Related papers: Information Geometry and the Renormalization Group
Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades…
What is the structure of general quantum processes on composite systems that respect a global or local symmetry principle? How does the irreversible use of quantum resources behave under such symmetry principles? Here we employ an…
In physics one attempts to infer the rules governing a system given only the results of imperfect measurements. Hence, microscopic theories may be effectively indistinguishable experimentally. We develop an operationally motivated procedure…
A hidden generalized gauge symmetry of a cutoff QED is used to show the renormalizability of QED. In particular, it is shown that corresponding Ward identities are valid all along the renormalization group flow. The exact Renormalization…
Applying recursive renormalization group transformations to a scalar field theory, we obtain an effective quantum gravity theory with an emergent extra dimension, described by a dual holographic Einstein-Klein-Gordon type action. Here, the…
The renormalization-group improved effective potential ---to leading-log and in the linear curvature approximation--- is constructed for ``finite'' theories in curved spacetime. It is not trivial and displays a quite interesting,…
The advantages of using more than one renormalization group (RG) in problems with more than one important length scale are discussed. It is shown that: i) using different RG's can lead to complementary information, i.e. what is very…
We study spherically-symmetric solutions to a modified Einstein-Hilbert action with Renormalization Group scale-dependent couplings, inspired by Weinberg's Asymptotic Safety scenario for Quantum Gravity. The Renormalization Group scale is…
We introduce a geometric scaling relation that characterizes the local scale behavior of correlations using the informational distance $d_E = K_0/\sqrt{I}$, where $I$ is the mutual information. We define a geometric conversion factor, $G…
A block spin renormalization group approach is proposed for the dynamical triangulation formulation of quantum gravity in arbitrary dimensions. Renormalization group flow diagrams are presented for the three-dimensional and four-dimensional…
While phases and phase transitions are conventionally described by local order parameters in real space, we present a unified framework characterizing the phase transition through the geometry of configuration space defined by the…
We use the system of p-adic numbers for the description of information processes. Basic objects of our models are so called transformers of information, basic processes are information processes, the statistics are information statistics…
Optimization in large language models (LLMs) unfolds over high-dimensional parameter spaces with non-Euclidean structure. Information geometry frames this landscape using the Fisher information metric, enabling more principled learning via…
It is well known that the renormalization group equations depend on the scale where they are applied. This phenomenon is especially relevant for the massive fields in curved space, because the decoupling effects may be responsible for…
In this paper, we consider the problem of quantifying parametric uncertainty in classical empirical interatomic potentials (IPs) using both Bayesian (Markov Chain Monte Carlo) and frequentist (profile likelihood) methods. We interface these…
For arbitrary scalar QFTs in four dimensions, renormalisation group equations of quartic and cubic interactions, mass terms, as well as field anomalous dimensions are computed at three-loop order in the $\overline{\text{MS}}$ scheme.…
Some recent results showed that renormalization group can be considered as a promising framework to address open issues in data analysis. In this work, we focus on one of these aspects, closely related to principal component analysis for…
The well-known phase structure of the two-dimensional sine-Gordon model is reconstructed by means of its renormalization group flow, the study of the sensitivity of the dynamics on microscopic parameters. Such an analysis resolves the…
The causal dynamical triangulations approach aims to construct a quantum theory of gravity as the continuum limit of a lattice-regularized model of dynamical geometry. A renormalization group scheme--in concert with finite size scaling…
A framework allowing for perturbative calculations to be carried out for quantum field theories with arbitrary smoothly curved boundaries is described. It is based on an expansion of the heat kernel derived earlier for arbitrary mixed…