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.

翻译：学习通过关系推理预测智能体运动对许多应用至关重要。在运动预测任务中，保持运动在欧几里得几何变换下的等变性以及智能体交互的不变性是一个关键且基础的原则。然而，大多数现有方法都忽略了这种等变性和不变性属性。为弥补这一空白，我们提出EqMotion，一种具有不变交互推理的高效等变运动预测模型。为实现运动等变性，我们提出一个等变几何特征学习模块，通过专门设计的等变操作来学习欧几里得可变换特征。为推理智能体交互，我们提出一个不变交互推理模块，以实现更稳定的交互建模。为进一步促进更全面的运动特征，我们提出一个不变模式特征学习模块，用于学习不变模式特征，该特征与等变几何特征协同作用以增强网络表达能力。我们在四个不同场景上对所提模型进行实验：粒子动力学、分子动力学、人体骨骼运动预测和行人轨迹预测。实验结果表明，我们的方法不仅具有普适性，而且在所有四个任务上均实现了最先进的预测性能，分别提升24.0%/30.1%/8.6%/9.2%。代码可在https://github.com/MediaBrain-SJTU/EqMotion获取。