Syntactic learning

The slides of my recent talk at the AI workshop at RL China are available below.

In this presentation I propose an interpretation of learning processes in terms of the notions of mathematical theory and proof, and advocate for the importance of empowering artificial learnings systems with large formal vocabularies that will serve for expressing the concepts (and relations between them) that they will learn from data.

The aim is to obtain more robust and structured forms of learning with generalisation capabilities, and greater resilience and adaptability, mimicking the distinctive features of human intelligence.

We also consider this project as an essential step for arriving at a toposic theory of semantic information; indeed, syntax and semantics are interwined (think, for instance, of the syntactic construction of classifying toposes).

I look forward to experimentally testing these ideas with our team at the Lagrange Center in Paris.

On women and mathematics

On the occasion of the release in France of the movie Marguerite’s theorem, I was interviewed at Radio France with Mélanie Guenais and Ariane Mézard about women and mathematics.

The discussion, lasting for about one hour, has touched several different themes, from statistics related to the numbers of female students and researchers in mathematics to ways to improve mathematics education at large.

You may listen to the podcast here.

A generalisation of Diaconescu’s theorem for relative toposes

A new paper, written jointly with my Ph.D. student Léo Bartoli, is available from the ArXiv:

The paper carries out a systematic investigation of the functors between sites which induce morphisms between relative toposes.

It culminates in a generalisation of Diaconescu’s theorem for relative toposes, formulated in the language of fibrations and stacks according to the foundations for relative topos theory introduced in the paper Relative topos theory via stacks.