Lenka Zdeborová

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Publications associées (72)

Large deviations in the perceptron model and consequences for active learning

Lenka Zdeborová, Luca Saglietti

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 ...

2021

Phase retrieval in high dimensions: Statistical and computational phase transitions

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

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 , ...

Curran Associates, Inc.2020

Optimization and Generalization of Shallow Neural Networks with Quadratic Activation Functions

Lenka Zdeborová

p>We study the dynamics of optimization and the generalization properties of one-hidden layer neural networks with quadratic activation function in the overparametrized regime where the layer width m is larger than the input dimension d. We conside ...

Curran Associates, Inc.2020

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

Francesca Mignacco, Florent Gérard Krzakala, Lenka Zdeborová

We analyze in a closed form the learning dynamics of 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 of ...

Curran Associates, Inc.2020

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

Florent Gérard Krzakala, Lenka Zdeborová

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 ...

Curran Associates, Inc.2020

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

Florent Gérard Krzakala, Lenka Zdeborová

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 ...

Curran Associates, Inc.2020

Machine learning and statistical physics: preface

Lenka Zdeborová

IOP PUBLISHING LTD2020

Optimal errors and phase transitions in high-dimensional generalized linear models

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala, Lenka Zdeborová

Generalized linear models (GLMs) are used in high-dimensional machine learning, statistics, communications, and signal processing. In this paper we analyze GLMs when the data matrix is random, as relevant in problems such as compressed sensing, error-corre ...

National Academy of Sciences2019

The committee machine: computational to statistical gaps in learning a two-layers neural network

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala, Lenka Zdeborová

Heuristic tools from statistical physics have been used in the past to locate the phase transitions and compute the optimal learning and generalization errors in the teacher-student scenario in multi-layer neural networks. In this paper, we provide a rigor ...

IOP PUBLISHING LTD2019

Entropy and mutual information in models of deep neural networks

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau, Florent Gérard Krzakala, Lenka Zdeborová

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) we show how entropies and mutual informations can be derived from heuristic statistical physics ...

2019

The committee machine: Computational to statistical gaps in learning a two-layers neural network

Nicolas Macris, Jean François Emmanuel Barbier, Florent Gérard Krzakala, Lenka Zdeborová

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Entropy and mutual information in models of deep neural networks

Nicolas Macris, Jean François Emmanuel Barbier, Clément Dominique Luneau, Florent Gérard Krzakala, Lenka Zdeborová

We examine a class of stochastic deep learning models with a tractable method to compute information-theoretic quantities. Our contributions are three-fold: (i) We show how entropies and mutual informations can be derived from heuristic statistical physics ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

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