# Measuring Diversity: Axioms and Challenges

arXiv: https://arxiv.org/abs/2410.14556 · HTML: https://mlsanity.com/paper/2410.14556/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 18 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generation](https://mlsanity.com/paper/2208.12242/) (2022)
- [Palette: Image-to-Image Diffusion Models](https://mlsanity.com/paper/2111.05826/) (2021)
- [Equivariant Diffusion for Molecule Generation in 3D](https://mlsanity.com/paper/2203.17003/) (2022)
- [A Survey of Deep Active Learning](https://mlsanity.com/paper/2009.00236/) (2020)
- [The Vendi Score: A Diversity Evaluation Metric for Machine Learning](https://mlsanity.com/paper/2210.02410/) (2022)
- [Neural Algorithmic Reasoning](https://mlsanity.com/paper/2105.02761/) (2021)
- [MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Design](https://mlsanity.com/paper/2203.14500/) (2022)
- [Submodularity In Machine Learning and Artificial Intelligence](https://mlsanity.com/paper/2202.00132/) (2022)
- [Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Tasks](https://mlsanity.com/paper/2211.00692/) (2022)
- [How Much Space Has Been Explored? Measuring the Chemical Space Covered by Databases and Machine-Generated Molecules](https://mlsanity.com/paper/2112.12542/) (2021)
- [Position: Measure Dataset Diversity, Don't Just Claim It](https://mlsanity.com/paper/2407.08188/) (2024)
- [Challenges of Generating Structurally Diverse Graphs](https://mlsanity.com/paper/2409.18859/) (2024)

## Built on by (most cited first, 6 of 6)

- [The Homogenization Problem in LLMs: Towards Meaningful Diversity in AI Safety](https://mlsanity.com/paper/2601.06116/) (2026)
- [MolPILE -- large-scale, diverse dataset for molecular representation learning](https://mlsanity.com/paper/2509.18353/) (2025)
- [Dataset Diversity Metrics and Impact on Classification Models](https://mlsanity.com/paper/2603.15276/) (2026)
- [Adaptive Quality-Diversity Trade-offs for Large-Scale Batch Recommendation](https://mlsanity.com/paper/2602.02024/) (2026)
- [Evaluating the Diversity of AI-Generated Content with Diversity Profiles](https://mlsanity.com/paper/2608.17731/) (2026)
- [TEAR: Table Extraction with Attribute Recommendation from Texts via Large Language Models](https://mlsanity.com/paper/2609.15205/) (2026)

## Abstract (arXiv)

This paper addresses the problem of quantifying diversity for a set of objects. First, we conduct a systematic review of existing diversity measures and explore their undesirable behavior in certain cases. Based on this review, we formulate three desirable properties (axioms) of a reliable diversity measure: monotonicity, uniqueness, and continuity. We show that none of the existing measures has all three properties and thus these measures are not suitable for quantifying diversity. Then, we construct two examples of measures that have all the desirable properties, thus proving that the list of axioms is not self-contradictory. Unfortunately, the constructed examples are too computationally expensive (NP-hard) for practical use. Thus, we pose an open problem of constructing a diversity measure that has all the listed properties and can be computed in practice or proving that all such measures are NP-hard to compute.