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Task-Induced Riemannian Metrics for Vision Transformer Feature Spaces

ArXiv|Wednesday, September 23, 2026|about 15 hours ago|Andrew Bond

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Why It Matters

Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity.

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Key Claims

This assumes that every direction is equally meaningful, but there is no reason to believe the true task geometry has this property.
The task-sensitive geometry of the feature space is given by the pullback metric $g(F) = J(F)^\top J(F)$, where $J$ is the Jacobian of the decoder's output fed to a task-specific distance, with respect to the features.
Storing the full $g$ is infeasible at modern scales, and for dense outputs such as depth maps even forming $J$ is impractical.

Original description

Methods operating on Vision Transformer (ViT) feature spaces typically rely on Euclidean distance or cosine similarity. This assumes that every direction is equally meaningful, but there is no reason to believe the true task geometry has this property. The task-sensitive geometry of the feature space is given by the pullback metric $g(F) = J(F)^\top J(F)$, where $J$ is the Jacobian of the decoder's output fed to a task-specific distance, with respect to the features. Storing the full $g$ is infeasible at modern scales, and for dense outputs such as depth maps even forming $J$ is impractical. W...

arxiv cs.CV cs.LG publisher:arxiv tier:research

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ID: http://arxiv.org/abs/2609.27988v1 · Indexed about 1 hour ago