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SMILE SIGNED

Statistical Mechanics of Learning

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EC-Contrib. €

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Project "SMILE" data sheet

The following table provides information about the project.

Coordinator
CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS 

Organization address
address: RUE MICHEL ANGE 3
city: PARIS
postcode: 75794
website: www.cnrs.fr

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country France [FR]
 Total cost 1˙346˙795 €
 EC max contribution 1˙346˙795 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-09-01   to  2022-08-31

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE CNRS FR (PARIS) coordinator 1˙346˙795.00

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 Project objective

'Computers are now able to recognize people, to tell a dog from a cat, or to process speech so efficiently that they can answer complicated questions. This was still impossible only a decade ago. This progress is largely due to the development of the artificial “deep-learned neural networks”. Nowadays, “deep learning” is revolutionizing our life, prompting an economic battle between internet giants and the creation of a myriad of start-ups. As attractive and performant as it is, however, many agree that deep learning is largely an empirical field that lacks a theoretical understanding of its capacity and limitations. The algorithms used to 'train' these networks explore a very complex and non-convex energy landscape that eludes most of the present theoretical methodology in machine learning. The behavior of the dynamics in such complicated 'glassy' landscape is, however, similar to those that have been studied for decades in the physics of disordered systems such as molecular and spin glasses.

In this project we pursue this analogy and use advanced methods of disordered systems to develop a statistical mechanics approach to deep neural networks. Our first main objective is to create a model for learning features from data via a multi-level neural network. We then regard this model as a kind of a spin glass system amenable to an exact asymptotic analysis via the replica and cavity method. Analyzing its phase diagram and phase transitions shall bring theoretical understanding of the principles behind the empirical success of deep neural networks. This approach will also lead to our second objective: the creation of a new class of fast, efficient, and asymptotically optimal message passing algorithms for deep learning. It is the synergy between the theoretical statistical physics approach and scientific questions from computer science that makes the project’s objectives feasible and enables a leap forward in our understanding of learning from data.'

