Florent Gérard Krzakala

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Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements in the model capabilities. Yet, a theoretical characterization of how such mecha ...

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 ...

This work investigates adversarial training in the context of margin-based linear classifiers in the high-dimensional regime where the dimension d and the number of data points n diverge with a fixed ratio α = n/d. We introduce a tractable mathematical mod ...

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 ...

We consider the phase retrieval problem of reconstructing a n -dimensional real or complex signal X ⋆ from m (possibly noisy) observations Y μ = | ∑ n i = 1 Φ μ i X ⋆ i / √ n | , for a large class of correlated real and complex random sensing matrices Φ , ...

A recent series of theoretical works showed that the dynamics of neural networks with a certain initialisation are well-captured by kernel methods. Concurrent empirical work demonstrated that kernel methods can come close to the performance of neural netwo ...

We discuss the inhomogeneous Wigner spike model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random matrix theory, with a specific focus on its spectral properties. Our primary o ...

We consider the phase retrieval problem, in which the observer wishes to recover a n-dimensional real or complex signal X⋆ from the (possibly noisy) observation of |ΦX⋆|, in which Φ is a matrix of size m×n. We consider a \emph{high-dimensional} setting whe ...

We study generalised linear regression and classification for a synthetically generated dataset encompassing different problems of interest, such as learning with random features, neural networks in the lazy training regime, and the hidden manifold model. ...

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 ...

Generalised linear models for multi-class classification problems are one of the fundamental building blocks of modern machine learning tasks. In this manuscript, we characterise the learning of a mixture of K Gaussians with generic means and covariances v ...

Despite the widespread use of gradient-based algorithms for optimizing high-dimensional non-convex functions, understanding their ability of finding good minima instead of being trapped in spurious ones remains to a large extent an open problem. Here we fo ...

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 ...

Teacher-student models provide a framework in which the typical-case performance of high-dimensional supervised learning can be described in closed form. The assumptions of Gaussian i.i.d. input data underlying the canonical teacher-student model may, howe ...

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 ...

We investigate popular resampling methods for estimating the uncertainty of statistical models, such as subsampling, bootstrap and the jackknife, and their performance in high-dimensional supervised regression tasks. We provide a tight asymptotic descripti ...

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 ...

In this manuscript, we investigate the problem of how two-layer neural networks learn features from data, and improve over the kernel regime, after being trained with a single gradient descent step. Leveraging the insight from (Ba et al., 2022), we model t ...

We study robust linear regression in highdimension, when both the dimension d and the number of data points n diverge with a fixed ratio α = n/d, and study a data model that includes outliers. We provide exact asymptotics for the performances of the empiri ...

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 ...

Florent Gérard Krzakala

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A phase transition between positional and semantic learning in a solvable model of dot-product attention

Multi-layer state evolution under random convolutional design

A High Dimensional Statistical Model for Adversarial Training: Geometry and Trade-Offs

Expectation consistency for calibration of neural networks

Phase retrieval in high dimensions: Statistical and computational phase transitions

Classifying high-dimensional Gaussian mixtures: Where kernel methods fail and neural networks succeed

Spectral Phase Transition and Optimal PCA in Block-Structured Spiked Models

Construction of optimal spectral methods in phase retrieval

Generalisation error in learning with random features and the hidden manifold model*

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

Learning Gaussian Mixtures with Generalized Linear Models: Precise Asymptotics in High-dimensions

Complex Dynamics in Simple Neural Networks: Understanding Gradient Flow in Phase Retrieval

Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime

Learning curves of generic features maps for realistic datasets with a teacher-student model

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

Analysis of Bootstrap and Subsampling in High-dimensional Regularized Regression

Theoretical characterization of uncertainty in high-dimensional linear classification

Asymptotics of feature learning in two-layer networks after one gradient-step

Asymptotic Characterisation of the Performance of Robust Linear Regression in the Presence of Outliers

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