Related papers: Naturalness and Fisher Information
We consider the problem of distributed estimation of a Gaussian vector with linear observation model. Each sensor makes a scalar noisy observation of the unknown vector, quantizes its observation, maps it to a digitally modulated symbol,…
We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…
Quantum Fisher information matrices (QFIMs) are fundamental to estimation theory: they encode the ultimate limit for the sensitivity with which a set of parameters can be estimated using a given probe. Since the limit invokes the inverse of…
Entanglement is the key quantum resource for improving measurement sensitivity beyond classical limits. However, the production of entanglement in mesoscopic atomic systems has been limited to squeezed states, described by Gaussian…
The net Fisher information measure, defined as the product of position and momentum Fisher information measures and derived from the non-relativistic Hartree-Fock wave functions for atoms with Z=1-102, is found to correlate well with the…
The Fisher information matrix (FIM) plays an essential role in statistics and machine learning as a Riemannian metric tensor or a component of the Hessian matrix of loss functions. Focusing on the FIM and its variants in deep neural…
In this study, we model the dark matter and baryon matter distribution in the Cosmic Web by means of highly nonlinear Schr\"{o}dinger type and reaction diffusion wave mechanical descriptions. The construction of these wave mechanical models…
We study the interrelationships between the Fisher information metric recently introduced, on the basis of maximum entropy considerations, by Brody and Hughston (quant-ph/9906085) and the monotone metrics, as explicated by Petz and Sudar.…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
Persuasion is the process of changing an agent's belief distribution from a given (or estimated) prior to a desired posterior. A common assumption in the acceptance of information or misinformation as fact is that the (mis)information must…
In this paper, we consider the problem of sensor selection for parameter estimation with correlated measurement noise. We seek optimal sensor activations by formulating an optimization problem, in which the estimation error, given by the…
An Edgeworth-type expansion is established for the relative Fisher information distance to the class of normal distributions of sums of i.i.d. random variables, satisfying moment conditions. The validity of the central limit theorem is…
Physics-Informed Neural Networks (PINNs) have emerged as a powerful tool for solving differential equations and modeling physical systems by embedding physical laws into the learning process. However, rigorously quantifying how well a PINN…
We report a similarity between the microscopic parameter dependance of emergent theories in physics and that of multiparameter models common in other areas of science. In both cases, predictions are possible despite large uncertainties in…
We demonstrate that many Naturalness tests of particle theories discussed in the literature can be reformulated as straightforward algorithmic finetuning assessments in the matching of Wilsonian effective theories above and below particle…
The Higgs boson discovery stirred interest in next-to-minimal supersymmetric models, due to the apparent fine-tuning required to accommodate it in minimal theories. To assess their naturalness, we compare fine-tuning in a $\mathbb{Z}_3$…
The problem of determining the achievable sensitivity with digitization exhibiting minimal complexity is addressed. In this case, measurements are exclusively available in hard-limited form. Assessing the achievable sensitivity via the…
A weak value is an effective description of the influence of a pre and post-selected 'principal' system on another 'meter' system to which it is weakly coupled. Weak values can describe anomalously large deflections of the meter, and…
We develop a new framework to optimize and understand uncertainty from in situ strong field measurements of laser field parameters. We present the first derivation of quantum and classical Fisher information for an electron undergoing…
I define a natural measure of the complexity of a parametric distribution relative to a given true distribution called the {\it razor} of a model family. The Minimum Description Length principle (MDL) and Bayesian inference are shown to…