Machine learning (ML) research has investigated prototypes: examples that are representative of the behavior to be learned. We systematically evaluate five methods for identifying prototypes, both ones previously introduced as well as new ones we propose, finding all of them to provide meaningful but different interpretations. Through a human study, we confirm that all five metrics are well matched to human intuition. Examining cases where the metrics disagree offers an informative perspective on the properties of data and algorithms used in learning, with implications for data-corpus construction, efficiency, adversarial robustness, interpretability, and other ML aspects. In particular, we confirm that the "train on hard" curriculum approach can improve accuracy on many datasets and tasks, but that it is strictly worse when there are many mislabeled or ambiguous examples. When reasoning about ML tasks, it is natural to look for a set of training or test examples that is somehow prototypical-i.e., that is representative of the desired learned behavior. Although such prototypical examples have been central to several research efforts, e.g., in interpretability BID5 and curriculum learning BID3 , no generally-agreed-upon definition seems to exist for prototypes, or their characteristics. For modern deep-learning models, whose behavior is often inscrutable, even the very existence and usefulness of prototypical examples has seemed uncertain until the recent work of Stock & Cisse (2017) .Inspired by that work we (1) identify a set of desirable properties for prototypicality definitions; (2) systematically explore different metrics used in prior work, as well as new metrics we develop, for identifying prototypical examples in both training and test data; (3) study the characteristics of those metrics' prototypes and their complement set-the outliers-using both quantitative measures and a qualitative human study; and, (4) evaluate the usefulness of prototypes for machine-learning purposes such as reducing sample complexity or improving adversarial robustness and interpretability.Our prototypicality metrics are based on adversarial robustness, retraining stability, ensemble agreement, and differentially-private learning. As an independent result, we show that predictive stability under retraining strongly correlates with adversarial distance, and may be used as an approximation.Unequivocally, we find that distinct sets of prototypical and outlier examples exist for the datasets we consider: MNIST (LeCun et al., 2010) , Fashion-MNIST (Xiao et al., 2017) , CIFAR-10 (Krizhevsky & Hinton, 2009), and ImageNet (Russakovsky et al., 2015) . Between all of our metrics, as well as human evaluators, there is overall agreement on the examples that are prototypes and those that are outliers. Furthermore, the differences between metrics constitute informative exceptions, e.g., identifying uncommon submodes in the data as well as spurious, ambiguous, or misleading examples.Usefully, there are advantages to training models using only prototypical examples: the models learn much faster, their accuracy loss is not great and occurs almost entirely on outlier test examples, and the models are both easier to interpret and more adversarially robust. Conversely, at the same sample complexity, significantly higher overall accuracy can be achieved by training models exclusively on outliers-once erroneous and misleading examples have been eliminated from the dataset. This paper explores prototypes: starting with the properties we would like them to satisfy, then evaluating metrics for computing them, and discussing how we can utilize them during training. The five metrics we study all are highly correlated, and capture human intuition behind what is meant by "prototypical". When the metrics disagree on the prototypicality of an example, we can often learn something interesting about that example (e.g., that it is from a rare submode of a class). Further, we explore the many reasons to utalize prototypes: we find that models trained on prototypes often have simpler decision boundaries and are thus more adversarially robust. However, training only on prototypes often yields inferior accuracy compared to training on outliers. We believe that further exploring metrics for identifying prototypes and developing methods for using them during training is an important area of future work, and hope that our analysis will be useful towards that end goal.
We can identify prototypical and outlier examples in machine learning that are quantifiably very different, and make use of them to improve many aspects of neural networks.
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