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Florent Gérard Krzakala

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Publications associées (66)

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

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

Artificial Neural Network Training on an Optical Processor via Direct Feedback Alignment

Florent Gérard Krzakala, Julien Marcel Daniel Emmanuel Launay

Artificial Neural Networks (ANN) are habitually trained via the back-propagation (BP) algorithm. This approach has been extremely successful: Current models like GPT-3 have O(10 11 ) parameters, are trained on O(10 11 ) words and produce awe-inspiring resu ...

IEEE2023

Fluctuations, bias, variance and 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 ...

Iop Publishing Ltd2023

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

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

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

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

Florent Gérard Krzakala, Luca Pesce, Ludovic Théo Stephan

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

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

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

Florent Gérard Krzakala, Lenka Zdeborová

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

Asymptotic Errors for Teacher-Student Convex Generalized Linear Models (Or: How to Prove Kabashima’s Replica Formula)

Florent Gérard Krzakala, Alia Abbara

There has been a recent surge of interest in the study of asymptotic reconstruction performance in various cases of generalized linear estimation problems in the teacher-student setting, especially for the case of i.i.d standard normal matrices. Here, we g ...

2022

Multi-layer State Evolution Under Random Convolutional Design

Florent Gérard Krzakala, Lenka Zdeborová

2022

Subspace clustering in high-dimensions: Phase transitions & Statistical-to-Computational gap

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Luca Pesce, Bruno Loureiro

A simple model to study subspace clustering is the high-dimensional k -Gaussian mixture model where the cluster means are sparse vectors. Here we provide an exact asymptotic characterization of the statistically optimal reconstruction error in this model i ...

2022

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

Florent Gérard Krzakala, Bruno Loureiro

JMLR-JOURNAL MACHINE LEARNING RESEARCH2022

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