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.
Southern University of Science and Technology（南方科技大学）；Tandon School of Engineering, New York University（纽约大学坦登工程学院）；School of Data Science, Lingnan University（岭南大学数据科学学院）
School of Computer Science（计算机科学学院）；Engineering, Sun Yat-sen University（工程，中山大学）；School of Software Engineering（软件工程学院）；Sun Yat-sen University（中山大学）；Zhuhai Key Laboratory of Trusted Large Language Models（珠海可信大语言模型实验室）；Tencent AI Lab（腾讯AI实验室）；National University of Singapore（新加坡国立大学）；Shenzhen University（深圳大学）；Shanghai Jiao Tong University（上海交通大学）
What and Whose Knowledge? Measuring Epistemic Diversity in Large Language Models
University of Copenhagen（哥本哈根大学）；Aalborg University Copenhagen（奥胡斯大学哥本哈根分校）；Stanford University（斯坦福大学）；University of Colorado Boulder（科罗拉多大学波德分校）；Microsoft Research（微软研究院）
