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

• URL: http://arxiv.org/abs/2303.14083v2
• Date: Thu, 6 Apr 2023 21:41:46 GMT
• Title: Online Learning for the Random Feature Model in the Student-Teacher Framework
• Authors: Roman Worschech and Bernd Rosenow
• Abstract summary: We study over-parametrization in the context of a student-teacher framework. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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