# Measuring Dataset Diversity from a Geometric Perspective

arXiv: https://arxiv.org/abs/2602.09340 · HTML: https://mlsanity.com/paper/2602.09340/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 33 of its 61 references that are in the map.
- First posted on arXiv 10 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Self-Instruct: Aligning Language Models with Self-Generated Instructions](https://mlsanity.com/paper/2212.10560/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Improved Precision and Recall Metric for Assessing Generative Models](https://mlsanity.com/paper/1904.06991/) (2019)
- [MAUVE: Measuring the Gap Between Neural Text and Human Text using Divergence Frontiers](https://mlsanity.com/paper/2102.01454/) (2021)
- [Reliable Fidelity and Diversity Metrics for Generative Models](https://mlsanity.com/paper/2002.09797/) (2020)
- [SeqGAN: Sequence Generative Adversarial Nets with Policy Gradient](https://mlsanity.com/paper/1609.05473/) (2016)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Self-Consuming Generative Models Go MAD](https://mlsanity.com/paper/2307.01850/) (2023)
- [Data Augmentation Can Improve Robustness](https://mlsanity.com/paper/2111.05328/) (2021)
- [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)
- [Improving Generalization in Reinforcement Learning with Mixture Regularization](https://mlsanity.com/paper/2010.10814/) (2020)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Diversity and Generalization in Neural Network Ensembles](https://mlsanity.com/paper/2110.13786/) (2021)
- [Representation Matters: Assessing the Importance of Subgroup Allocations in Training Data](https://mlsanity.com/paper/2103.03399/) (2021)
- [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)
- [When does Diversity Help Generalization in Classification Ensembles?](https://mlsanity.com/paper/1910.13631/) (2019)
- [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)
- [On the effectiveness of persistent homology](https://mlsanity.com/paper/2206.10551/) (2022)
- [Metric Space Magnitude for Evaluating the Diversity of Latent Representations](https://mlsanity.com/paper/2311.16054/) (2023)
- [Using persistent homology and dynamical distances to analyze protein binding](https://mlsanity.com/paper/1412.1394/) (2014)
- [Data Representativity for Machine Learning and AI Systems](https://mlsanity.com/paper/2203.04706/) (2022)

## Abstract (arXiv)

Diversity can be broadly defined as the presence of meaningful variation across elements, which can be viewed from multiple perspectives, including statistical variation and geometric structural richness in the dataset. Existing diversity metrics, such as feature-space dispersion and metric-space magnitude, primarily capture distributional variation or entropy, while largely neglecting the geometric structure of datasets. To address this gap, we introduce a framework based on topological data analysis (TDA) and persistence landscapes (PLs) to extract and quantify geometric features from data. This approach provides a theoretically grounded means of measuring diversity beyond entropy, capturing the rich geometric and structural properties of datasets. Through extensive experiments across diverse modalities, we demonstrate that our proposed PLs-based diversity metric (PLDiv) is powerful, reliable, and interpretable, directly linking data diversity to its underlying geometry and offering a foundational tool for dataset construction, augmentation, and evaluation.