Marvels and pitfalls of the langevin algorithm in noisy high-dimensional inference, 2018. ,
Deep learning without poor local minima, Advances in Neural Information Processing Systems, pp.586-594, 2016. ,
No bad local minima: Data independent training error guarantees for multilayer neural networks, 2016. ,
Matrix completion has no spurious local minimum, Advances in Neural Information Processing Systems, pp.2973-2981, 2016. ,
Topology and geometry of half-rectified network optimization, 2016. ,
Global optimality of local search for low rank matrix recovery, Advances in Neural Information Processing Systems, pp.3873-3881, 2016. ,
Non-square matrix sensing without spurious local minima via the Burer-Monteiro approach, In Artificial Intelligence and Statistics, pp.65-74, 2017. ,
Gradient descent learns one-hidden-layer cnn: Don't be afraid of spurious local minima, 2017. ,
No spurious local minima in nonconvex low rank problems: A unified geometric analysis, Proceedings of the 34th International Conference on Machine Learning, pp.1233-1242, 2017. ,
Depth creates no bad local minima, 2017. ,
Complexity of random energy landscapes, glass transition, and absolute value of the spectral determinant of random matrices, Physical review letters, vol.92, issue.24, p.240601, 2004. ,
The landscape of the spiked tensor model, 2017. ,
The spherical p-spin interaction spin-glass model, Zeitschrift für Physik B Condensed Matter, vol.92, issue.2, pp.257-271, 1993. ,
Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model, Physical Review Letters, vol.71, issue.1, p.173, 1993. ,
On the distribution of the largest eigenvalue in principal components analysis, Annals of statistics, pp.295-327, 2001. ,
A statistical model for tensor PCA, Advances in Neural Information Processing Systems, pp.2897-2905, 2014. ,
, , 2009.
High-dimensional random fields and random matrix theory, Markov Processes Relat. Fields, vol.21, pp.483-518, 2015. ,
Complex energy landscapes in spiked-tensor and simple glassy models: Ruggedness, arrangements of local minima, and phase transitions, Physical Review X, vol.9, issue.1, p.11003, 2019. ,
On the glassy nature of the hard phase in inference problems, 2018. ,
URL : https://hal.archives-ouvertes.fr/cea-01930645
Cugliandolo-Kurchan equations for dynamics of spin-glasses, Probability theory and related fields, vol.136, pp.619-660, 2006. ,
Message-passing algorithms for compressed sensing, Proceedings of the National Academy of Sciences, vol.106, issue.45, pp.18914-18919, 2009. ,
State evolution for general approximate message passing algorithms, with applications to spatial coupling. Information and Inference: A, Journal of the IMA, vol.2, issue.2, pp.115-144, 2013. ,
Constrained low-rank matrix estimation: Phase transitions, approximate message passing and applications, Journal of Statistical Mechanics: Theory and Experiment, vol.2017, issue.7, p.73403, 2017. ,
URL : https://hal.archives-ouvertes.fr/cea-01447222
Graphical models concepts in compressed sensing, Compressed Sensing: Theory and Applications, pp.394-438, 2012. ,
Typology of phase transitions in bayesian inference problems ,
URL : https://hal.archives-ouvertes.fr/cea-01933097