Scalable and Interpretable Representation Alignment with Ordinal Similarity
2026-06-15 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address problems in how we compare machine learning representations, like confusing results and sensitivity to unusual data points, as well as slow calculations for big datasets. They create a new method based on how data points are ordered relative to each other, introducing two scores called Triplet and Quadruplet Similarity Indices. These scores are easier to interpret, handle outliers better, and compute faster. The authors also show that one of these scores is closely connected to a well-known concept called Mutual Nearest Neighbors. Their tests confirm these benefits, making it easier for people to compare and improve representation learning.
Representation LearningSimilarity MetricsOrdinal RelationshipsTriplet Similarity IndexQuadruplet Similarity IndexMutual Nearest NeighborsRobustnessComputational EfficiencyOutliersLocal Neighborhood Alignment
Authors
Diogo Soares, Pankhil Gawade, Andrea Dittadi, Ewa Szczurek
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.