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Wide flat minima and optimal generalization in classifying high-dimensional Gaussian mixtures

Oct 27, 2020
Carlo Baldassi, Enrico M. Malatesta, Matteo Negri, Riccardo Zecchina

* 18 pages, 4 figures. arXiv admin note: text overlap with arXiv:2006.07897 

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Entropic gradient descent algorithms and wide flat minima

Jun 14, 2020
Fabrizio Pittorino, Carlo Lucibello, Christoph Feinauer, Enrico M. Malatesta, Gabriele Perugini, Carlo Baldassi, Matteo Negri, Elizaveta Demyanenko, Riccardo Zecchina

* 24 pages (main text: 8 pages) 

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Clustering of solutions in the symmetric binary perceptron

Nov 18, 2019
Carlo Baldassi, Riccardo Della Vecchia, Carlo Lucibello, Riccardo Zecchina


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Natural representation of composite data with replicated autoencoders

Sep 29, 2019
Matteo Negri, Davide Bergamini, Carlo Baldassi, Riccardo Zecchina, Christoph Feinauer

* 11 pages, 4 figures 

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On the geometry of solutions and on the capacity of multi-layer neural networks with ReLU activations

Jul 17, 2019
Carlo Baldassi, Enrico M. Malatesta, Riccardo Zecchina

* 11 pages, 3 figures 

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Shaping the learning landscape in neural networks around wide flat minima

May 21, 2019
Carlo Baldassi, Fabrizio Pittorino, Riccardo Zecchina

* 46 pages (20 main text), 7 figures (v2 fixes fig. 1 and a few typos in formulas) 

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On the role of synaptic stochasticity in training low-precision neural networks

Mar 20, 2018
Carlo Baldassi, Federica Gerace, Hilbert J. Kappen, Carlo Lucibello, Luca Saglietti, Enzo Tartaglione, Riccardo Zecchina

* Phys. Rev. Lett. 120, 268103 (2018) 
* 7 pages + 14 pages of supplementary material 

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Efficiency of quantum versus classical annealing in non-convex learning problems

Oct 16, 2017
Carlo Baldassi, Riccardo Zecchina

* Proceedings of the National Academy of Sciences Jan 2018, 201711456 
* 31 pages, 10 figures 

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Parle: parallelizing stochastic gradient descent

Sep 10, 2017
Pratik Chaudhari, Carlo Baldassi, Riccardo Zecchina, Stefano Soatto, Ameet Talwalkar, Adam Oberman


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Entropy-SGD: Biasing Gradient Descent Into Wide Valleys

Apr 21, 2017
Pratik Chaudhari, Anna Choromanska, Stefano Soatto, Yann LeCun, Carlo Baldassi, Christian Borgs, Jennifer Chayes, Levent Sagun, Riccardo Zecchina

* ICLR '17 

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Unreasonable Effectiveness of Learning Neural Networks: From Accessible States and Robust Ensembles to Basic Algorithmic Schemes

Oct 06, 2016
Carlo Baldassi, Christian Borgs, Jennifer Chayes, Alessandro Ingrosso, Carlo Lucibello, Luca Saglietti, Riccardo Zecchina

* Proc. Natl. Acad. Sci. U.S.A. 113(48):E7655-E7662, 2016 
* 31 pages (14 main text, 18 appendix), 12 figures (6 main text, 6 appendix) 

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Learning may need only a few bits of synaptic precision

May 27, 2016
Carlo Baldassi, Federica Gerace, Carlo Lucibello, Luca Saglietti, Riccardo Zecchina

* Phys. Rev. E 93, 052313 (2016) 
* 38 pages (main text: 16 pages), 5 figures; http://link.aps.org/doi/10.1103/PhysRevE.93.052313 

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Local entropy as a measure for sampling solutions in Constraint Satisfaction Problems

Feb 25, 2016
Carlo Baldassi, Alessandro Ingrosso, Carlo Lucibello, Luca Saglietti, Riccardo Zecchina

* J. Stat. Mech. 2016 (2) 023301 
* 46 pages (main text: 22), 7 figures. This is an author-created, un-copyedited version of an article published in Journal of Statistical Mechanics: Theory and Experiment. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at http://dx.doi.org/10.1088/1742-5468/2016/02/023301 

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Subdominant Dense Clusters Allow for Simple Learning and High Computational Performance in Neural Networks with Discrete Synapses

Sep 18, 2015
Carlo Baldassi, Alessandro Ingrosso, Carlo Lucibello, Luca Saglietti, Riccardo Zecchina

* Physical Review Letters, 15, 128101 (2015) url=http://journals.aps.org/prl/abstract/10.1103/PhysRevLett.115.128101 
* 11 pages, 4 figures (main text: 5 pages, 3 figures; Supplemental Material: 6 pages, 1 figure) 

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Message passing for quantified Boolean formulas

Feb 12, 2012
Pan Zhang, Abolfazl Ramezanpour, Lenka Zdeborová, Riccardo Zecchina

* J. Stat. Mech. (2012) P05025 
* 14 pages, 7 figures 

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Belief-Propagation for Weighted b-Matchings on Arbitrary Graphs and its Relation to Linear Programs with Integer Solutions

Aug 04, 2011
Mohsen Bayati, Christian Borgs, Jennifer Chayes, Riccardo Zecchina

* SIAM J. Discrete Math. 2011, Vol 25, Issue 2, pp. 989-1011 
* 28 pages, 2 figures. Submitted to SIAM journal on Discrete Mathematics on March 19, 2009; accepted for publication (in revised form) August 30, 2010; published electronically July 1, 2011 

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Efficient supervised learning in networks with binary synapses

Jul 09, 2007
Carlo Baldassi, Alfredo Braunstein, Nicolas Brunel, Riccardo Zecchina

* PNAS 104, 11079-11084 (2007) 
* 10 pages, 4 figures 

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Learning by message-passing in networks of discrete synapses

Dec 09, 2005
Alfredo Braunstein, Riccardo Zecchina

* Phys. Rev. Lett. 96, 030201 (2006) 
* 4 pages, 3 figures; references updated and minor corrections; accepted in PRL 

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