826 citations · 2.5k across the 25 of their papers we have counts for
24 papers
Matrix factorization with neural networks
Francesco Camilli, Marc Mézard
Matrix factorization is an important mathematical problem encountered in the context of dictionary learning, recommendation systems and machine learning. We introduce a new `decima…
Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising
Antoine Maillard, Florent Krzakala, Marc Mézard +1
Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning,…
The cavity method for quantum disordered systems: from transverse random field ferromagnets to directed polymers in random media
Olga Dimitrova, Marc Mezard
After reviewing the basics of the cavity method in classical systems, we show how its quantum version, with some appropriate approximation scheme, can be used to study a system of…
Superconductor-Insulator transition and energy localization
M. V. Feigel'man, L. B. Ioffe, M. Mézard
We develop an analytical theory for generic disorder-driven quantum phase transitions. We apply this formalism to the superconductor-insulator transition and we briefly discuss the…
Thermodynamics of the Lévy spin glass
K. Janzen, A. Engel, M. Mézard
We investigate the Lévy glass, a mean-field spin glass model with power-law distributed couplings characterized by a divergent second moment. By combining extensively many small co…
The Levy spin glass transition
K. Janzen, A. Engel, M. Mézard
We determine the phase transition of the Levy spin glass. A regularized model where the coupling constants smaller than some cutoff are neglected can be studied by the cavity m…