113 citations · 392 across the 22 of their papers we have counts for
5 papers · 1 filter
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…
Optimal scaling laws in learning hierarchical multi-index models
Leonardo Defilippis, Florent Krzakala, Bruno Loureiro +1
In this work, we provide a sharp theory of scaling laws for two-layer neural networks trained on a class of hierarchical multi-index targets, in a genuinely representation-limited…
Fundamental Limits of Matrix Sensing: Exact Asymptotics, Universality, and Applications
Yizhou Xu, Antoine Maillard, Lenka Zdeborová +1
In the matrix sensing problem, one wishes to reconstruct a matrix from (possibly noisy) observations of its linear projections along given directions. We consider this model in the…
Bayes-optimal learning of an extensive-width neural network from quadratically many samples
Antoine Maillard, Emanuele Troiani, Simon Martin +2
We consider the problem of learning a target function corresponding to a single hidden layer neural network, with a quadratic activation function after the first layer, and random…
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…