58 citations · 125 across the 9 of their papers we have counts for
9 papers
Singular perturbations and hierarchical learning in two-layer neural networks
Cédric Gerbelot, Jean-Christophe Mourrat
We study the population gradient flow of an infinitely wide two-layer neural network learning a misspecified single-index model in high dimension. The two layers are optimized join…
Asymptotics of Non-Convex Generalized Linear Models in High-Dimensions: A proof of the replica formula
Matteo Vilucchio, Yatin Dandi, Matéo Pirio Rossignol +2
The analytic characterization of the high-dimensional behavior of optimization for Generalized Linear Models (GLMs) with Gaussian data has been a central focus in statistics and pr…
Multi-layer State Evolution Under Random Convolutional Design
Mara Daniels, Cédric Gerbelot, Florent Krzakala +1
Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstructi…
Learning curves for the multi-class teacher-student perceptron
Elisabetta Cornacchia, Francesca Mignacco, Rodrigo Veiga +3
One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with the single-layer…
Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
Bruno Loureiro, Cédric Gerbelot, Maria Refinetti +2
From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered b…
Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions
Bruno Loureiro, Gabriele Sicuro, Cédric Gerbelot +3
Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise t…
Learning curves of generic features maps for realistic datasets with a teacher-student model
Bruno Loureiro, Cédric Gerbelot, Hugo Cui +4
Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussia…
Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)
Cedric Gerbelot, Alia Abbara, Florent Krzakala
There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student se…
Asymptotic errors for convex penalized linear regression beyond Gaussian matrices
Cédric Gerbelot, Alia Abbara, Florent Krzakala
We consider the problem of learning a coefficient vector in from noisy linear observations in in the high dimensional limit to infinity w…