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Seminar WS 23/24 Graduate Seminar on Numerical Simulation

Machine Learning methods for manifold embeddings

Offered by
Prof. Martin Rumpf
Florine Hartwig

A central machine learning task is to match high-dimensional objects from given data sets with points in a properly chosen low dimensional latent manifold. This is frequently obtained via an autoencoder, consisting of an encoder map mapping from the space of input objects into the latent space and a decoder mapping back points in latent space to points in the input space. Encoder and decoder are neural networks trained via the minimization of a loss functional. This approach is an instance of deep manifold learning.

In the seminar we will study recent approaches in this field and discuss their mathematical foundation. It will in particular be studied how to ensure certain desirable properties of the encoder mapping such as isometry and/or regularity.

The first meeting with the distribution of research articles will be on Wednesday, July 5th 2023 at 14:15 in Room 2.040, Endenicher Allee 60.