In the forthcoming weeks, in the framework of my D’Alembert Chair at the Université Paris-Saclay, I shall give a course at the MICS Laboratory of CentraleSupélec on “Relative toposes for artificial general intelligence“.

ABSTRACT:

Topos theory can be described as the science of invariants. The theory of relative toposes consists in methods and techniques for studying toposes in relation to each other. Viewing toposes as spaces embodying information, this theory notably paves the way for the development of new, very dynamical and structural forms of modelling, both of ‘real’ entities and phenomena, and of (natural or artificial) learning processes. In particular, it naturally leads to the design of systems implementing principles of meta-learning (in the sense of learning taking place at different levels of abstraction constructed on top of each other).

The first part of the course will provide a conceptual introduction to the theory of relative toposes and its relevance for AI, while the second will present some first applications of this theory in connection with the modelling and solution of Raven progressive matrices and, more generally, of ARC-type problems.

N.C. No previous knowledge of topos theory is necessary for understanding the key ideas and methods presented in the course.

DATES:

– Thursday 26 June 2025, 14-16, Amphi SC.046 (Peugeot), Bouygues building (9 Rue Joliot Curie, 91190 Gif-sur-Yvette).
– Thursday 3 July 2025, 14-16, Amphi SC.046 (Peugeot), Bouygues building (9 Rue Joliot Curie, 91190 Gif-sur-Yvette).

Looking forward to seeing many of you there!