# PLDiv: Measuring Dataset Diversity and Semantic Collapse via Persistence Landscapes

arXiv: https://arxiv.org/abs/2610.14031 · HTML: https://mlsanity.com/paper/2610.14031/

## 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.

## Builds on (most cited first, 29 of 29)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [A Diversity-Promoting Objective Function for Neural Conversation Models](https://mlsanity.com/paper/1510.03055/) (2015)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [Texygen: A Benchmarking Platform for Text Generation Models](https://mlsanity.com/paper/1802.01886/) (2018)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [ProcessBench: Identifying Process Errors in Mathematical Reasoning](https://mlsanity.com/paper/2412.06559/) (2024)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Does Writing with Language Models Reduce Content Diversity?](https://mlsanity.com/paper/2309.05196/) (2023)
- [Artificial Hivemind: The Open-Ended Homogeneity of Language Models (and Beyond)](https://mlsanity.com/paper/2510.22954/) (2025)
- [Evaluating the Evaluation of Diversity in Natural Language Generation](https://mlsanity.com/paper/2004.02990/) (2020)
- [On the Stability of Iterative Retraining of Generative Models on their own Data](https://mlsanity.com/paper/2310.00429/) (2023)
- [Geometry Score: A Method For Comparing Generative Adversarial Networks](https://mlsanity.com/paper/1802.02664/) (2018)
- [Semantic Diversity in Dialogue with Natural Language Inference](https://mlsanity.com/paper/2205.01497/) (2022)
- [Exploring Precision and Recall to assess the quality and diversity of LLMs](https://mlsanity.com/paper/2402.10693/) (2024)
- [Persistent homology detects curvature](https://mlsanity.com/paper/1905.13196/) (2019)
- [Scaling Data Diversity for Fine-Tuning Language Models in Human Alignment](https://mlsanity.com/paper/2403.11124/) (2024)
- [Towards a Scalable Reference-Free Evaluation of Generative Models](https://mlsanity.com/paper/2407.02961/) (2024)
- [DQI: Measuring Data Quality in NLP](https://mlsanity.com/paper/2005.00816/) (2020)
- [Diversity, Density, and Homogeneity: Quantitative Characteristic Metrics for Text Collections](https://mlsanity.com/paper/2003.08529/) (2020)
- [Metric Space Magnitude for Evaluating the Diversity of Latent Representations](https://mlsanity.com/paper/2311.16054/) (2023)
- [TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Models](https://mlsanity.com/paper/2306.08013/) (2023)
- [Topologically Densified Distributions](https://mlsanity.com/paper/2002.04805/) (2020)
- [Language of Thought Shapes Output Diversity in Large Language Models](https://mlsanity.com/paper/2601.11227/) (2026)
- [More Aligned, Less Diverse? Analyzing the Grammar and Lexicon of Two Generations of LLMs](https://mlsanity.com/paper/2605.06030/) (2026)

## 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.