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This paper introduces a novel ordinal-similarity framework (TSI/QSI) that resolves critical limitations in representation learning metrics by ensuring interpretability, outlier robustness, and computational efficiency for large-scale datasets. By formally linking these indices to local neighborhood alignment via Mutual Nearest Neighbors, the work provides practitioners with scalable tools to rigorously evaluate and design AI representations without relying on heuristic approximations.
Scalable and Interpretable Representation Alignment with Ordinal Similarity
arXiv:2606.16379v2 Announce Type: replace Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Machine Learning (stat.ML)
arXiv:2606.16379 [cs.LG]
(or arXiv:2606.16379v2 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.16379 Focus to learn more arXiv-issued DOI via DataCite
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