From quadratic equations to neural networks—the story of Hilbert’s 13th Problem

From quadratic equations to neural networks—the story of Hilbert’s 13th Problem

Speaker: Prof. Bill Moran
RMIT University

Title: From quadratic equations to neural networks—the story of Hilbert’s 13th Problem.
A beautiful theorem but totally useless!

Date and time: Friday 19 May 2017, 3:00–4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: I will chart the history of Hilbert’s 13th Problem and connect it to recent theoretical research in neural networks and statistical regression. The focus will be a remarkable theorem of Kolmogorov and Arnold to the effect that continuous functions of many dimensions do not really exist. Specifically, any continuous function defined on the unit cube in N dimensions can be written as a continuous function of one variable acting on the sum N continuous functions of each of the coordinate variables separately. I will discuss where the problem came from, deep in the history of mathematics, and going back to the solution of polynomial equations, and how its solution might (or might not) be relevant to neural networks.

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