Florent Gérard Krzakala

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We study the random binary symmetric perceptron problem, focusing on the behavior of rare high-margin solutions. While most solutions are isolated, we demonstrate that these rare solutions are part of clusters of extensive entropy, heuristically correspond ...

While classical in many theoretical settings-and in particular in statistical physics-inspired works-the assumption of Gaussian i.i.d. input data is often perceived as a strong limitation in the context of statistics and machine learning. In this study, we ...

Noiseless compressive sensing is a two-step setting that allows for undersampling a sparse signal and then reconstructing it without loss of information. The LASSO algorithm, based on l(1) regularization, provides an efficient and robust way to address thi ...

A recent line of work in high-dimensional statistics working under the Gaussian mixture hypothesis has led to a number of results in the context of empirical risk minimization, Bayesian uncertainty quantification, separation of kernel methods and neural ne ...

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 ...

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 ...

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 ...

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 ...

We study the maximum-average submatrix problem, wherein given an N x N matrix J, one needs to find the k x k submatrix with the largest average number of entries. We investigate the problem for random matrices J, whose entries are i.i.d. random variables, ...

For high-dimensional Gaussian data, we investigate theoretically how the features of a two-layer neural network adapt to the structure of the target function through a few large batch gradient descent steps, leading to an improvement in the approximation c ...

Inverse probability problems whose generative models are given by strictly nonlinear Gaussian random fields show the all-or-nothing behavior: There exists a critical rate at which Bayesian inference exhibits a phase transition. Below this rate, the optimal ...

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 ...

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 ...

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 ...

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 ...

We consider a commonly studied supervised classification of a synthetic dataset whose labels are generated by feeding a one-layer non-linear neural network with random iid inputs. We study the generalization performances of standard classifiers in the high ...

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 net-works, which tend to get stuck in badly-generalizing loca ...

We investigate the training dynamics of two-layer neural networks when learning multi-index target functions. We focus on multi-pass gradient descent (GD) that reuses the batches multiple times and show that it significantly changes the conclusion about wh ...

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 ...

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 ...

Florent Gérard Krzakala

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On the atypical solutions of the symmetric binary perceptron

Gaussian universality of perceptrons with random labels

Phase Diagram of Compressed Sensing with l0-norm Regularization

Universality laws for Gaussian mixtures in generalized linear models

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

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

On double-descent in uncertainty quantification in overparametrized models

Multi-layer State Evolution Under Random Convolutional Design

Statistical mechanics of the maximum-average submatrix problem

How Two-Layer Neural Networks Learn, One (Giant) Step at a Time

Secure Coding via Gaussian Random Fields

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

Rigorous Dynamical Mean-Field Theory for Stochastic Gradient Descent Methods

Bayesian reconstruction of memories stored in neural networks from their connectivity

Quenches in the Sherrington-Kirkpatrick model

Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization

Phase diagram of Stochastic Gradient Descent in high-dimensional two-layer neural networks

The Benefits of Reusing Batches for Gradient Descent in Two-Layer Networks: Breaking the Curse of Information and Leap Exponents

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

Low-rank matrix estimation with inhomogeneous noise