Title: Understanding neural networks and quantification of their uncertainty via exactly solvable models

Abstract: The affinity between statistical physics and machine learning has a long history. Theoretical physics often proceeds in terms of solvable synthetic models; I will describe the related line of work on solvable models of simple feed-forward neural networks. I will then discuss how this approach allows us to analyze uncertainty quantification in neural networks, a topic that gained urgency in the dawn of widely deployed artificial intelligence. I will conclude with what I perceive as important specific open questions in the field.

Bio: Lenka Zdeborová is a Professor of Physics and Computer Science at École Polytechnique Fédérale de Lausanne, where she leads the Statistical Physics of Computation Laboratory. She received a PhD in physics from University Paris-Sud and Charles University in Prague in 2008. She spent two years in the Los Alamos National Laboratory as the Director's Postdoctoral Fellow. Between 2010 and 2020, she was a researcher at CNRS, working in the Institute of Theoretical Physics in CEA Saclay, France. In 2014, she was awarded the CNRS bronze medal; in 2016 Philippe Meyer prize in theoretical physics and an ERC Starting Grant; in 2018, the Irène Joliot-Curie prize; in 2021, the Gibbs lectureship of AMS and the Neuron Fund award. Lenka's expertise is in applications of concepts from statistical physics, such as advanced mean field methods, the replica method and related message-passing algorithms, to problems in machine learning, signal processing, inference and optimization. She enjoys erasing the boundaries between theoretical physics, mathematics and computer science.

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