Understanding trajectories in multi-agent scenarios requires addressing various tasks, including predicting future movements, imputing missing observations, inferring the status of unseen agents, and classifying different global states. Traditional data-driven approaches often handle these tasks separately with specialized models. We introduce TranSPORTmer, a unified transformer-based framework capable of addressing all these tasks, showcasing its application to the intricate dynamics of multi-agent sports scenarios like soccer and basketball. Using Set Attention Blocks, TranSPORTmer effectively captures temporal dynamics and social interactions in an equivariant manner. The model's tasks are guided by an input mask that conceals missing or yet-to-be-predicted observations. Additionally, we introduce a CLS extra agent to classify states along soccer trajectories, including passes, possessions, uncontrolled states, and out-of-play intervals, contributing to an enhancement in modeling trajectories. Evaluations on soccer and basketball datasets show that TranSPORTmer outperforms state-of-the-art task-specific models in player forecasting, player forecasting-imputation, ball inference, and ball imputation. https://youtu.be/8VtSRm8oGoE
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