MDLW02 | Prof. Lorenzo Rosasco | Understanding neural networks with reproducing kernel Banach spaces

Описание: MDLW02 | Prof. Lorenzo Rosasco | Understanding neural networks with reproducing kernel Banach spaces

Speaker: Professor Lorenzo Rosasco (University of Genova)
Date: 27th Sept 2021 - 16:40 to 17:20
Venue: INI Seminar Room 1
Title: Understanding neural networks with reproducing kernel Banach spaces
Event: (MDLW02) Deep learning and inverse problems
Abstract: Characterizing the function spaces corresponding to neural networks can provide a way to understand their properties. In this paper, we discuss how the theory of reproducing kernel Banach spaces can be used to tackle this challenge. In particular, we prove a representer theorem for a wide class of reproducing kernel Banach spaces that admit a suitable integral representation and include one hidden layer neural net-works of possibly infinite width. Further, we show that for a suitable class of ReLU activation function the norm in the corresponding reproducing kernel Banach space can be characterized in terms of the inverse Radon transform of a bounded real measure, with norm given by the total variation norm of the measure. Our main contribution is simplifying and extending recent results.

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