IHP School: Artificial Intelligence for Mathematicians and Theoretical Physicists

Recent breakthroughs have shown that AI can now prove theorems. At the same time, many of the deepest open questions about AI are, at heart, questions of mathematics and physics: high-dimensional geometry, non-convex optimisation, the statistical mechanics of learning. AI is becoming both a tool for and a subject of research in our fields, and a working knowledge of it is fast becoming essential for every young researcher.

This one-week school, funded by Qube Research & Technologies, will introduce the fundamental concepts of modern AI. It is designed for PhD students and early-career researchers in mathematics and theoretical physics with no prior specialisation in AI. The programme combines lectures with hands-on lab sessions.

Topics covered and lecturers (one day per topic)

1. Fundamentals of AI: deep learning, neural networks. Lab session: training a simple neural network from scratch.

   • Course: Christophe Giraud (Laboratoire de Mathématiques d'Orsay, Université Paris-Saclay)
   • Lab session: TBA

2. Generative AI / LLMs. Lab session: fine-tuning: adapting a pre-trained LLM to a specific task

   • Course: Pierre Marion (Inria & École normale supérieure, Paris)
   • Lab session: Gaëtan Narozniak (Inria & FAIR, Meta)

3. AI-assisted research, agent-based AI

   • Frédéric Marbach (Département de mathématiques et applications, École normale supérieure, Paris)
   • Julia Kempe (Courant Institute of Mathematical Sciences, NYU & AmiLlabs)
   • Jorge Fernandez-de-Cossio-Diaz (Institut de Physique Théorique, CEA Saclay)

4. Formal methods. Lab session: using LLM agents

   • Scott Armstrong (Laboratoire Jacques-Louis Lions, Sorbonne Université and Courant Institute, NYU)
   • Rémy Degenne (Inria, Université de Lille)

5. Ethical, legal and environmental aspects of AI; Math & AI practices

   • Legal aspects: Arnaud Latil (Sciences, Normes, Démocratie, Sorbonne Université)
   • Ethical aspects: Anouk Barberousse (Sciences, Normes, Démocratie, Sorbonne Université)
   • Environmental aspects: TBA

All along the five days: 

Math & AI practices: Zoé Aegerter (organiser of Math&AI controversy workshop)

Scientific Committee:

• Gérard Biau (Sorbonne University)
• Claire Boyer (University of Paris-Saclay)
• Djalil Chafaï (Dauphine, Paris Sciences et Lettres)
• Xavier Fresquet (Sorbonne University, Abu Dhabi)
• Arnaud Guillin (Clermont-Auvergne University)
• Marc Lelarge (École normale supérieure)
• Emmanuel Sérié (École Polytechnique)

Organising committee

• Jérémie Bouttier (IHP)
• Mariana Graña (IHP)