让嵌入空间的相似度更准，且保持排序不变。
Calibrated Similarity for Reliable Geometric Analysis of Embedding Spaces
- 用序数回归对相似度做单调校准，不改变原有排序。
- 校准后98%的扰动类型下保持稳定性，绝对值更可信。
- 适合需要可靠相似度数值的场景，如语义分析、检索系统。
预训练嵌入空间中的原始余弦相似度虽与人类判断有强等级相关性，但各向异性导致绝对值系统性失准：得分集中在狭窄的高相似度区间，与实际语义相关性无关，限制了其作为定量度量的可解释性。以往方法通过修改嵌入空间（如白化、对比微调）解决，但会改变几何结构并需重算所有嵌入。我们使用在人类相似度判断上训练的序数回归，构建一个单调变换，在保持等级相关性和局部稳定性（7种扰动类型下达98%）的同时实现近乎完美的校准。本工作并非替代余弦相似度，而是通过单调校准恢复其绝对值的可解释性，而不改变其排序特性。我们将序数校准视为保序重参数化，并证明所有基于顺序的构造（角度排序、最近邻、阈值图、分位数决策）在此变换下保持不变。
原文摘要 · Abstract (English)
While raw cosine similarity in pretrained embedding spaces exhibits strong rank correlation with human judgments, anisotropy induces systematic miscalibration of absolute values: scores concentrate in a narrow high-similarity band regardless of actual semantic relatedness, limiting interpretability as a quantitative measure. Prior work addresses this by modifying the embedding space (whitening, contrastive fine tuning), but such transformations alter geometric structure and require recomputing all embeddings. Using isotonic regression trained on human similarity judgments, we construct a monotonic transformation that achieves near-perfect calibration while preserving rank correlation and local stability(98% across seven perturbation types). Our contribution is not to replace cosine similarity, but to restore interpretability of its absolute values through monotone calibration, without altering its ranking properties. We characterize isotonic calibration as an order-preserving reparameterization and prove that all order-based constructions (angular ordering, nearest neighbors, threshold graphs and quantile-based decisions) are invariant under this transformation.
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