Florent Gérard Krzakala

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Publications associées (66)

Gaussian universality of perceptrons with random labels

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

While classical in many theoretical settings-and in particular in statistical physics-inspired works-the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we ...

Amer Physical Soc2024

On the atypical solutions of the symmetric binary perceptron

Florent Gérard Krzakala, Lenka Zdeborová

We study the random binary symmetric perceptron problem, focusing on the behavior of rare high-margin solutions. While most solutions are isolated, we demonstrate that these rare solutions are part of clusters of extensive entropy, heuristically correspond ...

Iop Publishing Ltd2024

Statistical mechanics of the maximum-average submatrix problem

Florent Gérard Krzakala, Lenka Zdeborová, Vittorio Erba

We study the maximum-average submatrix problem, wherein given an N x N matrix J, one needs to find the k x k submatrix with the largest average number of entries. We investigate the problem for random matrices J, whose entries are i.i.d. random variables, ...

Iop Publishing Ltd2024

Sampling with flows, diffusion, and autoregressive neural networks from a spin-glass perspective

Florent Gérard Krzakala, Lenka Zdeborová

Recent years witnessed the development of powerful generative models based on flows, diffusion, or autoregressive neural networks, achieving remarkable success in generating data from examples with applications in a broad range of areas. A theoretical anal ...

Proceedings of the National Academy of Sciences2024

Les Houches 2022 Special Issue: Editorial

Florent Gérard Krzakala, Lenka Zdeborová

IOP Publishing Ltd2024

Spectral Phase Transition and Optimal PCA in Block-Structured Spiked Models

Florent Gérard Krzakala, Pierre Mergny

We discuss the inhomogeneous Wigner spike model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random matrix theory, with a specific focus on its spectral properties. Our primary o ...

2024

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

Florent Gérard Krzakala, Luca Pesce, Bruno Loureiro, Ludovic Théo Stephan

For high-dimensional Gaussian data, we investigate theoretically how the features of a two-layer neural network adapt to the structure of the target function through a few large batch gradient descent steps, leading to an improvement in the approximation c ...

2024

Asymptotic Characterisation of the Performance of Robust Linear Regression in the Presence of Outliers

Florent Gérard Krzakala, Emanuele Troiani, Vittorio Erba

We study robust linear regression in highdimension, when both the dimension d and the number of data points n diverge with a fixed ratio α = n/d, and study a data model that includes outliers. We provide exact asymptotics for the performances of the empiri ...

2024

Rigorous Dynamical Mean-Field Theory for Stochastic Gradient Descent Methods

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani

We prove closed-form equations for the exact high-dimensional asymptotics of a family of first-order gradient-based methods, learning an estimator (e.g., M-estimator, shallow neural network) from observations on Gaussian data with empirical risk minimizati ...

Society for Industrial & Applied Mathematics (SIAM)2024

Online Learning and Information Exponents: On The Importance of Batch size, and Time/Complexity Tradeoffs

Florent Gérard Krzakala, Luca Pesce, Bruno Loureiro, Ludovic Théo Stephan

We study the impact of the batch

n_b

on the iteration time

T

of training two-layer neural networks with one-pass stochastic gradient descent (SGD) on multi-index target functions of isotropic covariates. We characterize the optimal batch size minimizin ...

JMLR2024

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n_b

on the iteration time

T

of training two-layer neural networks with one-pass stochastic gradient descent (SGD) on multi-index target functions of isotropic covariates. We characterize the optimal batch size minimizin ...

JMLR2024