mlsanityData to 7 Oct 2026

Measuring Diversity: Axioms and Challenges

arXiv 2410.14556 ↗First posted 18 Oct 2024cs.LGcited by 6

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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.

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 12 of its 18 references that are in the map. First posted on arXiv 18 Oct 2024.

Builds on

12 of 18 references.

References · 12

  1. 2022DreamBooth: Fine Tuning Text-to-Image Diffusion Models for Subject-Driven Generationcited by 3,286
  2. 2021Palette: Image-to-Image Diffusion Modelscited by 1,296
  3. 2022Equivariant Diffusion for Molecule Generation in 3Dcited by 666
  4. 2020A Survey of Deep Active Learningcited by 547
  5. 2022The Vendi Score: A Diversity Evaluation Metric for Machine Learningcited by 299
  6. 2021Neural Algorithmic Reasoningcited by 92
  7. 2022MolGenSurvey: A Systematic Survey in Machine Learning Models for Molecule Designcited by 66
  8. 2022Submodularity In Machine Learning and Artificial Intelligencecited by 37
  9. 2022Towards Better Out-of-Distribution Generalization of Neural Algorithmic Reasoning Taskscited by 29
  10. 2021How Much Space Has Been Explored? Measuring the Chemical Space Covered by Databases and Machine-Generated Moleculescited by 27
  11. 2024Position: Measure Dataset Diversity, Don't Just Claim Itcited by 26
  12. 2024Challenges of Generating Structurally Diverse Graphscited by 6

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 1; 2026: 5.

6 papers.

  1. 2025MolPILE -- large-scale, diverse dataset for molecular representation learningcited by 1
  2. 2026The Homogenization Problem in LLMs: Towards Meaningful Diversity in AI Safetycited by 1
  3. 2026Dataset Diversity Metrics and Impact on Classification Modelscited by 1
  4. 2026Adaptive Quality-Diversity Trade-offs for Large-Scale Batch Recommendationcited by 0
  5. 2026Evaluating the Diversity of AI-Generated Content with Diversity Profilescited by 0
  6. 2026TEAR: Table Extraction with Attribute Recommendation from Texts via Large Language Modelscited by 0