Background

My scientific interests lie at the interface between mathematics, physics and computer science.

After undergraduate double-curriculum in mathematics and physics, I studied differential geometry, gauge theory and operator algebra, mostly motivated by the challenges posed by quantum physics and general relativity.

My doctoral research then focused on the relationships between algebraic topology and message-passing algorithms, leading me to propose a clear picture of their geometric structure, various regularisations of their dynamic and a better understanding of their equilibria and singularities.

Message-Passing Algorithms

Publications

• PhD thesis: Message Passing Algorithms and Homology, see here for numerical experiments.

  Message-passing algorithms have a wide variety of applications, from telecoms to statistical physics, neuroscience and artificial intelligence. They consist of an asynchronous and parallelised computing scheme where a collection of local units communicate until they eventually reach a consensual state, and estimate the marginals of a probabilistic graphical model. They for instance provide an alternative to contrastive divergence algorithms in training Boltzmann machines.

  Message-passing algorithms are shown equivalent to transport equations of the form \(\dot u = \delta \Phi(u)\), where $u$ is a collection of local interaction potentials, $\Phi(u)$ represents a heat flux from one region to the other, and the boundary opeator $\delta$ is the discrete analog of a divergence.

• Geomstats : A Python Package for Riemannian Geometry in Machine Learning

  This paper presents a great library for differential geometry and statistics I had the chance to work on with a fantastic team of 12 international contributors. The github repo for geomstats is available here.

  (Submitted to the Journal of Machine Learning Research and presented at the Scipy 2020 conference)

• SYCO’20: Homological Algebra for Message Passing Algorithms

  This is a short, 5 page-long resume I wrote for the SYCO conference, which should have taken place at the end of march. Although dense, it may give a quick overview of most of the results contained in the thesis. It was intended for an audience familiar with homological algebra and category theory.

• GSI’19: A Homological Approach to Belief Propagation and Belief Propagation

  This is a first proof of the equivalence between critical points of Bethe free energies and stationary states of message passing algorithms, which I presented at the Geometric Science of Information colloquium, held in Toulouse last summer.

  (Published in the GSI 19 proceedings.)