Initialization-Dependent Sample Complexity of Linear Predictors and Neural Networks

Roey Magen; Ohad Shamir

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arXiv · 2305.16475

Initialization-Dependent Sample Complexity of Linear Predictors and Neural Networks

Roey Magen·Ohad Shamir

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Abstract

We provide several new results on the sample complexity of vector-valued linear predictors (parameterized by a matrix), and more generally neural networks. Focusing on size-independent bounds, where only the Frobenius norm distance of the parameters from some fixed reference matrix $W_0$ is controlled, we show that the sample complexity behavior can be surprisingly different than what we may expect considering the well-studied setting of scalar-valued linear predictors. This also leads to new sample complexity bounds for feed-forward neural networks, tackling some open questions in the literature, and establishing a new convex linear prediction problem that is provably learnable without uniform convergence.

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Roey Magen, Ohad Shamir. 2023-05-25. Initialization-Dependent Sample Complexity of Linear Predictors and Neural Networks. https://arxiv.org/abs/2305.16475

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