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05/29/2023
Learning Two-Layer Neural Networks, One (Giant) Step at a Time
We study the training dynamics of shallow neural networks, investigating...
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05/29/2023
Escaping mediocrity: how two-layer networks learn hard single-index models with SGD
This study explores the sample complexity for two-layer neural networks ...
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03/05/2023
Expectation consistency for calibration of neural networks
Despite their incredible performance, it is well reported that deep neur...
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02/17/2023
Universality laws for Gaussian mixtures in generalized linear models
Let (x_i, y_i)_i=1,…,n denote independent samples from a general mixture...
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02/17/2023
Are Gaussian data all you need? Extents and limits of universality in high-dimensional generalized linear estimation
In this manuscript we consider the problem of generalized linear estimat...
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02/12/2023
From high-dimensional mean-field dynamics to dimensionless ODEs: A unifying approach to SGD in two-layers networks
This manuscript investigates the one-pass stochastic gradient descent (S...
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02/01/2023
Deterministic equivalent and error universality of deep random features learning
This manuscript considers the problem of learning a random Gaussian netw...
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10/23/2022
A study of uncertainty quantification in overparametrized high-dimensional models
Uncertainty quantification is a central challenge in reliable and trustw...
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05/26/2022
Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap
A simple model to study subspace clustering is the high-dimensional k-Ga...
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05/26/2022
Gaussian Universality of Linear Classifiers with Random Labels in High-Dimension
While classical in many theoretical settings, the assumption of Gaussian...
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05/18/2022
Secure Coding via Gaussian Random Fields
Inverse probability problems whose generative models are given by strict...
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03/22/2022
Learning curves for the multi-class teacher-student perceptron
One of the most classical results in high-dimensional learning theory pr...
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02/07/2022
Theoretical characterization of uncertainty in high-dimensional linear classification
Being able to reliably assess not only the accuracy but also the uncerta...
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02/01/2022
Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks
Despite the non-convex optimization landscape, over-parametrized shallow...
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01/31/2022
Fluctuations, Bias, Variance Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension
From the sampling of data to the initialisation of parameters, randomnes...
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01/29/2022
Error Rates for Kernel Classification under Source and Capacity Conditions
In this manuscript, we consider the problem of kernel classification und...
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01/19/2022
Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learning
Unlike the classical linear model, nonlinear generative models have been...
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06/07/2021
Learning Gaussian Mixtures with Generalised Linear Models: Precise Asymptotics in High-dimensions
Generalised linear models for multi-class classification problems are on...
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06/01/2021
The Gaussian equivalence of generative models for learning with shallow neural networks
Understanding the impact of data structure on the computational tractabi...
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05/31/2021
Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime
In this manuscript we consider Kernel Ridge Regression (KRR) under the G...
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02/16/2021
Capturing the learning curves of generic features maps for realistic data sets with a teacher-student model
Teacher-student models provide a powerful framework in which the typical...
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06/09/2020
Phase retrieval in high dimensions: Statistical and computational phase transitions
We consider the phase retrieval problem of reconstructing a n-dimensiona...
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02/21/2020
Generalisation error in learning with random features and the hidden manifold model
We study generalised linear regression and classification for a syntheti...
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12/04/2019
Exact asymptotics for phase retrieval and compressed sensing with random generative priors
We consider the problem of compressed sensing and of (real-valued) phase...
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05/29/2019