Recherche

Afficher tous les résultats pour

Accueil

Personne

Nicolas Macris

Cette personne a quitté l’EPFL

À propos
Confidentialité
Mentions légales

Graph Chatbot

Publications associées (64)

Page 1 sur 4

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

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

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

Adaptive Path Interpolation Method for Sparse Systems: Application to a Censored Block Model

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

Recently, a new adaptive path interpolation method has been developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and gen ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2021

Displacement Convexity in Spatially Coupled Scalar Recursions

Rüdiger Urbanke, Nicolas Macris, Rafah El-Khatib

We introduce a technique for the analysis of general spatially coupled systems that are governed by scalar recursions. Such systems can be expressed in variational form in terms of a potential function. We show, under mild conditions, that the potential fu ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Solving Non-linear Kolmogorov Equations in Large Dimensions by Using Deep Learning: A Numerical Comparison of Discretization Schemes

Nicolas Macris

Non-linear partial differential Kolmogorov equations are successfully used to describe a wide range of time dependent phenomena, in natural sciences, engineering or even finance. For example, in physical systems, the Allen-Cahn equation describes pattern f ...

SPRINGER/PLENUM PUBLISHERS2023

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

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

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

Mismatched Estimation of Non-Symmetric Rank-One Matrices Under Gaussian Noise

Nicolas Macris, Farzad Pourkamali

We consider the estimation of a nxm matrix uv(T) observed through an additive Gaussian noise channel, a problem that frequently arises in statistics and machine learning. We investigate a scenario involving mismatched Bayesian inference in which the stat ...

IEEE2022

Exact Solution of the Gauge Symmetric p-Spin Glass Model on a Complete Graph

Nicolas Macris

We consider a gauge symmetric version of the p-spin glass model on a complete graph. The gauge symmetry guarantees the absence of replica symmetry breaking and allows to fully use the interpolation scheme of Guerra to rigorously compute the free energy. In ...

2009

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

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

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 contribution, we provide ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Adaptive Path Interpolation for Sparse Systems: Application to a Simple Censored Block Model

Nicolas Macris, Jean François Emmanuel Barbier, Chun Lam Chan

A new adaptive path interpolation method has been recently developed as a simple and versatile scheme to calculate exactly the asymptotic mutual information of Bayesian inference problems defined on dense factor graphs. These include random linear and gene ...

IEEE2018

Entropy and mutual information in models of deep neural networks

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

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

On the Convergence to the Non-equilibrium Steady State of a Langevin Dynamics with Widely Separated Time Scales and Different Temperatures

Nicolas Macris, Emanuele Mingione, Diego Alberici

We study the solution of the two-temperature Fokker-Planck equation and rigorously analyse its convergence towards an explicit non-equilibrium stationary measure for long time and two widely separated time scales. The exponential rates of convergence are e ...

Springer Int Publ Ag2024

Universal Sparse Superposition Codes With Spatial Coupling and GAMP Decoding

Nicolas Macris, Jean François Emmanuel Barbier, Mohamad Baker Dia

Sparse superposition codes, or sparse regression codes, constitute a new class of codes, which was first introduced for communication over the additive white Gaussian noise (AWGN) channel. It has been shown that such codes are capacity-achieving over the A ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Chains of mean-field models

Rüdiger Urbanke, Nicolas Macris, Seyed Hamed Hassani

We consider a collection of Curie-Weiss (CW) spin systems, possibly with a random field, each of which is placed along the positions of a one-dimensional chain. The CW systems are coupled together by a Kac-type interaction in the longitudinal direction of ...

2012

Bell Diagonal and Werner State Generation: Entanglement, Non-Locality, Steering and Discord on the IBM Quantum Computer

Marc-André Dupertuis, Nicolas Macris, Chun Lam Chan, Samuel Bosch, Nicolas Schwaller, Su Yeon Chang

We propose the first correct special-purpose quantum circuits for preparation of Bell diagonal states (BDS), and implement them on the IBM Quantum computer, characterizing and testing complex aspects of their quantum correlations in the full parameter spac ...

2021

Exact solution for the conditional entropy of Poissonian LDPC codes over the Binary Erasure Channel

Nicolas Macris, Shrinivas Kudekar

We consider communication over a binary erasure channel with low density parity check codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code ensembles, in the asymptotic li ...

2007

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

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

IOP PUBLISHING LTD2019

Information theoretic limits of learning a sparse rule

Nicolas Macris, Clément Dominique Luneau

We consider generalized linear models in regimes where the number of nonzero components of the signal and accessible data points are sublinear with respect to the size of the signal. We prove a variational formula for the asymptotic mutual information per ...

IOP Publishing Ltd2022

Decay of Correlations: An Application to Low-Density Parity Check codes

Nicolas Macris, Shrinivas Kudekar

Recently the decay of correlations between bits of low density generator matrix (LDGM) codes have been investigated by using high temperature expansions from statistical physics \cite{KuMa07}. In this work we apply these ideas to a special class of low den ...

IEEE2008

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

Proof of replica formulas in the high noise regime for communication using LDGM codes

Nicolas Macris, Shrinivas Kudekar

We consider communication over a binary input memoryless output symmetric channel with low density generator matrix codes and optimal maximum a posteriori decoding. It is known that the problem of computing the average conditional entropy, over such code e ...

2008