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Topological Exploration of High-Dimensional Empirical Risk Landscapes: general approach, and applications to phase retrieval
Antoine Maillard, Tony Bonnaire, Giulio Biroli
We consider the landscape of empirical risk minimization for high-dimensional Gaussian single-index models (generalized linear models). The objective is to recover an unknown signa…
Boltzmann generators for amorphous particle systems
Louis Grenioux, Leonardo Galliano, Ludovic Berthier +2
Sampling configurations in thermodynamic equilibrium is a long-standing challenge in statistical physics. Boltzmann generators address this problem by employing generative models t…
An analytic theory of shallow networks dynamics for hinge loss classification
Franco Pellegrini, Giulio Biroli
Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is sti…
Landscape Complexity for the Empirical Risk of Generalized Linear Models
Antoine Maillard, Gérard Ben Arous, Giulio Biroli
We present a method to obtain the average and the typical value of the number of critical points of the empirical risk landscape for generalized linear estimation problems and vari…
How to iron out rough landscapes and get optimal performances: Averaged Gradient Descent and its application to tensor PCA
Giulio Biroli, Chiara Cammarota, Federico Ricci-Tersenghi
In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be…
Comparing Dynamics: Deep Neural Networks versus Glassy Systems
M. Baity-Jesi, L. Sagun, M. Geiger +6
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (…