Florent Krzakala

research

∙ 05/30/2023

Asymptotic Characterisation of Robust Empirical Risk Minimisation Performance in the Presence of Outliers

We study robust linear regression in high-dimension, when both the dimen...

0 Matteo Vilucchio, et al. ∙

research

∙ 05/29/2023

Learning Two-Layer Neural Networks, One (Giant) Step at a Time

We study the training dynamics of shallow neural networks, investigating...

0 Yatin Dandi, et al. ∙

research

∙ 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 ...

0 Luca Arnaboldi, et al. ∙

research

∙ 03/09/2023

Statistical mechanics of the maximum-average submatrix problem

We study the maximum-average submatrix problem, in which given an N × N ...

0 Vittorio Erba, et al. ∙

research

∙ 03/05/2023

Expectation consistency for calibration of neural networks

Despite their incredible performance, it is well reported that deep neur...

0 Lucas Clarté, et al. ∙

research

∙ 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...

1 Yatin Dandi, et al. ∙

research

∙ 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...

0 Luca Pesce, et al. ∙

research

∙ 02/13/2023

Optimal Algorithms for the Inhomogeneous Spiked Wigner Model

In this paper, we study a spiked Wigner problem with an inhomogeneous no...

0 Aleksandr Pak, et al. ∙

research

∙ 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...

8 Luca Arnaboldi, et al. ∙

research

∙ 02/01/2023

Optimal Learning of Deep Random Networks of Extensive-width

We consider the problem of learning a target function corresponding to a...

0 Hugo Cui, et al. ∙

research

∙ 10/23/2022

A study of uncertainty quantification in overparametrized high-dimensional models

Uncertainty quantification is a central challenge in reliable and trustw...

7 Lucas Clarté, et al. ∙

research

∙ 10/12/2022

Rigorous dynamical mean field theory for stochastic gradient descent methods

We prove closed-form equations for the exact high-dimensional asymptotic...

0 Cédric Gerbelot, et al. ∙

research

∙ 08/11/2022

Low-rank Matrix Estimation with Inhomogeneous Noise

We study low-rank matrix estimation for a generic inhomogeneous output c...

0 Alice Guionnet, et al. ∙

research

∙ 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...

2 Luca Pesce, et al. ∙

research

∙ 05/26/2022

Multi-layer State Evolution Under Random Convolutional Design

Signal recovery under generative neural network priors has emerged as a ...

0 Max Daniels, et al. ∙

research

∙ 05/26/2022

Gaussian Universality of Linear Classifiers with Random Labels in High-Dimension

While classical in many theoretical settings, the assumption of Gaussian...

8 Federica Gerace, et al. ∙

research

∙ 05/18/2022

Secure Coding via Gaussian Random Fields

Inverse probability problems whose generative models are given by strict...

0 Ali Bereyhi, et al. ∙

research

∙ 03/15/2022

Optimal denoising of rotationally invariant rectangular matrices

In this manuscript we consider denoising of large rectangular matrices: ...

0 Emanuele Troiani, et al. ∙

research

∙ 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...

5 Lucas Clarté, et al. ∙

research

∙ 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...

46 Rodrigo Veiga, et al. ∙

research

∙ 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...

6 Bruno Loureiro, et al. ∙

research

∙ 01/29/2022

Error Rates for Kernel Classification under Source and Capacity Conditions

In this manuscript, we consider the problem of kernel classification und...

7 Hugo Cui, et al. ∙

research

∙ 01/19/2022

Bayesian Inference with Nonlinear Generative Models: Comments on Secure Learning

Unlike the classical linear model, nonlinear generative models have been...

7 Ali Bereyhi, et al. ∙

research

∙ 10/17/2021

Perturbative construction of mean-field equations in extensive-rank matrix factorization and denoising

Factorization of matrices where the rank of the two factors diverges lin...

0 Antoine Maillard, et al. ∙

research

∙ 07/25/2021

LightOn Optical Processing Unit: Scaling-up AI and HPC with a Non von Neumann co-processor

We introduce LightOn's Optical Processing Unit (OPU), the first photonic...

0 Charles Brossollet, et al. ∙

research

∙ 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...

14 Bruno Loureiro, et al. ∙

research

∙ 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...

