Publications related to Statistical mechanics of the maximum-average submatrix problem

Related publications (10)

Dynamical cavity method for hypergraphs and its application to quenches in the k-XOR-SAT problem

Lenka Zdeborová, Freya Behrens, Aude Maier

The dynamical cavity method and its backtracking version provide a powerful approach to studying the properties of dynamical processes on large random graphs. This work extends these methods to hypergraphs, enabling the analysis of interactions involving m ...

2025

Deep Neural Networks: Large-Width Behavior and Generalization Bounds

Evgenii Golikov

During several decades, neural network architectures have undergone considerable evolution: from shallow to deep, from fully connected to structured (e.g. convolutional, recurrent, or residual), from unnormalized to normalized. The present thesis contribut ...

EPFL2025

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

A square-root speedup for finding the smallest eigenvalue

Thomas Arthur Louis Joseph Guilbaud

We describe a quantum algorithm for finding the smallest eigenvalue of a Hermitian matrix. This algorithm combines quantum phase estimation and quantum amplitude estimation to achieve a quadratic speedup with respect to the best classical algorithm in term ...

2024

Real-time quantum dynamics of thermal states with neural thermofields

Giuseppe Carleo, Jannes Willy E. Nys, Zakari Denis

Solving the time-dependent quantum many-body Schrödinger equation is a challenging task, especially for states at a finite temperature, where the environment affects the dynamics. Most existing approximating methods are designed to represent static thermal ...

2024

Information Spectrum Converse for Minimum Entropy Couplings and Functional Representations

Yanina Yurina Shkel, Anuj Kumar Yadav

Given two jointly distributed random variables (X,Y), a functional representation of X is a random variable Z independent of Y, and a deterministic function g(⋅,⋅) such that X=g(Y,Z). The problem of finding a minimum entropy functional representation is kn ...

2023

Bayes-optimal Learning of Deep Random Networks of Extensive-width

Lenka Zdeborová, Florent Gérard Krzakala, Hugo Chao Cui

We consider the problem of learning a target function corresponding to a deep, extensive-width, non-linear neural network with random Gaussian weights. We consider the asymptotic limit where the number of samples, the input dimension and the network width ...

2023

Improved inference for a boundary parameter

Anthony Christopher Davison, Soumaya Elkantassi

The limiting distributions of statistics used to test hypotheses about parameters on the boundary of their domains may provide very poor approximations to the finite-sample behaviour of these statistics, even for very large samples. We review theoretical w ...

WILEY2023

Fractional extreme distributions

Lotfi Boudabsa

We consider three classes of linear differential equations on distribution functions, with a fractional order alpha is an element of [0; 1]. The integer case alpha = 1 corresponds to the three classical extreme families. In general, we show that there is a ...

2020

Inducing Magnetic Phase Transitions in Monolayer CrI3 via Lattice Deformations

Oleg Yazyev, Michele Pizzochero

Atomically thin films of layered chromium triiodide (CrI3) have recently been regarded as suitable candidates for a wide spectrum of technologically relevant applications, mainly owing to the opportunities they offer for achieving a reversible transition b ...

AMER CHEMICAL SOC2020