Yury Korolev - Approximation properties of two-layer neural networks with values in a Banach space

Presentation given by Yury Korolev on 6th October in the one world seminar on the mathematics of machine learning on the topic "Approximation properties of two-layer neural networks with values in a Banach space".

Abstract: Approximation properties of infinitely wide neural networks have been studied by several authors in the last few years. New function spaces have been introduced that consist of functions that can be efficiently (i.e., with dimension-independent rates) approximated by neural networks of finite width. Typically, these functions are supposed to act between Euclidean spaces, typically with a high-dimensional input space and a lower-dimensional output space. As neural networks gain popularity in inherently infinite-dimensional settings such as inverse problems and imaging, it becomes necessary to analyse the properties of neural networks as nonlinear operators acting between infinite-dimensional spaces. In this talk, I will present dimension-independent Monte-Carlo rates for neural networks acting between Banach spaces with a partial order (vector lattices), where the ReLU nonlinearity will be interpreted as the lattice operation of taking the positive part.

Видео Yury Korolev - Approximation properties of two-layer neural networks with values in a Banach space канала One world theoretical machine learning