scholarly journals Geometry of Fisher Information Metric and the Barycenter Map

Entropy ◽  
2015 ◽  
Vol 17 (4) ◽  
pp. 1814-1849 ◽  
Author(s):  
Mitsuhiro Itoh ◽  
Hiroyasu Satoh
Keyword(s):  
Fisher Information ◽  
Fisher Information Metric ◽  
Information Metric

scholarly journals Holographic Fisher information metric in Schrödinger spacetime

2021 ◽  
Vol 136 (11) ◽  
Author(s):  
H. Dimov ◽  
I. N. Iliev ◽  
M. Radomirov ◽  
R. C. Rashkov ◽  
T. Vetsov
Keyword(s):  
Fisher Information ◽  
Fisher Information Metric ◽  
Information Metric

scholarly journals Appearance of Thermal Time

2021 ◽  
Vol 51 (2) ◽  
Author(s):  
Shigenori Tanaka
Keyword(s):  
Differential Geometry ◽  
Relaxation Process ◽  
Fisher Information ◽  
Basic Equation ◽  
Dynamical Process ◽  
Two Dimensional ◽  
Event Time ◽  
Fisher Information Metric ◽  
Intrinsic Correlation ◽  
Information Metric

AbstractIn this paper a viewpoint that time is an informational and thermal entity is presented. We consider a model for a simple relaxation process for which a relationship among event, time and temperature is mathematically formulated. It is then explicitly illustrated that temperature and time are statistically inferred through measurement of events. The probability distribution of the events thus provides an intrinsic correlation between temperature and time, which can relevantly be expressed in terms of the Fisher information metric. The two-dimensional differential geometry of temperature and time then leads us to a finding of a simple equation for the scalar curvature, $$R = -1$$ R = - 1 , in this case of relaxation process. This basic equation, in turn, may be regarded as characterizing a nonequilibrium dynamical process and having a solution given by the Fisher information metric. The time can then be interpreted so as to appear in a thermal way.

scholarly journals Coarse-graining of the Einstein–Hilbert action rewritten by the Fisher information metric

2020 ◽  
Vol 35 (26) ◽  
pp. 2050157
Author(s):  
Shingo Takeuchi
Keyword(s):  
Fixed Point ◽  
Fisher Information ◽  
Coarse Graining ◽  
Quantum Level ◽  
Classical Level ◽  
Transformation Rules ◽  
Fisher Information Metric ◽  
Information Metric ◽  
Fisher Metric ◽  
Hilbert Action

In this study, considering the Fisher information metric (Fisher metric) given by a specific form, which is the form of weights in statistics, we rewrite the Einstein–Hilbert (EH) action. Then, determining the transformation rules of the Fisher metric, etc under the coarse-graining, we perform the coarse-graining toward that rewritten EH action. We finally show an existence of a trivial fixed-point. Here, the existence of a trivial fixed-point is not trivial for us because we consider the metric given by the Fisher metric, which is not the normal metric and has to satisfy some constraint in the formalism of the Fisher metric. We use the path-integral in our analysis. At this time we have to accept that a fundamental constraint in the formalism of the Fisher metric is broken at the quantum level. However we consider we can accept this with the thought that some constraints and causal relations held at the classical level usually get broken at the quantum level. We finds some problems of the Fisher metric. The space–time we consider in this study is two-dimensional.

scholarly journals The Adversarial Attack and Detection under the Fisher Information Metric

2019 ◽  
Vol 33 ◽  
pp. 5869-5876 ◽  
Author(s):  
Chenxiao Zhao ◽  
P. Thomas Fletcher ◽  
Mixue Yu ◽  
Yaxin Peng ◽  
Guixu Zhang ◽  
...  
Keyword(s):  
Deep Learning ◽  
Fisher Information ◽  
Information Matrix ◽  
Superior Performance ◽  
Learning Models ◽  
Detection Algorithms ◽  
Fisher Information Metric ◽  
One Step ◽  
Information Metric ◽  
Adversarial Attack

Many deep learning models are vulnerable to the adversarial attack, i.e., imperceptible but intentionally-designed perturbations to the input can cause incorrect output of the networks. In this paper, using information geometry, we provide a reasonable explanation for the vulnerability of deep learning models. By considering the data space as a non-linear space with the Fisher information metric induced from a neural network, we first propose an adversarial attack algorithm termed one-step spectral attack (OSSA). The method is described by a constrained quadratic form of the Fisher information matrix, where the optimal adversarial perturbation is given by the first eigenvector, and the vulnerability is reflected by the eigenvalues. The larger an eigenvalue is, the more vulnerable the model is to be attacked by the corresponding eigenvector. Taking advantage of the property, we also propose an adversarial detection method with the eigenvalues serving as characteristics. Both our attack and detection algorithms are numerically optimized to work efficiently on large datasets. Our evaluations show superior performance compared with other methods, implying that the Fisher information is a promising approach to investigate the adversarial attacks and defenses.

scholarly journals Purification complexity without purifications

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Shan-Ming Ruan
Keyword(s):  
Fisher Information ◽  
Mixed State ◽  
Quantum Fisher Information ◽  
Quantum States ◽  
Density Matrices ◽  
Gaussian States ◽  
State Complexity ◽  
Quantum Operations ◽  
Fisher Information Metric ◽  
Information Metric

Abstract We generalize the Fubini-Study method for pure-state complexity to generic quantum states by taking Bures metric or quantum Fisher information metric (QFIM) on the space of density matrices as the complexity measure. Due to Uhlmann’s theorem, we show that the mixed-state complexity exactly equals the purification complexity measured by the Fubini-Study metric for purified states but without explicitly applying any purification. We also find the purification complexity is non-increasing under any trace-preserving quantum operations. We also study the mixed Gaussian states as an example to explicitly illustrate our conclusions for purification complexity.

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