Related papers: Parametric models and information geometry on W*-a…

We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the $L^2$ metric. The primary motivation for…

Let R be a discrete valuation ring of unequal characteristic with fraction field K which contains a primitive p^2-th root of unity. Let X be a faithfully flat R-scheme and G be a finite abstract group. Let us consider a G-torsor Y_K\to X_K…

Classical W-symmetry is globally parametrized by the Grassmannian Manifold which is associated with the non-relativistic fermions. We give the bosonization rule which defines the natural higher coordinates system to describe the W-geometry.…

Let (M,g) be a compact, connected and oriented Riemannian manifold. We denote D the space of smooth probability density functions on M. In this paper, we show that the Frechet manifold D is equipped with a Riemannian metric g^{D} and an…

The high-dimensional parameter space of deep neural networks -- the neuromanifold -- is endowed with a unique metric tensor defined by the Fisher information. Reliable and scalable computation of this metric tensor is valuable for theorists…

Let $V$ be a quasi-conformal grading-restricted vertex algebra, $W$ be its module, and $\W_{z_1, \ldots, z_n}$ be the space of rational differential forms with complex parameters $(z_1, \ldots, z_n)$ for $n \ge 0$. Using geometric…

Information geometry provides a geometric approach to families of statistical models. The key geometric structures are the Fisher quadratic form and the Amari-Chentsov tensor. In statistics, the notion of sufficient statistic expresses the…

Information geometry provides differential geometric concepts like a Riemannian metric, connections and covariant derivatives on spaces of probability distributions. We discuss here how these concepts apply to quantum field theories in the…

These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion of embedded noncommutative spaces…

Matrix models with continuous symmetry are powerful tools for studying quantum gravity and holography. Tensor models have also found applications in holographic quantum gravity. Matrix models with discrete permutation symmetry have been…

In this paper, we comparatively analyze the Bures-Wasserstein (BW) geometry with the popular Affine-Invariant (AI) geometry for Riemannian optimization on the symmetric positive definite (SPD) matrix manifold. Our study begins with an…

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the…

Physical systems, characterized by an ensemble of interacting elementary constituents, can be represented and studied by different algebras of observables or operators. For example, a fully polarized electronic system can be investigated by…

Thermal states play a fundamental role in various areas of physics, and they are becoming increasingly important in quantum information science, with applications related to semi-definite programming, quantum Boltzmann machine learning,…

We elucidate the geometry of matrix models based on simple formally real Jordan algebras. Such Jordan algebras give rise to a nonassociative geometry that is a generalization of Lorentzian geometry. We emphasize constructions for the…

We extend the results of Riemannian geometry over finite groups and provide a full classification of all linear connections for the minimal noncommutative differential calculus over a finite cyclic group. We solve the torsion-free and…

We introduce a dbar-formulation of the orthogonal polynomials on the complex plane, and hence of the related normal matrix model, which is expected to play the same role as the Riemann-Hilbert formalism in the theory of orthogonal…

The idea that a spacetime metric emerges as a Fisher-Rao `information metric' of instanton moduli space has been examined in several field theories such as the Yang-Mills theories and nonlinear sigma models. In this brief paper, we report…

In Theorem 1, we generalize the results of Szabo for Berwald metrics that are not necessary strictly convex: we show that for every Berwald metric F there always exists a Riemannian metric affine equivalent to F. As an application we show…

In this work we deal with an elliptic non-linear problem, which arises naturally from Riemannian geometry. This problem has clasically been studied in the the Euclidean $n$-dimensional space and it is known as the Moser-Bernstein problem.…