MARC MEZARD
Courses a.y. 2022/2023
Biographical note
I am a Professor of Theoretical Physics. I studied physics at Ecole normale supérieure in Paris and I obtained my PhD in 1984. Hired at CNRS in Paris, I was Research Director in Université Paris Sud. From 2012 and 2022 I became Director of Ecole normale supérieure, and I then joined Bocconi University as a professor, in the newly created department of computational sciences. My work focuses on statistical physics of disordered systems, with applications in various fields like information theory, computer science, machine learning, biophysics.
Research interests
I am interested in the emergent phenomena in complex systems with many interacting “atoms”, (that could be for instance agents on a market, information bits, or molecules are different or live in different environments. The statistical physics of disordered systems that I contribute to develop finds applications in various branches of science – biology, economics and finance, information theory, computer science, statistics, signal processing. In recent years my research has focused on information processing in neural networks, machine learning and deep networks. I am particularly interested in the theoretical impact of data structure on learning strategies and generalization performance.
Selected Publications
On the nature of the spin glass phase
Phys. Rev. Lett. 52, 1984
SK model: the replica solution without replicas
Europhys. Lett. 1 (1985) 77, 1985
The space of interactions in neural networks: Gardner's computation with the cavity method
J. Physics A22 (1989) 2181, 1989
Storage capacity of memory networks with binary couplings
Journal de Physique 50 (1989) 3057., 1989
Elasticity model of a supercoiled DNA molecule
Phys. Rev. Lett. 80 (1998) 1556, 1998
Thermodynamics of glasses: a first principle computation
J. Phys. Condens. Matter 11 (1999) A157-A165., 1999
Analytic and Algorithmic Solution of Random Satisfiability Problems
Science 297 (2002) 812, 2002
Reconstruction on trees and spin glass transition
, J. Stat. Phys. 124 (2006) 1317-1350, 2006
Threshold values of Random K-SAT from the cavity method
Arxiv, 2006
Statistical physics-based reconstruction in compressed sensing
Phys. Rev. X 2 (2012) 021005, 2012
Belief Propagation Reconstruction for Discrete Tomography
Inverse Problems 29, 3 (2013) 035003, 2013
Modelling the influence of data structure on learning in neural networks: the hidden manifold model
Phys.Rev. X.10.041044, 2019
Generalization in learning with random features and the hidden manifold model
International Conference of Machine Learning, ICML 2020, 2020
Epidemic mitigation by statistical inference from contact tracing data
, PNAS (2021 ): 118 (32) e2106548118, 2021