More is different.
"The constructionist hypothesis breaks down when confronted with the twin difficulties of scale and complexity. The behavior of large and complex aggregates of elementary particles, it turns out, is not to be understood in terms of a simple extrapolation of the properties of a few particles. Instead, at each level of complexity entirely new properties appear, and the understanding of the new behaviors requires research which I think is as fundamental in its nature as any other."
P. W. Anderson
Research interests
My research currently focuses on applications of Mathematical and Statistical Physics techniques to Statistics and Information Theory, with a particular emphasis on spin-glasses, whose theory earned Giorgio Parisi the Nobel Prize for Physics in 2021. Some of these techniques can also be used to establish the fundamental limits of performance of some simple neural networks of Artificial Intelligence.
I currently have active collaborations with the University of Bologna, Bocconi University (Milan), Harvard University, and more to come!
Publications and preprints
Fundamental limits of overparametrized shallow neural networks for supervised learning
Francesco Camilli, Daria Tieplova, Jean Barbier, arXive e-prints (2023) https://doi.org/10.48550/arXiv.2307.05635
Central limit theorem for the overlaps on the Nishimori line
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione, arXive e-prints (2023), https://doi.org/10.48550/arXiv.2305.19943
The Decimation Scheme for Symmetric Matrix Factorization
Francesco Camilli and Marc Mézard, arXive e-prints (2023), https://doi.org/10.48550/arXiv.2307.16564
Matrix factorization with neural networks
Francesco Camilli, Marc Mézard, Phys. Rev E 107, 064308 (2023), https://doi.org/10.1103/PhysRevE.107.064308
Fundamental limits in structured principal component analysis and how to reach them
Jean Barbier, Francesco Camilli, Marco Mondelli, Manuel Sáenz, PNAS 120 (30) e2302028120 (2023) https://doi.org/10.1073/pnas.230202812
An inference problem in a mismatched setting: a spin-glass model with Mattis interaction
Francesco Camilli, Pierluigi Contucci, Emanuele Mingione, SciPost Phys. 12, 125 (2022), doi: 10.21468/SciPostPhys.12.4.125
More structure in the noise!
Check out our interviews on "Fundamental limits in structured principal component analysis and how to reach them."
"Exploiting the Structure of Noise in Big Data", by Charlotte Philips
See also "Performance limits of Principal Components Analysis for large structured data sets" on Kudos!
The Multi-species Mean-Field Spin-Glass on the Nishimori Line
Alberici, D., Camilli, F., Contucci, P. et al., J Stat Phys 182, 2 (2021). https://doi.org/10.1007/s10955-020-02684-z
The Solution of the Deep Boltzmann Machine on the Nishimori Line
Alberici, D., Camilli, F., Contucci, P. et al. , Commun. Math. Phys. 387, 1191–1214 (2021). https://doi.org/10.1007/s00220-021-04165-0
A Statistical Physics approach to a multi-channel Wigner spiked model
Alberici, D., Camilli, F., Contucci, P. et al., Europhysics Letters 134 4 , 2022, DOI:10.1209/0295-5075/ac4794