Feature learning is decoupled from generalization in high capacity neural networks
This work addresses a foundational issue in machine learning theory by highlighting a disconnect between feature learning and generalization, which is incremental as it builds on prior theories without solving the generalization problem directly.
The paper tackles the problem that existing theories of feature learning in neural networks measure the strength rather than the quality of learned features, and introduces a concept called feature quality to address this gap, showing that current theories are insufficient for explaining generalization.
Neural networks outperform kernel methods, sometimes by orders of magnitude, e.g. on staircase functions. This advantage stems from the ability of neural networks to learn features, adapting their hidden representations to better capture the data. We introduce a concept we call feature quality to measure this performance improvement. We examine existing theories of feature learning and demonstrate empirically that they primarily assess the strength of feature learning, rather than the quality of the learned features themselves. Consequently, current theories of feature learning do not provide a sufficient foundation for developing theories of neural network generalization.