Characterizing Structural Regularities of Labeled Data in Overparameterized Models

Human learners appreciate that observations usually form hierarchies of regularities and sub-regularities. For example, English verbs have irregular cases that must be memorized (e.g., go -> went) and regular cases that generalize well (e.g., kiss -> kissed, miss -> missed). Likewise, deep neural networks have the capacity to memorize rare or irregular forms but nonetheless generalize across instances that share common patterns or structures. We analyze how individual instances are treated by a model via a consistency score. The score is the expected accuracy of a particular architecture for a held-out instance on a training set of a given size sampled from the data distribution. We obtain empirical estimates of this score for individual instances in multiple data sets, and we show that the score identifies out-of-distribution and mislabeled examples at one end of the continuum and regular examples at the other end. We explore two categories of proxies to the consistency score: pairwise distance based proxy and the training statistics based proxies. We conclude with two applications using C-scores to help understand the dynamics of representation learning and filter out outliers, and discussions of other potential applications such as curriculum learning, and active data collection.