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This paper introduces a novel ordinal-similarity framework (TSI/QSI) that resolves critical issues in representation learning by offering metrics that are both computationally efficient for large datasets and robust against outliers. By establishing formal equivalence with local neighborhood alignment, the work provides practitioners with an interpretable method to rigorously evaluate how well different AI representations align without relying on heuristic approximations or shifting baselines.
Scalable and Interpretable Representation Alignment with Ordinal Similarity
arXiv:2606.16379v1 Announce Type: new 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:2606.16379v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.16379 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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