 Publications

year authors and title journal last update
List of publications.
2019 Benjamin Aubin, Antoine Maillard, Jean Barbier, Florent Krzakala, Nicolas Macris, Lenka Zdeborová
The committee machine: computational to statistical gaps in learning a two-layers neural network
published pages: 124023, ISSN: 1742-5468, DOI: 10.1088/1742-5468/ab43d2
Journal of Statistical Mechanics: Theory and Experiment 2019/12 2020-04-03
2019 Goldt, Sebastian; Advani, Madhu S.; Saxe, Andrew M.; Krzakala, Florent; Zdeborová, Lenka
Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setup
published pages: , ISSN: , DOI:
Advances in Neural Information Processing Systems 32 2020-04-03
2020 Stefano Sarao Mannelli, Giulio Biroli, Chiara Cammarota, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová
Marvels and Pitfalls of the Langevin Algorithm in Noisy High-Dimensional Inference
published pages: , ISSN: 2160-3308, DOI: 10.1103/physrevx.10.011057
Physical Review X 10/1 2020-04-03
2019 Mannelli, Stefano Sarao; Biroli, Giulio; Cammarota, Chiara; Krzakala, Florent; Zdeborová, Lenka
Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model
published pages: , ISSN: , DOI:
Advances in Neural Information Processing Systems 32 2020-04-03
2020 Alia Abbara, Antoine Baker, Florent Krzakala, Lenka Zdeborová
On the universality of noiseless linear estimation with respect to the measurement matrix
published pages: 164001, ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab59ef
Journal of Physics A: Mathematical and Theoretical 53/16 2020-04-03
2020 Stefano Sarao Mannelli, Lenka Zdeborová
Thresholds of descending algorithms in inference problems
published pages: 34004, ISSN: 1742-5468, DOI: 10.1088/1742-5468/ab7123
Journal of Statistical Mechanics: Theory and Experiment 2020/3 2020-04-03
2019 Mannelli, Stefano Sarao; Krzakala, Florent; Urbani, Pierfrancesco; Zdeborová, Lenka
Passed & Spurious: Descent Algorithms and Local Minima in Spiked Matrix-Tensor Models
published pages: , ISSN: , DOI:
Proceedings of Machine Learning Research 2020-04-03
2019 Benjamin Aubin, Will Perkins, Lenka Zdeborová
Storage capacity in symmetric binary perceptrons
published pages: 294003, ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab227a
Journal of Physics A: Mathematical and Theoretical 52/29 2020-04-03
2019 Benjamin Aubin, Bruno Loureiro, Antoine Maillard, Florent Krzakala, Lenka Zdeborová
The spiked matrix model with generative priors
published pages: , ISSN: , DOI:
Advances in Neural Information Processing Systems 32 2020-04-03
2020 Christian Schmidt, Lenka Zdeborová
Dense limit of the Dawid–Skene model for crowdsourcing and regions of sub-optimality of message passing algorithms
published pages: 124001, ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab757f
Journal of Physics A: Mathematical and Theoretical 53/12 2020-04-03
2019 Antoine Maillard, Laura Foini, Alejandro Lage Castellanos, Florent Krzakala, Marc Mézard, Lenka Zdeborová
High-temperature expansions and message passing algorithms
published pages: 113301, ISSN: 1742-5468, DOI: 10.1088/1742-5468/ab4bbb
Journal of Statistical Mechanics: Theory and Experiment 2019/11 2020-04-03
2019 Goldt, Sebastian; Advani, Madhu S.; Saxe, Andrew M.; Krzakala, Florent; Zdeborová, Lenka
Generalisation dynamics of online learning in over-parameterised neural networks
published pages: , ISSN: , DOI:
https://hal-cea.archives-ouvertes.fr/cea-02009764 1 2020-04-03
2019 Marylou Gabrié, Andre Manoel, Clément Luneau, Jean Barbier, Nicolas Macris, Florent Krzakala, Lenka Zdeborová
Entropy and mutual information in models of deep neural networks
published pages: 124014, ISSN: 1742-5468, DOI: 10.1088/1742-5468/ab3430
Journal of Statistical Mechanics: Theory and Experiment 2019/12 2020-04-03
2019 Giuseppe Carleo, Ignacio Cirac, Kyle Cranmer, Laurent Daudet, Maria Schuld, Naftali Tishby, Leslie Vogt-Maranto, Lenka Zdeborová
Machine learning and the physical sciences
published pages: , ISSN: 0034-6861, DOI: 10.1103/RevModPhys.91.045002
Reviews of Modern Physics 91/4 2020-04-03
2020 Marylou Gabrié, Jean Barbier, Florent Krzakala, Lenka Zdeborova
Blind calibration for compressed sensing: State evolution and an online algorithm
published pages: , ISSN: 1751-8113, DOI: 10.1088/1751-8121/ab8416
Journal of Physics A: Mathematical and Theoretical 2020-04-03
2018 Amin Coja-Oghlan, Florent Krzakala, Will Perkins, Lenka Zdeborová
Information-theoretic thresholds from the cavity method
published pages: 694-795, ISSN: 0001-8708, DOI: 10.1016/j.aim.2018.05.029
Advances in Mathematics 333 2019-06-06
2019 Federico Ricci-Tersenghi, Guilhem Semerjian, Lenka Zdeborová
Typology of phase transitions in Bayesian inference problems
published pages: , ISSN: 2470-0045, DOI: 10.1103/PhysRevE.99.042109
Physical Review E 99/4 2019-06-06
2019 Fabrizio Antenucci, Silvio Franz, Pierfrancesco Urbani, Lenka Zdeborová
Glassy Nature of the Hard Phase in Inference Problems
published pages: , ISSN: 2160-3308, DOI: 10.1103/PhysRevX.9.011020
Physical Review X 9/1 2019-06-06
2019 Jean Barbier, Florent Krzakala, Nicolas Macris, Léo Miolane, Lenka Zdeborová
Optimal errors and phase transitions in high-dimensional generalized linear models
published pages: 5451-5460, ISSN: 0027-8424, DOI: 10.1073/pnas.1802705116
Proceedings of the National Academy of Sciences 116/12 2019-06-06
2019 Christian Schmidt, Henry D. Pfister, Lenka Zdeborová
Minimal sets to destroy the k -core in random networks
published pages: , ISSN: 2470-0045, DOI: 10.1103/PhysRevE.99.022310
Physical Review E 99/2 2019-06-06
2019 Fabrizio Antenucci, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová
Approximate survey propagation for statistical inference
published pages: 23401, ISSN: 1742-5468, DOI: 10.1088/1742-5468/aafa7d
Journal of Statistical Mechanics: Theory and Experiment 2019/2 2019-06-06

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