On the Joint Interaction of Models, Data, and Features
Authors: Yiding Jiang,Christina Baek,J Zico Kolter
Presentation: ICLR 2024,Oral

Abstract: Learning features from data is one of the defining characteristics of deep learning,
but the theoretical understanding of the role features play in deep learning is still in
early development. To address this gap, we introduce a new tool, the interaction
tensor, for empirically analyzing the interaction between data and model through
features. With the interaction tensor, we make several key observations about
how features are distributed in data and how models with different 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 of hypotheses can both be derived in
closed form. We demonstrate that the proposed framework can explain empirically
observed phenomena, including the recently discovered Generalization Disagreement Equality (GDE) that allows for estimating the generalization error with only
unlabeled data. Further, our theory also provides explicit construction of natural
data distributions that break the GDE. Thus, we believe this work provides valuable
new insight into our understanding of feature learning.