Lenka Zdeborová

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Publications associées (72)

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Entropy and mutual information in models of deep neural networks

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier, Clément Dominique Luneau

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) we show how entropies and mutual informations can be derived from heuristic statistical physics ...

2019

Entropy and mutual information in models of deep neural networks

Nicolas Macris, Florent Gérard Krzakala, Lenka Zdeborová, Jean François Emmanuel Barbier, Clément Dominique Luneau

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Dynamical cavity method for hypergraphs and its application to quenches in the k-XOR-SAT problem

Lenka Zdeborová, Freya Behrens, Aude Maier

The dynamical cavity method and its backtracking version provide a powerful approach to studying the properties of dynamical processes on large random graphs. This work extends these methods to hypergraphs, enabling the analysis of interactions involving m ...

2025

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

Lenka Zdeborová, Florent Gérard Krzakala

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype of ...

Curran Associates, Inc.2020

Dynamical phase transitions in graph cellular automata

Lenka Zdeborová, Freya Behrens

Discrete dynamical systems can exhibit complex behavior from the iterative application of straightforward local rules. A famous class of examples comes from cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we ...

American Physical Society (APS)2024

Epidemic mitigation by statistical inference from contact tracing data

Lenka Zdeborová, Florent Gérard Krzakala, Maria Refinetti, Indaco Biazzo

Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been ...

National Academy of Sciences2021

Optimal denoising of rotationally invariant rectangular matrices

Lenka Zdeborová, Florent Gérard Krzakala, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

Error scaling laws for kernel classification under source and capacity conditions

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

In this manuscript we consider the problem of kernel classification. While worst-case bounds on the decay rate of the prediction error with the number of samples are known for some classifiers, they often fail to accurately describe the learning curves of ...

2023

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

Lenka Zdeborová, Florent Gérard Krzakala

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

Backtracking Dynamical Cavity Method

Barbora Hudcová, Lenka Zdeborová, Freya Behrens

The cavity method is one of the cornerstones of the statistical physics of disordered systems such as spin glasses and other complex systems. It is able to analytically and asymptotically exactly describe the equilibrium properties of a broad range of mode ...

American Physical Society2023

Learning curves for the multi-class teacher-student perceptron

Lenka Zdeborová, Bruno Loureiro, Elisabetta Cornacchia, Rodrigo Soares Veiga

One of the most classical results in high-dimensional learning theory provides a closed-form expression for the generalisation error of binary classification with a single-layer teacher-student perceptron on i.i.d. Gaussian inputs. Both Bayes-optimal (BO) ...

IOP Publishing Ltd2023

Les Houches 2022 Special Issue: Editorial

Lenka Zdeborová, Florent Gérard Krzakala

IOP Publishing Ltd2024