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Session I.7 - Stochastic Computation

Tuesday, June 13, 14:00 ~ 14:30

On the existence of optimal shallow networks

Steffen Dereich

University Münster, Germany   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

In this talk, we discuss existence of global minima in optimisation problems over shallow neural networks. More explicitly, the function class over which we minimise is the family of all functions that can be expressed as artificial residual or feedforward neural networks with one hidden layer featuring a specified number of neurons with ReLU (or Leaky ReLU) activation. We give existence results. Moreover, we provide counterexamples that illustrate the relevance of the assumptions imposed in the theorems.

Joint work with Arnulf Jentzen (University Münster) and Sebastian Kassing (University Bielefeld).

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