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Lenka Zdeborová

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Publications associées (72)

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

Optimal Inference in Contextual Stochastic Block Models

Lenka Zdeborová

The contextual stochastic block model (CSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine learning on graphs, the ...

2024

Quenches in the Sherrington-Kirkpatrick model

Freya Behrens, Florent Gérard Krzakala, Lenka Zdeborová, Vittorio Erba

The Sherrington-Kirkpatrick model is a prototype of a complex non-convex energy landscape. Dynamical processes evolving on such landscapes and locally aiming to reach minima are generally poorly understood. Here, we study quenches, i.e. dynamics that local ...

2024

Backtracking Dynamical Cavity Method

Freya Behrens, Lenka Zdeborová, Barbora Hudcová

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

Phase diagram of stochastic gradient descent in high-dimensional two-layer neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Ludovic Théo Stephan

Despite the non-convex optimization landscape, over-parametrized shallow networks are able to achieve global convergence under gradient descent. The picture can be radically different for narrow networks, which tend to get stuck in badly-generalizing local ...

Iop Publishing Ltd2023

Neural-prior stochastic block model

Lenka Zdeborová

The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works modeled such data ...

2023

Multi-layer state evolution under random convolutional design

Florent Gérard Krzakala, Lenka Zdeborová

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

Bayes-optimal inference for spreading processes on random networks

Lenka Zdeborová, Indaco Biazzo

We consider a class of spreading processes on networks, which generalize commonly used epidemic models such as the SIR model or the SIS model with a bounded number of reinfections. We analyze the related problem of inference of the dynamics based on its pa ...

Amer Physical Soc2023

Bayesian reconstruction of memories stored in neural networks from their connectivity

Florent Gérard Krzakala, Lenka Zdeborová

The advent of comprehensive synaptic wiring diagrams of large neural circuits has created the field of connectomics and given rise to a number of open research questions. One such question is whether it is possible to reconstruct the information stored in ...

2023

High-dimensional Asymptotics of Denoising Autoencoders

Hugo Chao Cui, Lenka Zdeborová

We address the problem of denoising data from a Gaussian mixture using a twolayer non-linear autoencoder with tied weights and a skip connection. We consider the high-dimensional limit where the number of training samples and the input dimension jointly te ...

2023

Bayes-optimal Learning of Deep Random Networks of Extensive-width

Hugo Chao Cui, Florent Gérard Krzakala, Lenka Zdeborová

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 ...

2023

On double-descent in uncertainty quantification in overparametrized models

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

Uncertainty quantification is a central challenge in reliable and trustworthy machine learning. Naive measures such as last-layer scores are well-known to yield overconfident estimates in the context of overparametrized neural networks. Several methods, ra ...

PMLR Proceedings of Machine Learning Research2023

Compressed sensing with ℓ 0-norm: statistical physics analysis & algorithms for signal recovery

Florent Gérard Krzakala, Lenka Zdeborová

Noiseless compressive sensing is a protocol that enables undersampling and later recovery of a signal without loss of information. This compression is possible because the signal is usually sufficiently sparse in a given basis. Currently, the algorithm off ...

IEEE2023

Expectation consistency for calibration of neural networks

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

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

Error scaling laws for kernel classification under source and capacity conditions

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

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

Learning curves for the multi-class teacher-student perceptron

Elisabetta Cornacchia, Francesca Mignacco, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro

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

Theoretical characterization of uncertainty in high-dimensional linear classification

Florent Gérard Krzakala, Lenka Zdeborová, Lucas Andry Clarte

Being able to reliably assess not only the accuracy but also the uncertainty of models' predictions is an important endeavor in modern machine learning. Even if the model generating the data and labels is known, computing the intrinsic uncertainty after le ...

IOP Publishing Ltd2023

Generalization error rates in kernel regression: the crossover from the noiseless to noisy regime*

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

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 ...

2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, 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

Aligning random graphs with a sub-tree similarity message-passing algorithm

Giovanni Piccioli, Lenka Zdeborová

The problem of aligning Erdos-Renyi random graphs is a noisy, average-case version of the graph isomorphism problem, in which a pair of correlated random graphs is observed through a random permutation of their vertices. We study a polynomial time message- ...

IOP Publishing Ltd2022

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