GraphPoint: Semantic Entity Graphs and Point Trajectories for Compositional Robot Manipulation

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Robot manipulation policies often struggle to generalize beyond their demonstrations, even when new instructions involve familiar objects and behaviors. When language and scenes are strongly correlated during training, a policy can learn a fixed visual-action mapping rather than respond to the requested behavior. We investigate compositional reuse at two levels: within a subtask, combining familiar entities, action types, and action modifiers; and across subtasks, reusing learned subtasks in unseen long-horizon tasks. We introduce CoMani, a benchmark with controlled splits for evaluating both capabilities. Matched initial scenes and controlled changes to a single semantic factor encourage reliance on language rather than visual shortcuts. We further propose GraphPoint, which connects semantic entity graphs to geometric control by predicting future gripper point trajectories and converting them into actions using robot geometry. The framework organizes the gripper and objects by semantic roles and conditions their interactions on action types and modifiers, while predicted progress guides transitions during execution. Experiments and ablations on CoMani validate the effectiveness of our method for instruction-dependent generalization at both levels. Code will be released at GraphPoint.