What VGGT Knows About Overlap: Probing Geometric Foundation Models for Co-Visibility

A fundamental challenge in 3D reconstruction and robotic localization is co-visibility: determining which image pairs share overlapping visible surfaces, particularly in scenarios with minimal overlap. We demonstrate that VGGT implicitly encodes co-visibility as an emergent behavior: without any supervision for this task, its internal representations exhibit a clear hierarchical structure mirroring that of large language models, i.e. early layers build a 3D-aware scene representation, while late layers act as dedicated co-visibility reasoners. In particular, we identify layer L17 as a negative anchor that consistently routes non-co-visible pairs for this backbone, regardless of the evaluation setting, providing task-grounded evidence of layer specialization in a geometry-grounded foundation model. Building on this, we introduce Co-VGGT, which freezes VGGT and trains only a lightweight layer-wise mixture-of-experts head (less than 7.5M parameters) to classify co-visibility from RGB alone, treating each layer as a specialized expert whose geometric abstraction is adaptively weighted per input pair. On the Co-VisiON benchmark, Co-VGGT surpasses the human annotation baseline and improves over prior work by more than 25% pairwise and 10% multiview. Pairwise predictions are well-calibrated (ECE=0.030), enabling direct use as edge weights in visibility graphs for downstream SfM and SLAM pipelines without post-hoc correction. Code and data are available.