Interview with Francis Bach, invited speaker at ICM2022

Link to the virtual ICM 2022 talks

What is your field of research?

My research area is what is called "machine learning" in English. It is a recent scientific area, at the frontier between applied mathematics and IT, whose goal is to conceive and analyse algorithms that can make sense of potentially massive amounts of data. It is one of the current motors of the artificial intelligence boom, and we see its daily application in the recognition of objects within images, for example, and in automatic language translations.

More specifically, I work at the interface of statistics and optimization; the main aim of my research is to discover new algorithms and to assess their performance in terms of both calculating time and predictive power.

How would you describe your profession?

I think that research is not a profession like the others. My days are very full between giving courses, writing articles, keeping up with the most recent literature, learning about new mathematical fields, supervising doctoral candidates, round-table discussions with colleagues, seminars, and conferences (though there are not too many of those at present), and local and international scientific activities.

Lots of other professions involve such diversity but what is unique about being a researcher in France is the complete liberty we have to choose our own research subjects and the way in which we approach them.

What do you like about being a mathematician?

I like all its aspects! But the relationship with doctoral students is especially enriching. A great deal of my research is done through these supervisory relationships, and I’m grateful to the students for the energy and contributions they make to our research team.

What would you say to young people thinking about pursuing a scientific career?

Go ahead and pursue the research questions that you’re passionate about.

Have you already decided what you will say at the ICM in July?

I’m going to talk about work done in collaboration with Lénaïc Chizat, currently professor at the EPFL, in which we show that the descent gradient, the most-used optimization algorithm in the study of neuron networks, attains the global minimum of the objective function that it seeks to minimise. This occurs in an idealised context of a continuous time algorithm for a network with an infinite number of hidden neurons. The chief difficulty lies in the non-convexity of the objective function, and the proof uses the theory of optimal transport and gradient flows.