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Measuring diversity accurately is important for many scientific fields,including machine learning (ML), ecology, and chemistry. The Vendi Score wasintroduced as a generic similarity-based diversity metric that extends the Hillnumber of order q=1 by leveraging ideas from quantum statistical mechanics.Contrary to many diversity metrics in ecology, the Vendi Score accounts forsimilarity and does not require knowledge of the prevalence of the categoriesin the collection to be evaluated for diversity. However, the Vendi Scoretreats each item in a given collection with a level of sensitivity proportionalto the item's prevalence. This is undesirable in settings where there is asignificant imbalance in item prevalence. In this paper, we extend the otherHill numbers using similarity to provide flexibility in allocating sensitivityto rare or common items. This leads to a family of diversity metrics -- Vendiscores with different levels of sensitivity -- that can be used in a variety ofapplications. We study the properties of the scores in a synthetic controlledsetting where the ground truth diversity is known. We then test their utilityin improving molecular simulations via Vendi Sampling. Finally, we use theVendi scores to better understand the behavior of image generative models interms of memorization, duplication, diversity, and sample quality.

Cousins Of The Vendi Score: A Family Of Similarity-Based Diversity Metrics For Science And Machine Learning