Results 31 to 40 of about 1,328,298 (163)
The Information Geometry of UMAP
Le Matematiche, 2023 12 pages, 2 figures, 3 tables ; Github repo (https://github.com/sashakolpakov/info-geometry-umap) ; to appear in Le ...
Alexander Kolpakov \ University of Neuch\^atel, Switzerland +2 more
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On Monotone Embedding in Information Geometry
Entropy, 2015 A paper was published (Harsha and Subrahamanian Moosath, 2014) in which the authors claimed to have discovered an extension to Amari's \(\alpha\)-geometry through a general monotone embedding function. It will be pointed out here that this so-called \((F,
Jun Zhang
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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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, 2019 This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry.
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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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K\"ahlerian information geometry for signal processing
, 2015 We prove the correspondence between the information geometry of a signal filter and a K\"ahler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a K\"ahler manifold.
Choi, Jaehyung, Mullhaupt, Andrew P.
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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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Categorical Information Geometry
, 2023 Information geometry is the study of interactions between random variables by means of metric, divergences, and their geometry. Categorical probability has a similar aim, but uses algebraic structures, primarily monoidal categories, for that purpose.
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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
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Geometry of Information Integration
, 2017 Information geometry is used to quantify the amount of information integration within multiple terminals of a causal dynamical system. Integrated information quantifies how much information is lost when a system is split into parts and information ...
AB Barrett +16 more
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