2025/01/15 by Gabriel Peyré, Peyré, Gabriel · 6 voices
Computer Science · Mathematics · #Artificial intelligence #Computability, Logic, AI Algorithms #Computer science #Mathematics #Mathematics education
paper · pdf · doi:10.48550/arxiv.2501.10465
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2025/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.