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Learning features from data is one of the defining characteristics of deeplearning, but our theoretical understanding of the role features play in deeplearning is still rudimentary. To address this gap, we introduce a new tool,the interaction tensor, for empirically analyzing the interaction between dataand model through features. With the interaction tensor, we make several keyobservations about how features are distributed in data and how models withdifferent random seeds learn different features. Based on these observations,we propose a conceptual framework for feature learning. Under this framework,the expected accuracy for a single hypothesis and agreement for a pair ofhypotheses can both be derived in closed-form. We demonstrate that the proposedframework can explain empirically observed phenomena, including the recentlydiscovered Generalization Disagreement Equality (GDE) that allows forestimating the generalization error with only unlabeled data. Further, ourtheory also provides explicit construction of natural data distributions thatbreak the GDE. Thus, we believe this work provides valuable new insight intoour understanding of feature learning.

On the Joint Interaction of Models, Data, and Features