Ergodic observables in non-ergodic systems: the example of the harmonic chain

M Baldovin, R Marino, A Vulpiani - Physica A: Statistical Mechanics and its …, 2023 - Elsevier
In the framework of statistical mechanics the properties of macroscopic systems are deduced
starting from the laws of their microscopic dynamics. One of the key assumptions in this …

A Short Review on Novel Approaches for Maximum Clique Problem: from Classical algorithms to Graph Neural Networks and Quantum algorithms

R Marino, L Buffoni, B Zavalnij - arxiv preprint arxiv:2403.09742, 2024 - arxiv.org
This manuscript provides a comprehensive review of the Maximum Clique Problem, a
computational problem that involves finding subsets of vertices in a graph that are all …

Complex recurrent spectral network

L Chicchi, L Giambagli, L Buffoni, R Marino… - Chaos, Solitons & …, 2024 - Elsevier
This paper presents a novel approach to advancing artificial intelligence (AI) through the
development of the Complex Recurrent Spectral Network (ℂ-RSN), an innovative variant of …

Phase transitions in the mini-batch size for sparse and dense two-layer neural networks

R Marino, F Ricci-Tersenghi - Machine Learning: Science and …, 2024 - iopscience.iop.org
The use of mini-batches of data in training artificial neural networks is nowadays very
common. Despite its broad usage, theories explaining quantitatively how large or small the …

Stable attractors for neural networks classification via ordinary differential equations (SA-nODE)

R Marino, L Buffoni, L Chicchi… - Machine Learning …, 2024 - iopscience.iop.org
A novel approach for supervised classification is presented which sits at the intersection of
machine learning and dynamical systems theory. At variance with other methodologies that …

Where do hard problems really exist?

R Marino - arxiv preprint arxiv:2309.16253, 2023 - arxiv.org
This chapter delves into the realm of computational complexity, exploring the world of
challenging combinatorial problems and their ties with statistical physics. Our exploration …

Stochastic Gradient Descent-like relaxation is equivalent to Metropolis dynamics in discrete optimization and inference problems

MC Angelini, AG Cavaliere, R Marino… - Scientific Reports, 2024 - nature.com
Abstract Is Stochastic Gradient Descent (SGD) substantially different from Metropolis Monte
Carlo dynamics? This is a fundamental question at the time of understanding the most used …

Solving non-linear Kolmogorov equations in large dimensions by using deep learning: a numerical comparison of discretization schemes

R Marino, N Macris - Journal of Scientific Computing, 2023 - Springer
Non-linear partial differential Kolmogorov equations are successfully used to describe a
wide range of time dependent phenomena, in natural sciences, engineering or even …

Engineered ordinary differential equations as classification algorithm (eodeca): thorough characterization and testing

R Marino, L Buffoni, L Chicchi, L Giambagli… - arxiv preprint arxiv …, 2023 - arxiv.org
EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel
approach at the intersection of machine learning and dynamical systems theory, presenting …

Diffusion of a Brownian ellipsoid in a force field

E Aurell, S Bo, M Dias, R Eichhorn… - Europhysics letters, 2016 - iopscience.iop.org
We calculate the effective long-term convective velocity and dispersive motion of an
ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external …