English
Related papers

Related papers: Information geometric complexity of a trivariate G…

200 papers

Geometric frustration arises whenever the constituents of a physical assembly locally favor an arrangement that cannot be realized globally. Recently, such frustrated assemblies were shown to exhibit filamentation, size limitation, large…

Soft Condensed Matter · Physics 2021-12-15 Snir Meiri , Efi Efrati

Random fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this…

Information Theory · Computer Science 2017-03-14 Alexandre L. M. Levada

Understanding a complex system entails capturing the non-trivial collective phenomena that arise from interactions between its different parts. Information theory is a flexible and robust framework to study such behaviours, with several…

For a language model (LM) to faithfully model human language, it must compress vast, potentially infinite information into relatively few dimensions. We propose analyzing compression in (pre-trained) LMs from two points of view: geometric…

Computation and Language · Computer Science 2023-11-10 Emily Cheng , Corentin Kervadec , Marco Baroni

Information geometry promotes an investigation of the geometric structure of statistical manifolds, providing a series of elucidations in various areas of scientific knowledge. In the physical sciences, especially in quantum theory, this…

Quantum Physics · Physics 2020-12-08 Gabriel F. Magno , Carlos H. Grossi , Gerardo Adesso , Diogo O. Soares-Pinto

We present an information geometric analysis of entanglement generated by an s-wave scattering between two Gaussian wave packets. We conjecture that the pre and post-collisional quantum dynamical scenarios related to an elastic head-on…

Mathematical Physics · Physics 2015-05-20 D. -H. Kim , S. A. Ali , C. Cafaro , S. Mancini

Is the geometry of space a macroscopic manifestation of an underlying microscopic statistical structure? Is geometrodynamics - the theory of gravity - derivable from general principles of inductive inference? Tentative answers are suggested…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Ariel Caticha

We investigate the dynamics of information scrambling in bosonic systems undergoing Gaussian unitary evolution associated with quadratic Hamiltonians. For initial Gaussian states, we observe the disappearance of the memory effect in the…

Quantum Physics · Physics 2025-08-05 Ali Mollabashi , Saleh Rahimi-Keshari

We propose a unified theoretical framework for quantifying spatio-temporal interactions in a stochastic dynamical system based on information geometry. In the proposed framework, the degree of interactions is quantified by the divergence…

Neurons and Cognition · Quantitative Biology 2016-12-08 Masafumi Oizumi , Naotsugu Tsuchiya , Shun-ichi Amari

It is well known that quantum mechanics admits a geometric formulation on the complex projective space as a Kahler manifold. In this paper we consider the notion of mutual information among continuous random variables in relation to the…

Mathematical Physics · Physics 2020-04-07 Davide Pastorello

We formulate a geometric framework in which physical laws emerge from restricted access to microscopic information. Measurement constraints are modeled as a gauge symmetry acting on density operators, inducing a gauge-reduced space of…

Quantum Physics · Physics 2026-05-19 Tiago Pernambuco , Lucas Chibebe Céleri

Geometric frustration appears in a broad range of systems, generally emerging as disordered ground configurations, thereby impeding understanding of the phenomenon's underlying mechanics. We report on a continuum system featuring locally…

Applied Physics · Physics 2021-06-04 Janav P. Udani , Andres F. Arrieta

Despite the growing availability of sensing and data in general, we remain unable to fully characterise many in-service engineering systems and structures from a purely data-driven approach. The vast data and resources available to capture…

Machine Learning · Computer Science 2023-09-20 Elizabeth J Cross , Timothy J Rogers , Daniel J Pitchforth , Samuel J Gibson , Matthew R Jones

In recent years, the unified theory of information and thermodynamics has been intensively discussed in the context of stochastic thermodynamics. The unified theory reveals that information theory would be useful to understand…

Statistical Mechanics · Physics 2018-07-23 Sosuke Ito

We study the geometrical frustration scenario of glass formation for simple hard sphere models. We find that the dual picture in terms of defects brings little insight and no theoretical simplification for the understanding of the slowing…

Disordered Systems and Neural Networks · Physics 2015-03-19 Benoit Charbonneau , Patrick Charbonneau , Gilles Tarjus

Choice overload occurs when individuals feel overwhelmed by an excessive number of options. Experimental evidence suggests that a larger selection can complicate the decision-making process. Consequently, choice satisfaction may diminish…

Physics and Society · Physics 2024-12-18 Mojtaba Madadi Asl , Kamal Hajian , Rouzbeh Torabi , Mehdi Sadeghi

Although the notion of entropy lies at the core of statistical mechanics, it is not often used in statistical mechanical models to characterize phase transitions, a role more usually played by quantities such as various order parameters,…

Statistical Mechanics · Physics 2016-08-31 D. A. Johnston , W. Janke , R. Kenna

Partial differential equations describing compressible fluids are prone to the formation of shock singularities, arising from faster upstream fluid particles catching up to slower, downstream ones. In geometric terms, this causes the…

Analysis of PDEs · Mathematics 2026-01-07 Ruijia Cao , Florian Schäfer

In this paper, I propose a theoretical information-geometric framework suitable to characterize chaotic dynamical behavior of arbitrary complex systems on curved statistical manifolds. Specifically, I present an information-geometric…

Mathematical Physics · Physics 2015-05-13 Carlo Cafaro

Information geometry is concerned with the application of differential geometry concepts in the study of the parametric spaces of statistical models. When the random variables are independent and identically distributed, the underlying…

Information Theory · Computer Science 2021-10-05 Alexandre L. M. Levada