The Mathematics of Artificial Intelligence
It addresses the need for mathematical insights to improve AI, but is incremental as it reviews existing intersections without presenting new results.
This overview article highlights the role of mathematics in understanding and enhancing AI systems, focusing on analytical and probabilistic tools to model neural network architectures and optimization, while encouraging mathematicians to contribute to the field.
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.