The Mathematics of Artificial Intelligence

TL;DR

This paper discusses how mathematical tools underpin AI development, focusing on neural network modeling and optimization, and highlights the evolving mathematical techniques that have driven advances in AI architectures.

Contribution

It provides an overview of the mathematical foundations of AI, emphasizing analytical and probabilistic methods, and encourages mathematicians to engage with AI research.

Findings

Mathematics is essential for understanding and improving AI systems.

Different AI architectures are driven by specific mathematical techniques.

The paper advocates for increased mathematical involvement in AI development.

Abstract

This overview article highlights the critical role of mathematics in artificial intelligence (AI), emphasizing that mathematics provides tools to better understand and enhance AI systems. Conversely, AI raises new problems and drives the development of new mathematics at the intersection of various fields. This article focuses on the application of analytical and probabilistic tools to model neural network architectures and better understand their optimization. Statistical questions (particularly the generalization capacity of these networks) are intentionally set aside, though they are of crucial importance. We also shed light on the evolution of ideas that have enabled significant advances in AI through architectures tailored to specific tasks, each echoing distinct mathematical techniques. The goal is to encourage more mathematicians to take an interest in and contribute to this exciting field.