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Lenka Zdeborová

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Publications associées (72)

Probing transfer learning with a model of synthetic correlated datasets

Lenka Zdeborová, Luca Saglietti

Transfer learning can signiﬁcantly improve the sample eﬃciency of neural networks, by exploiting the relatedness between a data-scarce target task and a data-abundant source task. Despite years of successful applications, transfer learning practice often r ...

2022

Large deviations of semisupervised learning in the stochastic block model

Hugo Chao Cui, Lenka Zdeborová, Luca Saglietti

In semisupervised community detection, the membership of a set of revealed nodes is known in addition to the graph structure and can be leveraged to achieve better inference accuracies. While previous works investigated the case where the revealed nodes ar ...

AMER PHYSICAL SOC2022

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

Disordered systems insights on computational hardness

Lenka Zdeborová

In this review article we discuss connections between the physics of disordered systems, phase transitions in inference problems, and computational hardness. We introduce two models representing the behavior of glassy systems, the spiked tensor model and t ...

2022

Planted XY model: Thermodynamics and inference

Siyu Chen, Guanhao Huang, Giovanni Piccioli, Lenka Zdeborová

In this paper we study a fully connected planted spin glass named the planted XY model. Motivation for studying this system comes both from the spin glass field and the one of statistical inference where it models the angular synchronization problem. We de ...

2022

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 ...

2022

(Dis)assortative partitions on random regular graphs

Freya Behrens, Yaroslav Kivva, Lenka Zdeborová

We study the problem of assortative and disassortative partitions on random dregular graphs. Nodes in the graph are partitioned into two non-empty groups. In the assortative partition every node requires at least H of their neighbors to be in their own gro ...

IOP Publishing Ltd2022

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

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

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Bruno Loureiro, 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 net-works, which tend to get stuck in badly-generalizing loca ...

2022

Epidemic mitigation by statistical inference from contact tracing data

Maria Refinetti, Giovanni Catania, Florent Gérard Krzakala, Lenka Zdeborová, Indaco Biazzo

Contact tracing is an essential tool to mitigate the impact of a pandemic, such as the COVID-19 pandemic. In order to achieve efficient and scalable contact tracing in real time, digital devices can play an important role. While a lot of attention has been ...

National Academy of Sciences2021

The Gaussian equivalence of generative models for learning with shallow neural networks

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro

Understanding the impact of data structure on the computational tractability of learning is a key challenge for the theory of neural networks. Many theoretical works do not explicitly model training data, or assume that inputs are drawn component-wise inde ...

2021

Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification*

Florent Gérard Krzakala, Lenka Zdeborová

We analyze in a closed form the learning dynamics of the stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype ...

2021

The planted k-factor problem

Lenka Zdeborová, Gabriele Sicuro

We consider the problem of recovering an unknown k-factor, hidden in a weighted random graph. For k = 1 this is the planted matching problem, while the k = 2 case is closely related to the planted traveling salesman problem. The inference problem is solved ...

IOP PUBLISHING LTD2021

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

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro, Gabriele Sicuro

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 ...

2021

Construction of optimal spectral methods in phase retrieval

Florent Gérard Krzakala, Lenka Zdeborová

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 ...

2021

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 ...

2021

Stochasticity helps to navigate rough landscapes: comparing gradient-descent-based algorithms in the phase retrieval problem

Francesca Mignacco, Lenka Zdeborová

In this paper we investigate how gradient-based algorithms such as gradient descent (GD), (multi-pass) stochastic GD, its persistent variant, and the Langevin algorithm navigate non-convex loss-landscapes and which of them is able to reach the best general ...

2021

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

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

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 ...

2021

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

Maria Refinetti, Florent Gérard Krzakala, Lenka Zdeborová

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 ...

PMLR2021

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

Florent Gérard Krzakala, Lenka Zdeborová, Bruno Loureiro

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. ...

IOP Publishing Ltd2021

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