Fig. 2: Learning on invariants.
From: A Euclidean transformer for fast and stable machine learned force fields
SO(3) convolutions are constructed as triplet tensor products in the spherical harmonics basis, which is performed F times along the feature dimension F. We replace SO(3) convolutions by a parametrized filter function on the invariants (red blocks), which effectively reduces the tripled tensor product to taking the partial (per-degree) trace of a simple tensor product. Colored volumes correspond to the non-zero entries in the Clebsch-Gordan coefficients \({C}_{{l}_{1}{l}_{2}L}^{{m}_{1}{m}_{2}M}\), which mask the tensor products, l denotes the degree and \({Y}_{l}^{m}\) is the spherical harmonics function.
