The Slow Deterioration of the Generalization Error of the Random Feature Model
This addresses the problem of overfitting in machine learning models for practitioners, though it is incremental as it builds on known resonance behavior in random feature models.
The paper investigates the dynamic behavior of gradient descent in random feature models when the number of parameters is near the training sample size, showing that a self-correction mechanism causes larger generalization gaps to develop more slowly, allowing early stopping to achieve good generalization.
The random feature model exhibits a kind of resonance behavior when the number of parameters is close to the training sample size. This behavior is characterized by the appearance of large generalization gap, and is due to the occurrence of very small eigenvalues for the associated Gram matrix. In this paper, we examine the dynamic behavior of the gradient descent algorithm in this regime. We show, both theoretically and experimentally, that there is a dynamic self-correction mechanism at work: The larger the eventual generalization gap, the slower it develops, both because of the small eigenvalues. This gives us ample time to stop the training process and obtain solutions with good generalization property.