Transversal mappings and flows, 1967. ,
Convergence of the iterates of descent methods for analytic cost functions, SIAM Journal on Optimization, vol.16, issue.2, pp.531-547, 2005. ,
Gradient flows: in metric spaces and in the space of probability measures, 2008. ,
Breaking the curse of dimensionality with convex neural networks, Journal of Machine Learning Research, vol.18, issue.19, pp.1-53, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01098505
A family of functional inequalities: ?ojasiewicz inequalities and displacement convex functions, 2016. ,
DOI : 10.1016/j.jfa.2018.06.014
URL : http://publications.ut-capitole.fr/26111/1/Blanchet_2611.pdf
The alternating descent conditional gradient method for sparse inverse problems, SIAM Journal on Optimization, vol.27, issue.2, pp.616-639, 2017. ,
DOI : 10.1109/camsap.2015.7383735
URL : http://arxiv.org/pdf/1507.01562
Inverse problems in spaces of measures. ESAIM: Control, Optimisation and Calculus of Variations, vol.19, pp.190-218, 2013. ,
DOI : 10.1051/cocv/2011205
URL : https://www.esaim-cocv.org/articles/cocv/pdf/2013/01/cocv110109.pdf
Fixed point theory and nonlinear problems, Proc. Sym. Pure. Math, vol.39, pp.49-88, 1983. ,
A low-rank approach to off-the-grid sparse deconvolution, Journal of Physics: Conference Series, vol.904, issue.1, p.12015, 2017. ,
DOI : 10.1088/1742-6596/904/1/012015
URL : https://hal.archives-ouvertes.fr/hal-01672896
Measure theory, vol.165, 1980. ,
Proximal splitting methods in signal processing, Fixed-point algorithms for inverse problems in science and engineering, pp.185-212, 2011. ,
Exact reconstruction using Beurling minimal extrapolation, Journal of Mathematical Analysis and applications, vol.395, issue.1, pp.336-354, 2012. ,
URL : https://hal.archives-ouvertes.fr/hal-00678423
Exact support recovery for sparse spikes deconvolution, Foundations of Computational Mathematics, vol.15, issue.5, pp.1315-1355, 2015. ,
DOI : 10.1007/s10208-014-9228-6
URL : https://hal.archives-ouvertes.fr/hal-00839635
Deep Learning, 2016. ,
Implicit regularization in matrix factorization, Advances in Neural Information Processing Systems, vol.30, 2017. ,
DOI : 10.1109/ita.2018.8503198
URL : http://arxiv.org/pdf/1705.09280
Global optimality in neural network training, Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp.7331-7339, 2017. ,
Kurdyka-?ojasiewicz-Simon inequality for gradient flows in metric spaces, 2017. ,
Neural Networks: A Comprehensive Foundation, 1994. ,
Revisiting Frank-Wolfe: Projection-free sparse convex optimization, Proceedings of the International Conference on Machine Learning (ICML), 2013. ,
Low-rank optimization on the cone of positive semidefinite matrices, SIAM Journal on Optimization, vol.20, issue.5, pp.2327-2351, 2010. ,
Stochastic approximation and recursive algorithms and applications, vol.35, 2003. ,
, Moments, positive polynomials and their applications, vol.1, 2010.
DOI : 10.1142/p665
Convergence analysis of two-layer neural networks with ReLU activation, Advances in Neural Information Processing Systems, pp.597-607, 2017. ,
A mean field view of the landscape of two-layer neural networks, Proceedings of the National Academy of Sciences, vol.115, issue.33, pp.7665-7671, 2018. ,
Stochastic particle gradient descent for infinite ensembles, 2017. ,
A dual certificates analysis of compressive off-the-grid recovery, 2018. ,
, Convex Analysis, 1997.
, Neural networks as interacting particle systems: Asymptotic convexity of the loss landscape and universal scaling of the approximation error, 2018.
Optimal transport for applied mathematicians, 2015. ,
DOI : 10.1007/978-3-319-20828-2
, Filippo Santambrogio. {Euclidean, metric, and Wasserstein} gradient flows: an overview, Bulletin of Mathematical Sciences, vol.7, issue.1, pp.87-154, 2017.
Integration methods and optimization algorithms, Advances in Neural Information Processing Systems, pp.1109-1118, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01474045
, Mean field analysis of neural networks, 2018.
Theoretical insights into the optimization landscape of over-parameterized shallow neural networks, 2017. ,
Exponentially vanishing sub-optimal local minima in multilayer neural networks, 2017. ,
Neural networks with finite intrinsic dimension have no spurious valleys, 2018. ,
Functional Frank-Wolfe boosting for general loss functions, 2015. ,
A function not constant on a connected set of critical points, Duke Mathematical Journal, vol.1, issue.4, pp.514-517, 1935. ,