EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning (2303.10876v2)

Abstract: 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.

• The paper introduces EqMotion, a novel model that integrates motion equivariance with invariant interaction reasoning for robust multi-agent motion prediction.
• It employs equivariant geometric feature learning and invariant pattern reasoning, ensuring consistent handling of Euclidean transformations.
• Experimental validation across particle dynamics, molecule dynamics, 3D human skeleton motion, and pedestrian trajectory prediction shows state-of-the-art accuracy.

An Expert Overview of EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning

The paper "EqMotion: Equivariant Multi-agent Motion Prediction with Invariant Interaction Reasoning" introduces an advanced model, EqMotion, to address the frequently overlooked yet fundamental need for motion equivariance and interaction invariance in motion prediction tasks. The authors argue that these properties are critical for ensuring robustness and generalization in multi-agent motion prediction, and present EqMotion as a solution that inherently satisfies these criteria.

Core Contributions

EqMotion distinguishes itself by ensuring both motion equivariance and interaction invariance through several innovative module designs:

1. Equivariant Geometric Feature Learning: This module captures geometric features that remain consistent under Euclidean transformations. By linearly combining temporal motion data, the model retains crucial spatial information that is responsive to translation, rotation, and reflection.
2. Invariant Interaction Reasoning Module: In cases where interaction information between agents is not explicitly available, this module infers interaction categories using invariant features, ensuring the model's interpretative reasoning remains unchanged under geometric transformations.
3. Invariant Pattern Feature Learning: Complementing the geometric features, this module extracts pattern features invariant to transformations, providing a holistic representation for robust prediction across varied motion scenarios.

Experimental Validation

The authors validate EqMotion across four diverse application areas: particle dynamics, molecule dynamics, 3D human skeleton motion prediction, and pedestrian trajectory prediction. The results highlight EqMotion's superior performance:

• In particle and molecule dynamics, EqMotion demonstrated state-of-the-art prediction accuracy, emphasizing the model's capability in predicting complex physical interactions.
• For 3D human skeleton motion, EqMotion outperformed other methods in both short-term and long-term pose predictions, reinforcing the model's ability to generalize across temporal movements.
• In pedestrian trajectories, the model effectively handled multi-agent interactions, further evidenced by both single and multiple trajectory predictions.

Theoretical Implications and Future Directions

From a theoretical standpoint, EqMotion’s approach could redefine how motion prediction models incorporate symmetry principles inherent in physical interactions. The explicit integration of equivariance and invariance not only fosters model robustness but also potentially reduces computational overhead by minimizing the need for data augmentation strategies commonly employed to achieve rotational and translational invariance.

Future research arising from this work could explore extending EqMotion to broader AI and robotics applications, where real-time motion prediction is critical. Enhancements might include integrating sensor data or leveraging EqMotion for real-world robotic systems that require dynamic interaction modeling under a variety of physical constraints.

EqMotion stands out as a significant advancement in the multi-agent motion prediction landscape, where addressing fundamental geometric principles can lead to far-reaching improvements in both theoretical understanding and practical applications in AI-driven environments.