Anchor Divergence for Semantic Geometry in Contrastive Learning

Computer Science > Artificial Intelligence arXiv:2610.06919 (cs) [Submitted on 2 Oct 2026] Title: Anchor Divergence for Semantic Geometry in Contrastive Learning Authors: Akash Kannan, Kiho Park, Victor Veitch.

计算机科学 > 人工智能 arXiv:2610.06919 (cs) [提交于 2026 年 10 月 2 日] 标题：对比学习中用于语义几何的锚点散度 作者：Akash Kannan, Kiho Park, Victor Veitch。

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.

摘要：本文探讨了语义上下文如何决定学习向量表示中的几何结构。相似度通常使用余弦相似度来衡量，它提供了一种单一的固定几何结构。然而，语义相似度本质上是依赖于上下文的：两张图像可能因为描绘了相同的物体、共享视觉风格或与相同的临床发现相关而显得相似。

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.

我们展示了对比表示自然地包含了一系列可以针对特定语义结构进行专门化的几何结构。其核心思想是利用对比学习、指数族和信息几何之间的相互作用，在“锚点”的概率分布与表示空间上的 Bregman 几何之间建立对应关系。

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.

我们利用这种对应关系定义了“锚点散度”（Anchor Divergences），这是一种在固定表示上指定特定于上下文的语义几何的方法。在这种对应关系下，对锚点分布进行建模即是对几何结构本身的建模。检索实验表明，锚点散度为指定特定于上下文的语义相似度提供了一种有效且高效的方法。