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PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapes

arXiv 2610.14031 ↗First posted 30 Sep 2026cs.LG cs.AI cs.CVcited by 0

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Abstract (arXiv)

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.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 29 of its 50 references that are in the map. First posted on arXiv 30 Sep 2026.

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References · 29

  1. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  2. 2022Large Language Models are Zero-Shot Reasonerscited by 4,374
  3. 2023Let's Verify Step by Stepcited by 3,789
  4. 2022Self-Instruct: Aligning Language Models with Self-Generated Instructionscited by 2,724
  5. 2015A Diversity-Promoting Objective Function for Neural Conversation Modelscited by 1,077
  6. 2019Improved Precision and Recall Metric for Assessing Generative Modelscited by 944
  7. 2021Deduplicating Training Data Makes Language Models Bettercited by 714
  8. 2018Texygen: A Benchmarking Platform for Text Generation Modelscited by 491
  9. 2021MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontierscited by 470
  10. 2022The Vendi Score: A Diversity Evaluation Metric for Machine Learningcited by 311
  11. 2024ProcessBench: Identifying Process Errors in Mathematical Reasoningcited by 292
  12. 2023Self-Consuming Generative Models Go MADcited by 250
17 more
  1. 2023Does Writing with Language Models Reduce Content Diversity?cited by 192
  2. 2025Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)cited by 141
  3. 2020Evaluating the Evaluation of Diversity in Natural Language Generationcited by 129
  4. 2023On the Stability of Iterative Retraining of Generative Models on their own Datacited by 100
  5. 2018Geometry Score: A Method For Comparing Generative Adversarial Networkscited by 57
  6. 2022Semantic Diversity in Dialogue with Natural Language Inferencecited by 29
  7. 2024Exploring Precision and Recall to assess the quality and diversity of LLMscited by 29
  8. 2019Persistent homology detects curvaturecited by 26
  9. 2024Scaling Data Diversity for Fine-Tuning Language Models in Human Alignmentcited by 26
  10. 2024Towards a Scalable Reference-Free Evaluation of Generative Modelscited by 26
  11. 2020DQI: Measuring Data Quality in NLPcited by 24
  12. 2020Diversity, Density, and Homogeneity: Quantitative Characteristic Metrics for Text Collectionscited by 22
  13. 2023Metric Space Magnitude for Evaluating the Diversity of Latent Representationscited by 17
  14. 2023TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Modelscited by 14
  15. 2020Topologically Densified Distributionscited by 8
  16. 2026Language of Thought Shapes Output Diversity in Large Language Modelscited by 4
  17. 2026More Aligned, Less Diverse? Analyzing the Grammar and Lexicon of Two Generations of LLMscited by 3

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  1. 2025Measuring Diversity in Synthetic Datasets
  2. 2026ECOKV: Geometry-Aware KV Cache Eviction via Complementary Diversity Metrics
  3. 2025Data Value in the Age of Scaling: Understanding LLM Scaling Dynamics Under Real-Synthetic Data Mixtures
  4. 2025Prismatic Synthesis: Gradient-based Data Diversification Boosts Generalization in LLM Reasoning
  5. 2026"I've Seen How This Goes": Characterizing Diversity via Progressive Conditional Surprise
  6. 2024Image Generation Diversity Issues and How to Tame Them
  7. 2026Where does output diversity collapse in post-training?
  8. 2024Conditional Vendi Score: Prompt-Aware Diversity Evaluation for Generative AI Models and LLMs