of Equivariant Graph Neural Networks: High-Rank Irreducible Cartesian Tensor Decomposition and Bases of Equivariant Spaces

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