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arXiv · 2303.14083

Online Learning for the Random Feature Model in the Student-Teacher Framework

Roman Worschech·Bernd Rosenow
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Abstract

Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the last layer is trainable, known as the random feature model. We study over-parametrization in the context of a student-teacher framework by deriving a set of differential equations for the learning dynamics. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly, and we compute the non-zero asymptotic generalization error. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible.

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BibTeXRIS

Roman Worschech, Bernd Rosenow. 2023-03-24. Online Learning for the Random Feature Model in the Student-Teacher Framework. https://arxiv.org/abs/2303.14083

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