Session II.6 - Computational Algebraic Geometry
Thursday, June 15, 15:00 ~ 15:30
Sparse Factorizations of Real Polynomials & Linear Convolutional Neural Networks
Kathlén Kohn
KTH Royal Institute of Technology, Sweden - This email address is being protected from spambots. You need JavaScript enabled to view it.
This talk will explain that Convolutional Neural Networks without activation parametrize semialgebraic sets of real homogeneous polynomials that admit a certain space factorization. We will investigate how the geometry of these semialgebraic sets (e.g., its singularities and relative boundary) changes with the network architecture. Moreover, we will start to explore how these geometric properties affect the optimization of a loss function for given training data.
Joint work with Guido Montúfar (MPI MiS Leipzig / UCLA), Vahid Shahverdi (KTH) and Matthew Trager (Amazon).