Hilbert, Deep Neural Nets and Empirical Moduli Spaces

Abstract: The motivation behind Hilbert's 13th problem is often overlooked. In his original statement, he opens with: "nomography deals with the problem of solving equations by means of drawing families of curves depending on an arbitrary parameter". The question he posed sought to identify a family of functions amenable to such graphical solvers that were essential tools of his time. More formally, he asked if it was possible to solve algebraic equations in terms of towers of algebraic functions of a single parameter. While the question in its original form remains open to this day, in the continuous realm it turns out that there is no such thing as a truly multivariate function. In this talk, we will see how these ideas fit into the modern deep learning framework, forming a bridge between algebra and analysis.

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar