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Diversity is an important criterion for many areas of machine learning (ML), including generative modeling and dataset curation. However, existing metrics for measuring diversity are often domain-specific and limited in flexibility. In this paper we address the diversity evaluation problem by proposing the Vendi Score, which connects and extends ideas from ecology and quantum statistical mechanics to ml. The Vendi Score is defined as the exponential of the Shannon entropy of the eigenvalues of a similarity matrix. This matrix is induced by a user-defined similarity function applied to the sample to be evaluated for diversity. In taking a similarity function as input, the Vendi Score enables its user to specify any desired form of diversity. Importantly, unlike many existing metrics in ML, the Vendi Score does not require a reference dataset or distribution over samples or labels, it is therefore general and applicable to any generative model, decoding algorithm, and dataset from any domain where similarity can be defined. We showcase the Vendi Score on molecular generative modeling where we found it addresses shortcomings of the current diversity metric of choice in that domain. We also applied the Vendi Score to generative models of images and decoding algorithms of text where we found it confirms known results about diversity in those domains. Furthermore, we used the Vendi Score to measure mode collapse, a known shortcoming of generative adversarial networks (GANs). In particular, the Vendi Score revealed that even GANs that capture all the modes of a labelled dataset can be less diverse than the original dataset. Finally, the interpretability of the Vendi Score allowed us to diagnose several benchmark ML datasets for diversity, opening the door for diversity-informed data augmentation. 

In-context learning (ICL) is an important paradigm for adapting large language models (LLMs) to new tasks, but the generalization behavior of ICL remains poorly understood. We investigate the inductive biases of ICL from the perspective of feature bias: which feature ICL is more likely to use given a set of underspecified demonstrations in which two features are equally predictive of the labels. First, we characterize the feature biases of GPT-3 models by constructing underspecified demonstrations from a range of NLP datasets and feature combinations. We find that LLMs exhibit clear feature biases—for example, demonstrating a strong bias to predict labels according to sentiment rather than shallow lexical features, like punctuation. Second, we evaluate the effect of different interventions that are designed to impose an inductive bias in favor of a particular feature, such as adding a natural language instruction or using semantically relevant label words. We find that, while many interventions can influence the learner to prefer a particular feature, it can be difficult to overcome strong prior biases. Overall, our results provide a broader picture of the types of features that ICL may be more likely to exploit and how to impose inductive biases that are better aligned with the intended task.