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Rotation equivariance is a desirable property in many practical applicationssuch as motion forecasting and 3D perception, where it can offer benefits likesample efficiency, better generalization, and robustness to inputperturbations. Vector Neurons (VN) is a recently developed framework offering asimple yet effective approach for deriving rotation-equivariant analogs ofstandard machine learning operations by extending one-dimensional scalarneurons to three-dimensional "vector neurons." We introduce a novel"VN-Transformer" architecture to address several shortcomings of the current VNmodels. Our contributions are: $(i)$ we derive a rotation-equivariant attentionmechanism which eliminates the need for the heavy feature preprocessingrequired by the original Vector Neurons models; $(ii)$ we extend the VNframework to support non-spatial attributes, expanding the applicability ofthese models to real-world datasets; $(iii)$ we derive a rotation-equivariantmechanism for multi-scale reduction of point-cloud resolution, greatly speedingup inference and training; $(iv)$ we show that small tradeoffs in equivariance($\epsilon$-approximate equivariance) can be used to obtain large improvementsin numerical stability and training robustness on accelerated hardware, and webound the propagation of equivariance violations in our models. Finally, weapply our VN-Transformer to 3D shape classification and motion forecasting withcompelling results.

VN-Transformer: Rotation-Equivariant Attention for Vector Neurons