Publications by Lenka Zdeborová

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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 ...

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 ...

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 ...

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 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 ...

We study the fixed points of outer-totalistic cellular automata on sparse random regular graphs. These can be seen as constraint satisfaction problems, where each variable must adhere to the same local constraint, which depends solely on its state and the ...

Active learning (AL) is a branch of machine learning that deals with problems where unlabeled data is abundant yet obtaining labels is expensive. The learning algorithm has the possibility of querying a limited number of samples to obtain the corresponding ...

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 ...

The stochastic block model (SBM) is widely studied as a benchmark for graph clustering aka community detection. In practice, graph data often come with node attributes that bear additional information about the communities. Previous works modeled such data ...

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 ...

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. ...

The contextual stochastic block model (CSBM) was proposed for unsupervised community detection on attributed graphs where both the graph and the high-dimensional node information correlate with node labels. In the context of machine learning on graphs, the ...

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 ...

Lenka Zdeborová

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Probing transfer learning with a model of synthetic correlated datasets

Low-rank matrix estimation with inhomogeneous noise

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

Multi-layer state evolution under random convolutional design

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

(Dis)assortative partitions on random regular graphs

Counting and hardness-of-finding fixed points in cellular automata on random graphs

Large deviations in the perceptron model and consequences for active learning

Construction of optimal spectral methods in phase retrieval

Neural-prior stochastic block model

Planted XY model: Thermodynamics and inference

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

Optimal Inference in Contextual Stochastic Block Models

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*