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Florent Gérard Krzakala

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Related publications (66)

Secure Coding via Gaussian Random Fields

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 ...

IEEE2022

Adversarial Robustness by Design Through Analog Computing And Synthetic Gradients

Florent Gérard Krzakala, Ruben Elie Ohana, Julien Marcel Daniel Emmanuel Launay

We propose a new defense mechanism against adversarial at-tacks inspired by an optical co-processor, providing robustness without compromising natural accuracy in both white-box and black-box settings. This hardware co-processor performs a nonlinear fixed ...

IEEE2022

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

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

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

Mutual Information and Optimality of Approximate Message-Passing in Random Linear Estimation

Nicolas Macris, Mohamad Baker Dia, Jean François Emmanuel Barbier, Florent Gérard Krzakala

We consider the estimation of a signal from the knowledge of its noisy linear random Gaussian projections. A few examples where this problem is relevant are compressed sensing, sparse superposition codes, and code division multiple access. There has been a ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

Reservoir Computing meets Recurrent Kernels and Structured Transforms

Florent Gérard Krzakala, Jonathan Yuelin Dong, Ruben Elie Ohana

Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel m ...

Curran Associates, Inc.2020

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

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

Direct Feedback Alignment Scales to Modern Deep Learning Tasks and Architectures

Florent Gérard Krzakala, Julien Marcel Daniel Emmanuel Launay

Despite being the workhorse of deep learning, the backpropagation algorithm is no panacea. It enforces sequential layer updates, thus preventing efficient parallelization of the training process. Furthermore, its biological plausibility is being challenged ...

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

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

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