Oral
Approximation and non-parametric estimation of ResNet-type convolutional neural networks
Kenta Oono · Taiji Suzuki

Thu Jun 13th 12:00 -- 12:05 PM @ Grand Ballroom

Convolutional neural networks (CNNs) have been shown to achieve optimal approximation and estimation error rates (in minimax sense) in several function classes. However, previous known optimal CNNs are unrealistically wide and difficult to obtain via optimization due to sparse constraints in important function classes, including the H\"older class. We show a ResNet-type CNN can attain the minimax optimal error rates in these classes in more plausible situations -- it can be dense, and its width, channel size, and filter size are constant with respect to sample size. The key idea is that we can replicate the learning ability of Fully-connected neural networks (FNNs) by tailored CNNs, as long as the FNNs have \textit{block-sparse} structures. Our theory is general in that we can automatically translate any approximation rate achieved by block-sparse FNNs into that by CNNs. As an application, we derive approximation and estimation error rates of the aformentioned type of CNNs for the Barron and H\"older classes with the same strategy.

Author Information

Kenta Oono (University of Tokyo / Preferred Networks)
Taiji Suzuki (The University of Tokyo / RIKEN)

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