Results 61 to 70 of about 1,600,993 (289)
Geometric Structures Induced by Deformations of the Legendre Transform
Entropy, 2023 The recent link discovered between generalized Legendre transforms and non-dually flat statistical manifolds suggests a fundamental reason behind the ubiquity of Rényi’s divergence and entropy in a wide range of physical phenomena.
Pablo A. Morales +2 more
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Sentience and the Origins of Consciousness: From Cartesian Duality to Markovian Monism
Entropy, 2020 This essay addresses Cartesian duality and how its implicit dialectic might be repaired using physics and information theory. Our agenda is to describe a key distinction in the physical sciences that may provide a foundation for the distinction between ...
Karl J. Friston +2 more
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Information geometry, dynamics and discrete quantum mechanics [PDF]
, 2013 We consider a system with a discrete configuration space. We show that the geometrical structures associated with such a system provide the tools necessary for a reconstruction of discrete quantum mechanics once dynamics is brought into the picture.
Hall, Michael J. W., Reginatto, Marcel
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Lifting Dual Connections with the Riemann Extension
Mathematics, 2020 Let (M,g) be a Riemannian manifold equipped with a pair of dual connections (∇,∇*). Such a structure is known as a statistical manifold since it was defined in the context of information geometry.
Stéphane Puechmorel
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Qualia: The Geometry of Integrated Information
PLoS Computational Biology, 2009 According to the integrated information theory, the quantity of consciousness is the amount of integrated information generated by a complex of elements, and the quality of experience is specified by the informational relationships it generates. This paper outlines a framework for characterizing the informational relationships generated by such systems.
Balduzzi, D., Tononi, G.
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Generalized potential functions in differential geometry and information geometry [PDF]
International Journal of Geometric Methods in Modern Physics, 2019 Potential functions can be used for generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study whether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from
Florio M. Ciaglia +3 more
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On the Fisher Metric of Conditional Probability Polytopes
Entropy, 2014 We consider three different approaches to define natural Riemannian metrics on polytopes of stochastic matrices. First, we define a natural class of stochastic maps between these polytopes and give a metric characterization of Chentsov type in terms of ...
Guido Montúfar, Johannes Rauh, Nihat Ay
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Entropy, 2017 Information geometry enables a deeper understanding of the methods of statistical inference. In this paper, the problem of nonlinear parameter estimation is considered from a geometric viewpoint using a natural gradient descent on statistical manifolds ...
Yongqiang Cheng, Xuezhi Wang, Bill Moran
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Lie groupoids in information geometry
, 2019 We demonstrate that the proper general setting for contrast (potential) functions in statistical and information geometry is the one provided by Lie groupoids and Lie algebroids.
Amari S-I +11 more
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Information geometry in quantum field theory: lessons from simple examples [PDF]
, 2020 Motivated by the increasing connections between information theory and high-energy physics, particularly in the context of the AdS/CFT correspondence, we explore the information geometry associated to a variety of simple systems. By studying their Fisher
Erdmenger, Johanna +2 more
core +3 more sources