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Workshop

Understanding Linear Convolutional Neural Networks via Sparse Factorizations of Real Polynomials

  • Vahid Shahverdi (KTH Royal Institute of Technology)
E1 05 (Leibniz-Saal)

Abstract

This talk will explain that Convolutional Neural Networks without activation parametrize semialgebraic sets of real homogeneous polynomials that admit a certain sparse factorization. We will investigate how the geometry of these semialgebraic sets (e.g., their singularities and relative boundary) changes with the network architecture. Moreover, we will explore how these geometric properties affect the optimization of a loss function for given training data. This talk is based on joint work with Kathlén Kohn, Guido Montúfar, and Matthew Trager.

Katharina Matschke

Max Planck Institute for Mathematics in the Sciences Contact via Mail

Samantha Fairchild

Max Planck Institute for Mathematics in the Sciences

Diaaeldin Taha

Max Planck Institute for Mathematics in the Sciences

Anna Wienhard

Max Planck Institute for Mathematics in the Sciences