Web: http://arxiv.org/abs/2208.01003

Sept. 19, 2022, 1:12 a.m. | Francesco Cagnetta, Alessandro Favero, Matthieu Wyart

cs.LG updates on arXiv.org arxiv.org

Understanding how convolutional neural networks (CNNs) can efficiently learn
high-dimensional functions remains a fundamental challenge. A popular belief is
that these models harness the local and hierarchical structure of natural data
such as images. Yet, we lack a quantitative understanding of how such structure
affects performance, e.g. the rate of decay of the generalisation error with
the number of training samples. In this paper, we study deep CNNs in the kernel
regime. First, we show that the spectrum of the …


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