One World Seminar Series on the

Mathematics of Machine Learning


The One World Seminar Series on the Mathematics of Machine Learning is an online platform for research seminars, workshops and seasonal schools in theoretical machine learning. The focus of the series lies on theoretical advances in machine learning and deep learning as a complement to the one world seminars on probability, on Information, Signals and Data (MINDS), on methods for arbitrary data sources (MADS), and on imaging and inverse problems (IMAGINE).

The series was started during the Covid-19 epidemic in 2020 to bring together researchers from all over the world for presentations and discussions in a virtual environment. It follows in the footsteps of other community projects under the One World Umbrella which originated around the same time.

We welcome suggestions for speakers concerning new and exciting developments and are committed to providing a platform also for junior researchers. We recognize the advantages that online seminars provide in terms of flexibility, and we are experimenting with different formats. Any feedback on different events is welcome.

Next Event

Wed Nov 25
12 noon ET

Neural network performance for classification problems with boundaries of Barron class

We study classification problems in which the distances between the different classes are not necessarily positive, but for which the boundaries between the classes are well-behaved. More precisely, we assume these boundaries to be locally described by graphs of functions of Barron-class. ReLU neural networks can approximate and estimate classification functions of this type with rates independent of the ambient dimension. More formally, three-layer networks with $N$ neurons can approximate such functions with $L^1$-error bounded by $O(N^{-1/2})$. Furthermore, given $m$ training samples from such a function, and using ReLU networks of a suitable architecture as the hypothesis space, any empirical risk minimizer has generalization error bounded by $O(m^{-1/4})$. All implied constants depend only polynomially on the input dimension. We also discuss the optimality of these rates. Our results mostly rely on the "Fourier-analytic" Barron spaces that consist of functions with finite first Fourier moment. But since several different function spaces have been dubbed "Barron spaces'' in the recent literature, we discuss how these spaces relate to each other. We will see that they differ more than the existing literature suggests.


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Format

Seminars are held online on Zoom. The presentations are recorded and video is made available on our youtube channel. A list of past seminars can be found here. All seminars, unless otherwise stated, are held on Wednesdays at 12 noon ET. The invitation will be shared on this site before the talk and distributed via email.

Board

Simon Shaolei Du (University of Washington)

Surbhi Goel (Microsoft Research NY)

Song Mei (UC Berkeley)

Matthew Thorpe (University of Manchester)


Franca Hoffmann (University of Bonn)

Chao Ma (Stanford University)

Philipp Petersen (University of Vienna)

Stephan Wojtowytsch (Princeton University)