Anchor Divergence for Semantic Geometry in Contrastive Learning
Abstract
This paper concerns how semantic context determines geometry in learned vector representations. Similarity is typically measured using cosine similarity, which provides a single fixed geometry. Semantic similarity, however, is inherently context dependent: two images may be similar because they depict the same object, share a visual style, or are relevant to the same clinical finding. We show that contrastive representations naturally encompass a family of geometries that can be specialized to particular semantic structure. The key idea is to use an interplay between contrastive learning, exponential families, and information geometry to establish a correspondence between probability distributions over "anchors" and Bregman geometries on the representation space. We use this correspondence to define "Anchor Divergences", a method for specifying context-specific semantic geometries on fixed representations. Under this correspondence, modeling the anchor distribution models the geometry itself. Experiments on retrieval show that anchor divergences provide an effective and efficient way to specify context-specific semantic similarity.
Related
- Multi-Marginal Inverse Optimal Transport for Contrastive Learning Via Explicit Anchor-Positive-Negative Coupling
- Rethinking Representation Geometry in Supervised Contrastive Learning under Long-Tailed Data
- Geodesic Divergence on Riemannian Planes with Bounded Geometry
- The information geometry of the Sinkhorn divergence on a Hilbert manifold
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BibTeX
@misc{kannan2026anchor,
title = {{Anchor Divergence for Semantic Geometry in Contrastive Learning}},
author = {Akash Kannan and Kiho Park and Victor Veitch},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.06919},
eprint = {2610.06919},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.06919},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Anchor Divergence for Semantic Geometry in Contrastive Learning
AU - Akash Kannan
AU - Kiho Park
AU - Victor Veitch
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.06919
UR - https://arxiv.org/abs/2610.06919
AB - This paper concerns how semantic context determines geometry in learned vector representations. Similarity is typically measured using cosine similarity, which provides a single fixed geometry. Semantic similarity, however, is inherently context dependent: two images may be similar because they depict the same object, share a visual style, or are relevant to the same clinical finding. We show that contrastive representations naturally encompass a family of geometries that can be specialized to particular semantic structure. The key idea is to use an interplay between contrastive learning, exponential families, and information geometry to establish a correspondence between probability distributions over "anchors" and Bregman geometries on the representation space. We use this correspondence to define "Anchor Divergences", a method for specifying context-specific semantic geometries on fixed representations. Under this correspondence, modeling the anchor distribution models the geometry itself. Experiments on retrieval show that anchor divergences provide an effective and efficient way to specify context-specific semantic similarity.
ER -