提出可解释且高效的新方法，衡量表示间的有序相似性。
Scalable and Interpretable Representation Alignment with Ordinal Similarity
- 基于序数关系的一致性度量表示对齐
- 在大规模数据上计算高效，对异常值鲁棒
- 与局部邻域对齐等价，适合模型设计分析
表示相似性评估是表示学习的基础。然而现有度量存在显著局限：因基线偏移导致可解释性差，对异常值不鲁棒，且在大规模数据上计算不可行，迫使依赖启发式近似。为此，我们提出基于序数相似性的框架，通过三元组（TSI）和四元组（QSI）相似性指数量化有序关系的一致性。理论上证明该方法具有内在可解释性、对异常值鲁棒、计算高效。最终建立TSI与互最近邻（Mutual Nearest Neighbors）测量的局部邻域对齐之间的形式等价性。实证验证了这些性质，并表明序数相似性为表示对齐提供了一种可扩展的度量方式，使从业者能更深入理解与设计表示。
原文摘要 · Abstract (English)
Evaluating representation similarity is fundamental to representation learning. However, existing metrics suffer from significant limitations: they lack interpretability due to shifting baselines, lack robustness to outliers, and are computationally intractable for large datasets, forcing reliance on heuristic approximations. To address this, we develop an ordinal-similarity framework, instantiated by the Triplet (TSI) and Quadruplet (QSI) Similarity Indices, which measure alignment by quantifying the consistency of ordinal relationships. We theoretically demonstrate this formulation is inherently interpretable, robust to outliers, and computationally efficient. Finally, we establish a formal equivalence between TSI and local neighborhood alignment, measured by Mutual Nearest Neighbors. Empirically, we validate these properties and show that ordinal similarity offers a scalable approach to measuring alignment, enabling practitioners to better understand and design representations.
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