3 Hugo Cui, et al. ∙

research

∙ 05/16/2021

Bayesian reconstruction of memories stored in neural networks from their connectivity

The advent of comprehensive synaptic wiring diagrams of large neural cir...

0 Sebastian Goldt, et al. ∙

research

∙ 02/23/2021

Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed

A recent series of theoretical works showed that the dynamics of neural ...

0 Maria Refinetti, et al. ∙

research

∙ 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...

6 Bruno Loureiro, et al. ∙

research

∙ 01/06/2021

Adversarial Robustness by Design through Analog Computing and Synthetic Gradients

We propose a new defense mechanism against adversarial attacks inspired ...

5 Alessandro Cappelli, et al. ∙

research

∙ 12/11/2020

Hardware Beyond Backpropagation: a Photonic Co-Processor for Direct Feedback Alignment

The scaling hypothesis motivates the expansion of models past trillions ...

16 Julien Launay, et al. ∙

research

∙ 12/08/2020

Construction of optimal spectral methods in phase retrieval

We consider the phase retrieval problem, in which the observer wishes to...

0 Antoine Maillard, et al. ∙

research

∙ 09/20/2020

Epidemic mitigation by statistical inference from contact tracing data

Contact-tracing is an essential tool in order to mitigate the impact of ...

4 Antoine Baker, et al. ∙

research

∙ 06/25/2020

The Gaussian equivalence of generative models for learning with two-layer neural networks

Understanding the impact of data structure on learning in neural network...

87 Sebastian Goldt, et al. ∙

research

∙ 06/23/2020

Direct Feedback Alignment Scales to Modern Deep Learning Tasks and Architectures

Despite being the workhorse of deep learning, the backpropagation algori...

5 Julien Launay, et al. ∙

research

∙ 06/12/2020

Reservoir Computing meets Recurrent Kernels and Structured Transforms

Reservoir Computing is a class of simple yet efficient Recurrent Neural ...

0 Jonathan Dong, et al. ∙

research

∙ 06/12/2020

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Despite the widespread use of gradient-based algorithms for optimizing h...

0 Stefano Sarao Mannelli, et al. ∙

research

∙ 06/11/2020

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (or : How to Prove Kabashima's Replica Formula)

There has been a recent surge of interest in the study of asymptotic rec...

11 Cédric Gerbelot, et al. ∙

research

∙ 06/11/2020

Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization

We consider a commonly studied supervised classification of a synthetic ...

9 Benjamin Aubin, et al. ∙

research

∙ 06/10/2020

Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification

We analyze in a closed form the learning dynamics of stochastic gradient...

57 Francesca Mignacco, et al. ∙

research

∙ 06/09/2020

Phase retrieval in high dimensions: Statistical and computational phase transitions

We consider the phase retrieval problem of reconstructing a n-dimensiona...

0 Antoine Maillard, et al. ∙

research

∙ 06/02/2020

Light-in-the-loop: using a photonics co-processor for scalable training of neural networks

As neural networks grow larger and more complex and data-hungry, trainin...

11 Julien Launay, et al. ∙

research

∙ 04/03/2020

TRAMP: Compositional Inference with TRee Approximate Message Passing

We introduce tramp, standing for TRee Approximate Message Passing, a pyt...

19 Antoine Baker, et al. ∙

research

∙ 03/02/2020

Double Trouble in Double Descent : Bias and Variance(s) in the Lazy Regime

Deep neural networks can achieve remarkable generalization performances ...

19 Stéphane d'Ascoli, et al. ∙

research

∙ 02/26/2020

The role of regularization in classification of high-dimensional noisy Gaussian mixture

We consider a high-dimensional mixture of two Gaussians in the noisy reg...

35 Francesca Mignacco, et al. ∙

research

∙ 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...

28 Federica Gerace, et al. ∙

research

∙ 02/11/2020

Asymptotic errors for convex penalized linear regression beyond Gaussian matrices

We consider the problem of learning a coefficient vector x_0 in R^N from...

2 Cédric Gerbelot, et al. ∙

research

∙ 12/05/2019

Rademacher complexity and spin glasses: A link between the replica and statistical theories of learning

Statistical learning theory provides bounds of the generalization gap, u...

12 Alia Abbara, et al. ∙

research

∙ 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...

5 Benjamin Aubin, et al. ∙

Florent Krzakala

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