Event Detail

Event Type: 
Geometry-Topology Seminar
Date/Time: 
Monday, November 15, 2021 - 12:00 to 12:50
Location: 
Kidd 280 or contact Christine Escher for a zoom link.

Speaker Info

Institution: 
University of Oregon
Abstract: 

Piecewise linear (PL) functions are used in most modern machine learning models due to their speed of computation. For example, a binary classification ReLU neural network can be considered as a PL functionfrom its input space to the real line, dividing its input space into binary categories via the choice of a sublevel set. Classically, sublevel sets of functions are the domain of Morse theory, but PL functions are not smooth. Furthermore, even tools such as discrete Morse theory are cumbersome in this setting. Following an introduction to PL topology via polyhedral complexes, we discuss the differences between these classical theories and PL Morse theory, as outlined in the thesis of Romain Grunert (2017), including examples and nonexamples in the space of ReLU neural networks.