Emergence of Structure in Ensembles of Random Neural Networks

Fuente: arXiv
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Autores principales: Muscarnera, Luca, Loreti, Luigi, Todeschini, Giovanni, Fumagalli, Alessio, Regazzoni, Francesco
Formato: Preprint
Publicado: 2025
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author Muscarnera, Luca
Loreti, Luigi
Todeschini, Giovanni
Fumagalli, Alessio
Regazzoni, Francesco
author_facet Muscarnera, Luca
Loreti, Luigi
Todeschini, Giovanni
Fumagalli, Alessio
Regazzoni, Francesco
contents Randomness is ubiquitous in many applications across data science and machine learning. Remarkably, systems composed of random components often display emergent global behaviors that appear deterministic, manifesting a transition from microscopic disorder to macroscopic organization. In this work, we introduce a theoretical model for studying the emergence of collective behaviors in ensembles of random classifiers. We argue that, if the ensemble is weighted through the Gibbs measure defined by adopting the classification loss as an energy, then there exists a finite temperature parameter for the distribution such that the classification is optimal, with respect to the loss (or the energy). Interestingly, for the case in which samples are generated by a Gaussian distribution and labels are constructed by employing a teacher perceptron, we analytically prove and numerically confirm that such optimal temperature does not depend neither on the teacher classifier (which is, by construction of the learning problem, unknown), nor on the number of random classifiers, highlighting the universal nature of the observed behavior. Experiments on the MNIST dataset underline the relevance of this phenomenon in high-quality, noiseless, datasets. Finally, a physical analogy allows us to shed light on the self-organizing nature of the studied phenomenon.
format Preprint
id arxiv_https___arxiv_org_abs_2505_10331
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Emergence of Structure in Ensembles of Random Neural Networks
Muscarnera, Luca
Loreti, Luigi
Todeschini, Giovanni
Fumagalli, Alessio
Regazzoni, Francesco
Machine Learning
Artificial Intelligence
Randomness is ubiquitous in many applications across data science and machine learning. Remarkably, systems composed of random components often display emergent global behaviors that appear deterministic, manifesting a transition from microscopic disorder to macroscopic organization. In this work, we introduce a theoretical model for studying the emergence of collective behaviors in ensembles of random classifiers. We argue that, if the ensemble is weighted through the Gibbs measure defined by adopting the classification loss as an energy, then there exists a finite temperature parameter for the distribution such that the classification is optimal, with respect to the loss (or the energy). Interestingly, for the case in which samples are generated by a Gaussian distribution and labels are constructed by employing a teacher perceptron, we analytically prove and numerically confirm that such optimal temperature does not depend neither on the teacher classifier (which is, by construction of the learning problem, unknown), nor on the number of random classifiers, highlighting the universal nature of the observed behavior. Experiments on the MNIST dataset underline the relevance of this phenomenon in high-quality, noiseless, datasets. Finally, a physical analogy allows us to shed light on the self-organizing nature of the studied phenomenon.
title Emergence of Structure in Ensembles of Random Neural Networks
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2505.10331