Ergodic observables in non-ergodic systems: the example of the harmonic chain
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 …
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
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 …
computational problem that involves finding subsets of vertices in a graph that are all …
Complex recurrent spectral network
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 …
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
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 …
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)
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 …
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 …
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
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 …
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
Non-linear partial differential Kolmogorov equations are successfully used to describe a
wide range of time dependent phenomena, in natural sciences, engineering or even …
wide range of time dependent phenomena, in natural sciences, engineering or even …
Engineered ordinary differential equations as classification algorithm (eodeca): thorough characterization and testing
EODECA (Engineered Ordinary Differential Equations as Classification Algorithm) is a novel
approach at the intersection of machine learning and dynamical systems theory, presenting …
approach at the intersection of machine learning and dynamical systems theory, presenting …
Diffusion of a Brownian ellipsoid in a force field
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 …
ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external …