Wilhelm Killing Kolloquium: Postdocs of Mathematics Münster (WWU Münster) via Zoom: Scientific postdoc presentations
Thursday, 02.12.2021 16:30 im Raum ZOOM
Get an insight into the research of eight new postdoctoral researchers of Mathematics Münster. In short scientific presentations they will introduce their topics. After the talks, there will be the opportunity to exchange ideas in breakout rooms.
Sam Evington: C*-algebras, K-Theory and Traces
Fabian Hebestreit: Hermitian K-theory
Jonas Jalowy: Random Matrix Theory: The Wasserstein distance to the Circular Law
Roberta Marziani: The Calculus of Variations: from the Plateau problem to Solid Mechanics
Mario Schulz: Free boundary minimal surfaces
Sebastian Throm: tba
Yifei Zhao: Interpolating automorphic and Galois
Tingxiang Zou: What can model theory say about combinatorics?
Wilhelm Killing Kolloquium: Prof. Dr. Guido Montúfar (University of California, Los Angeles) via ZOOM: Geometry of Linear Convolutional Networks
Thursday, 09.12.2021 16:30 im Raum ZOOM
We study the family of functions that are represented by a linear convolutional neural network (LCN). These functions form a semi-algebraic subset of the set of linear maps from input space to output space. In contrast, the families of functions represented by fully-connected linear networks form algebraic sets. We observe that the functions represented by LCNs can be identified with polynomials that admit certain factorizations, and we use this perspective to describe the impact of the network's architecture on the geometry of the resulting function space. We further study the optimization of an objective function over an LCN, analyzing critical points in function space and in parameter space, and describing dynamical invariants for gradient descent. Overall, our theory predicts that the optimized parameters of an LCN will often correspond to repeated filters across layers, or filters that can be decomposed as repeated filters. We also conduct numerical and symbolic experiments that illustrate our results and present an in-depth analysis of the landscape for small architectures.
This talk is based on joint work with Kathlén Kohn, Thomas Merkh and