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Learning to predict agent motions with relationship reasoning is importantfor many applications. In motion prediction tasks, maintaining motionequivariance under Euclidean geometric transformations and invariance of agentinteraction is a critical and fundamental principle. However, such equivarianceand invariance properties are overlooked by most existing methods. To fill thisgap, we propose EqMotion, an efficient equivariant motion prediction model withinvariant interaction reasoning. To achieve motion equivariance, we propose anequivariant geometric feature learning module to learn a Euclideantransformable feature through dedicated designs of equivariant operations. Toreason agent's interactions, we propose an invariant interaction reasoningmodule to achieve a more stable interaction modeling. To further promote morecomprehensive motion features, we propose an invariant pattern feature learningmodule to learn an invariant pattern feature, which cooperates with theequivariant geometric feature to enhance network expressiveness. We conductexperiments for the proposed model on four distinct scenarios: particledynamics, molecule dynamics, human skeleton motion prediction and pedestriantrajectory prediction. Experimental results show that our method is not onlygenerally applicable, but also achieves state-of-the-art predictionperformances on all the four tasks, improving by 24.0/30.1/8.6/9.2%. Code isavailable at https://github.com/MediaBrain-SJTU/EqMotion.

EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning