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Article

TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State

by 1,2,*,† and 1,*,†
1
Department of Physics, Sapienza University of Rome, 00184 Rome, Italy
2
Center for Life Nano- & Neuro Science, Istituto Italiano di Tecnologia, 00161 Rome, Italy
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Academic Editors: Viola Folli, Giorgio Gosti and Edoardo Milanetti
Entropy 2021, 23(9), 1138; https://doi.org/10.3390/e23091138
Received: 30 July 2021 / Revised: 24 August 2021 / Accepted: 25 August 2021 / Published: 31 August 2021
(This article belongs to the Special Issue Memory Storage Capacity in Recurrent Neural Networks)
We present ToloMEo (TOpoLogical netwOrk Maximum Entropy Optimization), a program implemented in C and Python that exploits a maximum entropy algorithm to evaluate network topological information. ToloMEo can study any system defined on a connected network where nodes can assume N discrete values by approximating the system probability distribution with a Pottz Hamiltonian on a graph. The software computes entropy through a thermodynamic integration from the mean-field solution to the final distribution. The nature of the algorithm guarantees that the evaluated entropy is variational (i.e., it always provides an upper bound to the exact entropy). The program also performs machine learning, inferring the system’s behavior providing the probability of unknown states of the network. These features make our method very general and applicable to a broad class of problems. Here, we focus on three different cases of study: (i) an agent-based model of a minimal ecosystem defined on a square lattice, where we show how topological entropy captures a crossover between hunting behaviors; (ii) an example of image processing, where starting from discretized pictures of cell populations we extract information about the ordering and interactions between cell types and reconstruct the most likely positions of cells when data are missing; and (iii) an application to recurrent neural networks, in which we measure the information stored in different realizations of the Hopfield model, extending our method to describe dynamical out-of-equilibrium processes. View Full-Text
Keywords: entropy; maximum entropy; hopfield model; machine learning entropy; maximum entropy; hopfield model; machine learning
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MDPI and ACS Style

Miotto, M.; Monacelli, L. TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State. Entropy 2021, 23, 1138. https://doi.org/10.3390/e23091138

AMA Style

Miotto M, Monacelli L. TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State. Entropy. 2021; 23(9):1138. https://doi.org/10.3390/e23091138

Chicago/Turabian Style

Miotto, Mattia, and Lorenzo Monacelli. 2021. "TOLOMEO, a Novel Machine Learning Algorithm to Measure Information and Order in Correlated Networks and Predict Their State" Entropy 23, no. 9: 1138. https://doi.org/10.3390/e23091138

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