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 December 1
12 noon ET

Deep Learning in High Dimension: Neural Network Approximation of Analytic Maps of Gaussians

For artificial deep neural networks with ReLU activation,
we prove new expression rate bounds for parametric, analytic functions where the parameter dimension could be infinite.

Approximation rates are in mean square on the unbounded parameter range with respect to product gaussian measure. Approximation rate bounds are free from the CoD, and determined by summability of Wiener-Hermite PC expansion coefficients.

Sufficient conditions for summability are quantified holomorphy on products of strips in the complex domain. Applications comprise DNN expression rate bounds of deep-NNs for response surfaces of elliptic PDEs with log-gaussian random field inputs, and for the posterior densities of the corresponding Bayesian inverse problems.

Variants of proofs which are constructive are outlined.

(joint work with Jakob Zech, University of Heidelberg, Germany, and with Dinh Dung and Nguyen Van Kien, Hanoi, Vietnam)


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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.


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)