Geometric structure is essential for robotic manipulation and understanding the 3D world.
Most VLA models rely on 2D representations of current observations, while geometry-aware approaches often require additional 3D information.
However, geometry inferred independently from individual observations is often discarded rather than accumulated into a persistent task representation.
Our key insight is that action generation needs a compact, task-relevant geometric abstraction that can be continuously updated, rather than a complete, renderable 3D reconstruction at every step.
We introduce GeoMem-VLA, a VLA framework that internalizes explicit 3D supervision into dedicated geometric tokens and maintains them as temporal memory for action generation, without directly aligning the VLM's native visual embeddings with the teacher feature space.
During training, a frozen geometry foundation model supervises learnable GeoPlan tokens through a geometric flow-matching objective over the current scene point map and future end-effector tracks.
These tokens are integrated with the memory of observation representations, where historical information is retrieved, adaptively fused with current observations, and consolidated to retain event frames as the task progresses.
At inference, the policy retrieves historical representations and fuses them with the current working representation to predict actions, without invoking the 3D teacher or explicitly reconstructing the scene.
After benchmark-specific downstream adaptation, GeoMem-VLA achieves 98.9% average success on LIBERO and 91.10% / 91.24% on RoboTwin's clean/randomized settings.
Across five real-world tasks, GeoMem-VLA achieves 78.0% average success.
These results suggest that internalizing and remembering 3D scene understanding is a promising approach to robot control.
