The Mathematics of Artificial Intelligence

TL;DR

This survey explores the current state of mathematical foundations for AI, focusing on deep neural networks, highlighting key theoretical directions, results, and open problems in the field.

Contribution

It provides a comprehensive overview of the mathematical theories underpinning deep neural networks and discusses open challenges, advancing the understanding of AI's theoretical basis.

Findings

Summarizes main theoretical directions in neural network mathematics

Highlights key results achieved in understanding neural network behavior

Discusses open problems and future research directions

Abstract

We currently witness the spectacular success of artificial intelligence in both science and public life. However, the development of a rigorous mathematical foundation is still at an early stage. In this survey article, which is based on an invited lecture at the International Congress of Mathematicians 2022, we will in particular focus on the current "workhorse" of artificial intelligence, namely deep neural networks. We will present the main theoretical directions along with several exemplary results and discuss key open problems.