Publications by Florent Gérard Krzakala

A phase transition between positional and semantic learning in a solvable model of dot-product attention

Florent Gérard Krzakala, Lenka Zdeborová, Freya Behrens, Hugo Chao Cui

Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements in the model capabilities. Yet, a theoretical characterization of how such mecha ...

2025

Estimating Rank-One Matrices with Mismatched Prior and Noise: Universality and Large Deviations

Florent Gérard Krzakala, Lenka Zdeborová

We prove a universality result that reduces the free energy of rank-one matrix estimation problems in the setting of mismatched prior and noise to the computation of the free energy for a modified Sherrington–Kirkpatrick spin glass. Our main result is an a ...

2025

Phase Diagram of Compressed Sensing with l0-norm Regularization

Florent Gérard Krzakala, Lenka Zdeborová

Noiseless compressive sensing is a two-step setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on l(1) regularization, provides an efficient and robust way to address thi ...

IOP Publishing Ltd2025

Bayes-optimal learning of deep random networks of extensive-width*

Florent Gérard Krzakala, Lenka Zdeborová, Hugo Chao Cui

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

IOP Publishing Ltd2025

Low-rank matrix estimation with inhomogeneous noise

Florent Gérard Krzakala, Lenka Zdeborová

We study low-rank matrix estimation for a generic inhomogeneous output channel through which the matrix is observed. This generalizes the commonly considered spiked matrix model with homogeneous noise to include for instance the dense degree-corrected stoc ...

2025

A High Dimensional Statistical Model for Adversarial Training: Geometry and Trade-Offs

Florent Gérard Krzakala, Bruno Loureiro

This work investigates adversarial training in the context of margin-based linear classifiers in the high-dimensional regime where the dimension d and the number of data points n diverge with a fixed ratio α = n/d. We introduce a tractable mathematical mod ...

2025

Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression

Florent Gérard Krzakala, Lenka Zdeborová, Adrien Vandenbroucque, Lucas Andry Clarte, Bruno Loureiro

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic descripti ...

ACM2024

Asymptotics of feature learning in two-layer networks after one gradient-step

Florent Gérard Krzakala, Lenka Zdeborová, Luca Pesce, Yue Lu, Bruno Loureiro, Hugo Chao Cui

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al., 2022), we model t ...

2024

Universality laws for Gaussian mixtures in generalized linear models

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Ludovic Théo Stephan

A recent line of work in high-dimensional statistics working under the Gaussian mixture hypothesis has led to a number of results in the context of empirical risk minimization, Bayesian uncertainty quantification, separation of kernel methods and neural ne ...

2024

The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Luca Pesce

We investigate the training dynamics of two-layer neural networks when learning multi-index target functions. We focus on multi-pass gradient descent (GD) that reuses the batches multiple times and show that it significantly changes the conclusion about wh ...

JMLR2024