Lenka Zdeborová

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Related publications (72)

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 ...

2023

On double-descent in uncertainty quantification in overparametrized models

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

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

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

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*

Florent Gérard Krzakala, Lenka Zdeborová, 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 ...

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

Lenka Zdeborová, Giovanni Piccioli

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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