### Abstract

In this talk, I will explore the work of Kileel, Trager, and Bruna in their 2019 paper On the Expressive power of Polynomial Neural Networks. In the talk, I will look at 1) what a polynomial neural network is and how we can interpret the output such networks as varieties, 2) why the dimension of this variety and the expressive power of this network are related, and 3) how the study of these varieties might tell us something about the architecture of the network.

Date

Oct 6, 2021 4:00 PM — 5:00 PM

Location

UW Madison Math Department

###### PhD Student, Mathematics

My research interests include algebraic geometry, number theory, and machine learning