The Mathematics of Artificial Intelligence

Abstract: The new wave of artificial intelligence is impacting industry, public life, and the sciences in an unprecedented manner. A similarly strong impact can currently be witnessed within mathematics on areas such as inverse problems and numerical analysis of partial differential equations. However, one major drawback worldwide, in particular, in light of regulations such as the EU AI Act and the G7 Hiroshima AI Process, is the lack of reliability of such methodologies.

The goal of this first lecture is to first provide an introduction into this new vibrant research area. We will then survey recent advances on a profound mathematical understanding of deep neural networks, in particular, concerning their expressive power, the learning process, and overall performance guarantees. Due to the importance of explainability for reliability, we will also touch upon this area by highlighting an explainability approach which is itself reliable due to its mathematical foundation.

Mathematics

Audience: researchers in the topic

UCLA distinguished lecture series

Series comments: Description: Lectures by distinguished mathematicians, hosted at UCLA

Every year, the Distinguished Lecture Series (DLS) brings two to four eminent mathematicians to UCLA for a week or more to give a lecture series on their field, and to meet with faculty and graduate students.

The first lecture of each series is aimed at a general mathematical audience, and offers a rare opportunity to see the state of an area of mathematics from the perspective of one of its leaders. The remaining lectures in the series are usually more advanced, concerning recent developments in the area.