PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapes

arXiv:2610.14031v1 Announce Type: cross Abstract: Modern data pipelines increasingly combine human-created and human-curated data with AI-generated data for model training and evaluation. As datasets grow, they often add semantically redundant samples rather than expanding semantic coverage, which deteriorates the quality of the whole dataset. Existing diversity metrics primarily summarize lexical variation, entropy, or pairwise similarity, but provide limited characterization of the shape of the underlying data distribution. In this paper, we propose PLDiv, a diversity metric derived from persistence landscapes that quantifies the structural organization of a dataset from its geometric representation. PLDiv summarizes how data neighborhoods evolve as nearby samples progressively connect, producing an interpretable scalar measure of structural diversity without requiring task-specific supervision. Whether measuring intrinsic diversity in text generations or image embeddings, or detecting semantic collapse in instruction datasets and reasoning trajectories, PLDiv performs competitively against evaluated baselines and aligns strongly with diversity labels during semantic collapse. Consequently, it effectively supports applications in synthetic data monitoring, dataset construction, data augmentation, and generative model evaluation.

Abstract:Modern data pipelines increasingly combine human-created and human-curated data with AI-generated data for model training and evaluation. As datasets grow, they often add semantically redundant samples rather than expanding semantic coverage, which deteriorates the quality of the whole dataset. Existing diversity metrics primarily summarize lexical variation, entropy, or pairwise similarity, but provide limited characterization of the shape of the underlying data distribution. In this paper, we propose PLDiv, a diversity metric derived from persistence landscapes that quantifies the structural organization of a dataset from its geometric representation. PLDiv summarizes how data neighborhoods evolve as nearby samples progressively connect, producing an interpretable scalar measure of structural diversity without requiring task-specific supervision. Whether measuring intrinsic diversity in text generations or image embeddings, or detecting semantic collapse in instruction datasets and reasoning trajectories, PLDiv performs competitively against evaluated baselines and aligns strongly with diversity labels during semantic collapse. Consequently, it effectively supports applications in synthetic data monitoring, dataset construction, data augmentation, and generative model evaluation.

Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computer Vision and Pattern Recognition (cs.CV); Machine Learning (stat.ML)

arXiv:2610.14031 [cs.LG]

(or arXiv:2610.14031v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.14031 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapes

Related coverage