Scalable and Interpretable Representation Alignment with Ordinal Similarity

2026-06-15

AI Summary

Existing representation similarity measures often suffer from poor interpretability, sensitivity to outliers, and limited scalability to large datasets. This work proposes a representation alignment framework grounded in ordinal similarity, which quantifies the consistency of local ordinal relationships between representations using triplet (TSI) and quadruplet (QSI) similarity indices. The study establishes, for the first time, a theoretical equivalence between ordinal similarity and local alignment criteria such as mutual nearest neighbors. Combining interpretability, robustness, and scalability, the proposed method leverages efficient ranking algorithms and demonstrates significant performance gains over existing metrics in large-scale experiments, offering a reliable tool for representation understanding and design.

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.

Problem

• representation similarity
• interpretability
• scalability
• robustness
• computational tractability

Innovation

• ordinal similarity
• representation alignment
• TSI
• QSI
• scalable evaluation