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Mutual information $I(X;Y)$ is a useful definition in information theory to estimate how much information the random variable $Y$ holds about the random variable $X$. One way to define the mutual information is by comparing the joint…

Information Theory · Computer Science 2022-04-14 Bulut Kuskonmaz , Jaron Skovsted Gundersen , Rafal Wisniewski

We derive a tight lower bound on equivocation (conditional entropy), or equivalently a tight upper bound on mutual information between a signal variable and channel outputs. The bound is in terms of the joint distribution of the signals and…

Information Theory · Computer Science 2019-01-14 Michal Hledík , Thomas R. Sokolowski , Gašper Tkačik

We use holographic methods to characterize the RG flow of quantum information in a Chern-Simons theory coupled to massive fermions. First, we use entanglement entropy and mutual information between strips to derive the dimension of the…

High Energy Physics - Theory · Physics 2019-02-20 Vijay Balasubramanian , Niko Jokela , Arttu Pönni , Alfonso V. Ramallo

We derive information theoretic generalization bounds for supervised learning algorithms based on a new measure of leave-one-out conditional mutual information (loo-CMI). Contrary to other CMI bounds, which are black-box bounds that do not…

Machine Learning · Computer Science 2022-07-04 Mohamad Rida Rammal , Alessandro Achille , Aditya Golatkar , Suhas Diggavi , Stefano Soatto

We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information.…

Quantum Physics · Physics 2015-11-18 Jason Pye , William Donnelly , Achim Kempf

Mutual information I in infinite sequences (and in their finite prefixes) is essential in theoretical analysis of many situations. Yet its right definition has been elusive for a long time. I address it by generalizing Kolmogorov Complexity…

Computational Complexity · Computer Science 2021-08-03 Leonid A. Levin

We propose a new framework for reasoning about information in complex systems. Our foundation is based on a variational extension of Shannon's information theory that takes into account the modeling power and computational constraints of…

Machine Learning · Computer Science 2020-02-26 Yilun Xu , Shengjia Zhao , Jiaming Song , Russell Stewart , Stefano Ermon

We show that known entropy bounds constrain the information carried off by radiation to null infinity. We consider distant, planar null hypersurfaces in asymptotically flat spacetime. Their focussing and area loss can be computed…

High Energy Physics - Theory · Physics 2016-09-14 Raphael Bousso

We consider the problem of recovering the community structure in the stochastic block model with two communities. We aim to describe the mutual information between the observed network and the actual community structure in the sparse…

Probability · Mathematics 2023-08-30 Tomas Dominguez , Jean-Christophe Mourrat

The often-asked question whether space-time is discrete or continuous may not be the right question to ask: Mathematically, it is possible that space-time possesses the differentiability properties of manifolds as well as the ultraviolet…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Achim Kempf

The uncertainty principle is one of the characteristic properties of quantum theory based on incompatibility. Apart from the incompatible relation of quantum states, mutually exclusiveness is another remarkable phenomenon in the…

Quantum Physics · Physics 2016-11-09 Yunlong Xiao , Naihuan Jing

Using the algebraic approach to entanglement entropy, we study several dual pairs of lattice theories and show how the entropy is completely preserved across each duality. Our main result is that a maximal algebra of observables in a region…

High Energy Physics - Theory · Physics 2016-08-26 Djordje Radicevic

A trade-off relation on our knowledge about two noncommuting observables of a qubit system in simultaneous measurement is formulated. The obtained inequality offers a quantitative information-theoretic representation of Bohr's principle of…

Quantum Physics · Physics 2009-11-13 Yuji Kurotani , Takahiro Sagawa , Masahito Ueda

The entanglement entropy in a quantum field theory between two regions of space has been shown in simple cases to be proportional to the volume of the hypersurface separating the regions. We prove that this is true for a free scalar field…

High Energy Physics - Theory · Physics 2008-11-26 Micheal S. Berger , Roman V. Buniy

We are interested in learning data-driven representations that can generalize well, even when trained on inherently biased data. In particular, we face the case where some attributes (bias) of the data, if learned by the model, can severely…

Computer Vision and Pattern Recognition · Computer Science 2020-03-17 Ruggero Ragonesi , Riccardo Volpi , Jacopo Cavazza , Vittorio Murino

The classical information metric provides a unique notion of distance on the space of probability distributions with a well-defined operational interpretation: two distributions are far apart if they are readily distinguishable from one…

High Energy Physics - Theory · Physics 2021-06-23 John Stout

The information metric provides a unique notion of distance along any continuous family of physical theories, placing two theories further apart the more distinguishable they are. As such, the information metric is typically singular at…

High Energy Physics - Theory · Physics 2022-08-19 John Stout

Recently we conjectured that a certain set of universal topological quantities characterize topological order in any dimension. Those quantities can be extracted from the universal overlap of the ground state wave functions. For systems…

Strongly Correlated Electrons · Physics 2015-03-05 Heidar Moradi , Xiao-Gang Wen

Feature selection methods are usually evaluated by wrapping specific classifiers and datasets in the evaluation process, resulting very often in unfair comparisons between methods. In this work, we develop a theoretical framework that…

Machine Learning · Statistics 2016-10-11 Cláudia Pascoal , M. Rosário Oliveira , António Pacheco , Rui Valadas

One of the main notions of information theory is the notion of mutual information in two messages (two random variables in Shannon information theory or two binary strings in algorithmic information theory). The mutual information in $x$…

Information Theory · Computer Science 2012-06-19 Ilya Razenshteyn