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We use a formal correspondence between thermodynamics and inference, where the number of samples can be thought of as the inverse temperature, to study a quantity called ``learning capacity'' which is a measure of the effective…

Machine Learning · Computer Science 2024-10-22 Daiwei Chen , Wei-Kai Chang , Pratik Chaudhari

Using the formalism of information theory, we analyze the mechanism of information transduction in a simple one-step signaling cascade S$\rightarrow$X representing the gene regulatory network. Approximating the signaling channel to be…

Molecular Networks · Quantitative Biology 2018-11-14 Mintu Nandi , Ayan Biswas , Suman K Banik , Pinaki Chaudhury

Cell decision-making refers to the process by which cells gather information from their local microenvironment and regulate their internal states to create appropriate responses. Microenvironmental cell sensing plays a key role in this…

Biological Physics · Physics 2023-04-19 Arnab Barua , Haralampos Hatzikirou

Predicting future observations plays a central role in machine learning, biology, economics, and many other fields. It lies at the heart of organizational principles such as the variational free energy principle and has even been shown --…

Machine Learning · Computer Science 2025-04-09 Lukas J. Fiderer , Paul C. Barth , Isaac D. Smith , Hans J. Briegel

There are numerous characterizations of Shannon entropy and Tsallis entropy as measures of information obeying certain properties. Using work by Faddeev and Furuichi, we derive a very simple characterization. Instead of focusing on the…

Information Theory · Computer Science 2017-08-22 John C. Baez , Tobias Fritz , Tom Leinster

A model of an organism as an autonomous intelligent system has been proposed. This model was used to analyze learning of an organism in various environmental conditions. Processes of learning were divided into two types: strong and weak…

Artificial Intelligence · Computer Science 2007-05-23 Alexey V. Melkikh

Fluctuations in biochemical networks, e.g., in a living cell, have a complex origin that precludes a description of such systems in terms of bipartite or multipartite processes, as is usually done in the framework of stochastic and/or…

Statistical Mechanics · Physics 2020-01-29 R. Chétrite , M. L. Rosinberg , T. Sagawa , G. Tarjus

We propose a new way of investigating phase transitions in the context of information theory. We use an information-entropic measure of spatial complexity known as configurational entropy (CE) to quantify both the storage and exchange of…

Statistical Mechanics · Physics 2018-03-23 Damian Sowinski , Marcelo Gleiser

This letter exposes a tight connection between the thermodynamic efficiency of information processing and predictive inference. A generalized lower bound on dissipation is derived for partially observable information engines which are…

Statistical Mechanics · Physics 2020-02-12 Susanne Still

We define a neural network as a septuple consisting of (1) a state vector, (2) an input projection, (3) an output projection, (4) a weight matrix, (5) a bias vector, (6) an activation map and (7) a loss function. We argue that the loss…

Machine Learning · Computer Science 2021-02-15 Vitaly Vanchurin

Fisher information and Shannon entropy are fundamental tools for understanding and analyzing dynamical systems from complementary perspectives. They can characterize unknown parameters by quantifying the information contained in variables,…

Information Theory · Computer Science 2025-12-19 Yuxuan Bao , J. Nathan Kutz

Understanding how the complex connectivity structure of the brain shapes its information-processing capabilities is a long-standing question. By focusing on a paradigmatic architecture, we study how the neural activity of excitatory and…

Statistical Mechanics · Physics 2024-10-18 Giacomo Barzon , Daniel Maria Busiello , Giorgio Nicoletti

We characterize different cell states, related to cancer and ageing phenotypes, by a measure of entropy of network ensembles, integrating gene expression values and protein interaction networks. The entropy measure estimates the parameter…

Molecular Networks · Quantitative Biology 2013-05-24 G. Menichetti , G. Bianconi , E. Giampieri , G. Castellani , D. Remondini

Coordinated responses to environmental stimuli are critical for multicellular organisms. To overcome the obstacles of cell-to-cell heterogeneity and noisy signaling dynamics within individual cells, cells must effectively exchange…

Biological Physics · Physics 2022-10-12 Guanyu Li , Ryan LeFebre , Alia Starman , Patrick Chappell , Andrew Mugler , Bo Sun

In the first chapter of Shannon's "A Mathematical Theory of Communication," it is shown that the maximum entropy rate of an input process of a constrained system is limited by the combinatorial capacity of the system. Shannon considers…

Information Theory · Computer Science 2009-11-20 Georg Böcherer , Valdemar Cardoso da Rocha Junior , Cecilio Pimentel

In the theoretical modelling of a physical system a crucial step consists in the identification of those degrees of freedom that enable a synthetic, yet informative representation of it. While in some cases this selection can be carried out…

Statistical Mechanics · Physics 2020-06-30 Marco Giulini , Roberto Menichetti , M. Scott Shell , Raffaello Potestio

The problems of causality, modeling, and control for chaotic, high-dimensional dynamical systems are formulated in the language of information theory. The central quantity of interest is the Shannon entropy, which measures the amount of…

Dynamical Systems · Mathematics 2022-06-01 Adrián Lozano-Durán , Gonzalo Arranz

The mammalian brain is a metabolically expensive device, and evolutionary pressures have presumably driven it to make productive use of its resources. For sensory areas, this concept has been expressed more formally as an optimality…

Neurons and Cognition · Quantitative Biology 2016-03-02 Deep Ganguli , Eero P. Simoncelli

In many complex systems, whether biological or artificial, the thermodynamic costs of communication among their components are large. These systems also tend to split information transmitted between any two components across multiple…

Statistical Mechanics · Physics 2024-02-12 Farita Tasnim , Nahuel Freitas , David H. Wolpert

The study of intelligent systems explains behaviour in terms of economic rationality. This results in an optimization principle involving a function or utility, which states that the system will evolve until the configuration of maximum…

Information Theory · Computer Science 2024-06-18 Pedro Hack
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