The Mathematics of Artificial Intelligence
It provides a foundational overview for researchers in mathematics and AI, but is incremental as a survey.
This survey article addresses the lack of a rigorous mathematical foundation for artificial intelligence, focusing on deep neural networks, and presents current theoretical directions, exemplary results, and key open problems.
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.