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Florent Gérard Krzakala

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Publications associées (66)

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Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Nicolas Macris, Florent Gérard Krzakala, Jean François Emmanuel Barbier, Mohamad Baker Dia

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

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

Lenka Zdeborová, Florent Gérard Krzakala

Factorization of matrices where the rank of the two factors diverges linearly with their sizes has many applications in diverse areas such as unsupervised representation learning, dictionary learning or sparse coding. We consider a setting where the two fa ...

2022

Low-rank matrix estimation with inhomogeneous noise

Lenka Zdeborová, Florent Gérard Krzakala

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 ...

Oxford University Press2025

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

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

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

Multi-layer state evolution under random convolutional design

Lenka Zdeborová, Florent Gérard Krzakala

Signal recovery under generative neural network priors has emerged as a promising direction in statistical inference and computational imaging. Theoretical analysis of reconstruction algorithms under generative priors is, however, challenging. For generati ...

2023

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

Florent Gérard Krzakala, Bruno Loureiro, Matteo Vilucchio

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

Expectation consistency for calibration of neural networks

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

Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour tow ...

2023

Phase retrieval in high dimensions: Statistical and computational phase transitions

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

Curran Associates, Inc.2020

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

Lenka Zdeborová, Florent Gérard Krzakala, Maria Refinetti

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance of neural netwo ...

PMLR2021

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

Construction of optimal spectral methods in phase retrieval

Lenka Zdeborová, Florent Gérard Krzakala

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

2021

Fluctuations, Bias, Variance & Ensemble of Learners: Exact Asymptotics for Convex Losses in High-Dimension

Florent Gérard Krzakala, Bruno Loureiro

From the sampling of data to the initialisation of parameters, randomness is ubiquitous in modern Machine Learning practice. Understanding the statistical fluctuations engendered by the different sources of randomness in prediction is therefore key to unde ...

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

Generalisation error in learning with random features and the hidden manifold model*

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro, Federica Gerace

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold model. ...

IOP Publishing Ltd2021

Are Gaussian data all you need? the extents and limits of universality in high-dimensional generalized linear estimation

Florent Gérard Krzakala, Ludovic Théo Stephan, Luca Pesce

In this manuscript we consider the problem of generalized linear estimation on Gaussian mixture data with labels given by a single-index model. Our first result is a sharp asymptotic expression for the test and training errors in the high-dimensional regim ...

PMLR2023

Reservoir Computing meets Recurrent Kernels and Structured Transforms

Florent Gérard Krzakala, Jonathan Yuelin Dong

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel m ...

Curran Associates, Inc.2020

Learning Gaussian Mixtures with Generalized Linear Models: Precise Asymptotics in High-dimensions

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro, Gabriele Sicuro

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 the learning of a mixture of K Gaussians with generic means and covariances v ...

2021

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

Lenka Zdeborová, Florent Gérard Krzakala

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

Curran Associates, Inc.2020

Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro, Hugo Chao Cui

In this manuscript we consider Kernel Ridge Regression (KRR) under the Gaussian design. Exponents for the decay of the excess generalization error of KRR have been reported in various works under the assumption of power-law decay of eigenvalues of the feat ...

2021

Scampi: a robust approximate message-passing framework for compressive imaging

Florent Gérard Krzakala, Jean François Emmanuel Barbier

Reconstruction of images from noisy linear measurements is a core problem in image processing, for which convex optimization methods based on total variation (TV) minimization have been the long-standing state-of-the-art. We present an alternative probabil ...

Iop Publishing Ltd2016

Learning curves of generic features maps for realistic datasets with a teacher-student model

Lenka Zdeborová, Florent Gérard Krzakala, Bruno Loureiro, Hugo Chao Cui

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 Gaussian i.i.d. input data underlying the canonical teacher-student model may, howe ...

2021