no code implementations • 19 Oct 2021 • Gérard Ben Arous, Daniel Zhengyu Huang, Jiaoyang Huang
In this paper, we consider the singular values and singular vectors of low rank perturbations of large rectangular random matrices, in the regime the matrix is "long": we allow the number of rows (columns) to grow polynomially in the number of columns (rows).
no code implementations • 18 Jun 2020 • Gérard Ben Arous, Alexander S. Wein, Ilias Zadik
We study a variant of the sparse PCA (principal component analysis) problem in the "hard" regime, where the inference task is possible yet no polynomial-time algorithm is known to exist.
no code implementations • 4 Dec 2019 • Antoine Maillard, Gérard Ben Arous, Giulio Biroli
Under a technical hypothesis, we obtain a rigorous explicit variational formula for the annealed complexity, which is the logarithm of the average number of critical points at fixed value of the empirical risk.
1 code implementation • 30 Nov 2014 • Anna Choromanska, Mikael Henaff, Michael Mathieu, Gérard Ben Arous, Yann Lecun
We show that for large-size decoupled networks the lowest critical values of the random loss function form a layered structure and they are located in a well-defined band lower-bounded by the global minimum.
