  Learning to predict agent motions with relationship reasoning is important
for many applications. In motion prediction tasks, maintaining motion
equivariance under Euclidean geometric transformations and invariance of agent
interaction is a critical and fundamental principle. However, such equivariance
and invariance properties are overlooked by most existing methods. To fill this
gap, we propose EqMotion, an efficient equivariant motion prediction model with
invariant interaction reasoning. To achieve motion equivariance, we propose an
equivariant geometric feature learning module to learn a Euclidean
transformable feature through dedicated designs of equivariant operations. To
reason agent's interactions, we propose an invariant interaction reasoning
module to achieve a more stable interaction modeling. To further promote more
comprehensive motion features, we propose an invariant pattern feature learning
module to learn an invariant pattern feature, which cooperates with the
equivariant geometric feature to enhance network expressiveness. We conduct
experiments for the proposed model on four distinct scenarios: particle
dynamics, molecule dynamics, human skeleton motion prediction and pedestrian
trajectory prediction. Experimental results show that our method is not only
generally applicable, but also achieves state-of-the-art prediction
performances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code is
available at https://github.com/MediaBrain-SJTU/EqMotion.
