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具有重要意义。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和智能体交互的不变性是一个关键且基础的原则。然而，现有方法大多忽视了这种等变性和不变性特性。为填补这一空白，我们提出EqMotion——一种高效且具有不变交互推理能力的等变运动预测模型。为实现运动等变性，我们设计了等变几何特征学习模块，通过专用等变操作学习可随欧几里得变换同步变换的特征。为推理智能体交互，我们提出不变交互推理模块，以实现更稳定的交互建模。为进一步增强运动特征的全面性，我们设计了不变模式特征学习模块，学习不变模式特征，该特征与等变几何特征协同作用以提升网络表达能力。我们在四种不同场景下进行实验：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，该方法不仅具有通用性，还在所有四项任务中均达到最优预测性能，分别提升24.0%、30.1%、8.6%和9.2%。代码开源地址：https://github.com/MediaBrain-SJTU/EqMotion。