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This study challenges the prevailing reliance on global embedding geometry as a proxy for representational competence in vision models, revealing its near-zero correlation with compositional binding capabilities. The authors demonstrate that functional sensitivity, measured via the input-output Jacobian, provides a more reliable metric for assessing how models handle composite structures. Consequently, future training objectives and evaluation protocols should incorporate local mapping constraints to fully capture a model's representational depth.
Global Geometry Is Not Enough for Vision Representations
arXiv:2602.03282v3 Announce Type: replace-cross Abstract: A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating global geometry as a proxy for representational competence. While global geometry effectively encodes which elements are present, it is often insensitive to how they are composed. We investigate this limitation by testing the ability of geometric metrics to predict compositional binding across a diverse suite of vision encoders. We find that standard geometry-based statistics exhibit near-zero correlation with compositional binding. In contrast, functional sensitivity, as measured by the input--output Jacobian, reliably tracks this capability. We further provide an analytic account showing that this disparity arises from objective design, as existing losses explicitly constrain embedding geometry but leave the local input--output mapping unconstrained. These results suggest that global embedding geometry captures only a partial view of representational competence and establish functional sensitivity as a critical complementary axis for modeling composite structure.
Abstract:A common assumption in representation learning is that globally well-distributed embeddings support robust and generalizable representations. This focus has shaped both training objectives and evaluation protocols, implicitly treating global geometry as a proxy for representational competence. While global geometry effectively encodes which elements are present, it is often insensitive to how they are composed. We investigate this limitation by testing the ability of geometric metrics to predict compositional binding across a diverse suite of vision encoders. We find that standard geometry-based statistics exhibit near-zero correlation with compositional binding. In contrast, functional sensitivity, as measured by the input--output Jacobian, reliably tracks this capability. We further provide an analytic account showing that this disparity arises from objective design, as existing losses explicitly constrain embedding geometry but leave the local input--output mapping unconstrained. These results suggest that global embedding geometry captures only a partial view of representational competence and establish functional sensitivity as a critical complementary axis for modeling composite structure.
Computer Vision and Pattern Recognition (cs.CV); Artificial Intelligence (cs.AI)
arXiv:2602.03282 [cs.CV]
(or arXiv:2602.03282v3 [cs.CV] for this version)
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