Explains geometric structures of information manifolds.
problem Understanding information geometry.
method Differential geometry concepts.
result Fundamental theorem of information geometry.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
169,051 papers · 148 categories
Trend · papers per month
48 results for “information manifolds”
Symplectic and Poisson structures proved for information geometry's Frobenius manifold.
problem Connecting disconnected theories in information geometry.
method Proving symplectic and Poisson structures on the Frobenius manifold.
result Established a bridge between Vinberg, Souriau, and Koszul's theories.
Kähler information manifolds for signal filters in weighted Hardy spaces are explored.
problem Developing a geometric framework for signal processing filters in weighted Hardy spaces.
method Introducing weighted Hardy spaces and smooth transformations of transfer functions, demonstrating the Kähler manifold structure.
result The Riemannian geometry of weighted Hardy norms for transfer functions forms a Kähler manifold.
Information geometry offers new tools for statistical analysis.
problem Statistical analysis of probability distributions.
method Geometric perspective on statistical manifolds.
result New applications in radar sensing, signal processing, etc.
Warped product affects divergences in information geometry.
problem Warped product's impact on divergences in information geometry.
method Study of warped product on information geometry.
result Warped product does not preserve canonical divergences.
We review basic notions in the field of information geometry such as Fisher metric on statistical manifold, -connection and corresponding curvature following Amari's work . We show application of information geometry to asymptotic statistical inference.
New DDMs use neural networks for solving equations on manifold shapes.
problem Solving equations on complex, high-dimensional shapes.
method Physics-informed neural networks combined with domain decomposition methods.
result Validated methods work well on various shapes in high dimensions.
Optimal persuasion involves projecting state vectors onto lower-dimensional 'optimal information manifolds'.
problem Optimal persuasion of another agent observing multi-dimensional data.
method Performing non-linear dimension reduction by projecting state vectors onto the 'optimal information manifold'.
result Optimal information design splits information into 'good' and 'bad' components, revealing only the direction of good information.
This paper shows any Kähler metric can be a Fisher information metric.
problem Establishing a new characterization of Kähler and coKähler manifolds.
method Statistical approach using Fisher information and exponential families.
result Any Kähler metric is a Fisher information metric.
Develops theory of homogeneous statistical manifolds and classifies Lie groups.
problem Understanding statistical manifolds and Lie groups.
method Constructs examples and classifies Lie groups using information geometry.
result Explicit examples of homogeneous statistical manifolds of low dimension constructed.
We extend manifold capacity to nonlinear neural representations with contextual information.
problem Efficient processing of information through neural representations.
method Theoretical framework leveraging latent directions in input space related to contextual information.
result Derivation of an exact formula for context-dependent manifold capacity.
We prove the correspondence between the information geometry of a signal filter and a Kähler manifold. The information geometry of a minimum-phase linear system with a finite complex cepstrum norm is a Kähler manifold. The square of the complex cepstrum norm of the signal filter corresponds to the Kähler potential. The…
Develops information geometry for Lévy processes in finance.
problem Understanding the statistical properties of Lévy processes for financial modeling.
method Deriving -divergences from Lévy triplets, identifying Fisher information matrix and -connection.
result Identifies statistical implications and differential-geometric structures of Lévy processes.
Inequalities linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
problem Linking entropy, Fisher info, Stein discrepancy, and Wasserstein distance on Riemannian manifolds.
method Deriving inequalities linking these measures on Riemannian manifolds.
result Strengthening and extending existing inequalities to Riemannian manifolds.
Stokes' theorem's boundary maximizes entropy.
problem Characterizing the boundary of a manifold using entropy.
method Maximizing entropy for codimension-1 submanifolds satisfying Stokes' theorem.
result The boundary of a manifold maximizes the entropy functional.
The paper studies geometric properties of statistical manifolds.
problem Understanding the geometric structure of statistical manifolds.
method Analyzing the geometric properties of generalized normal distribution manifold and constructing p-dimensional statistical manifolds.
result The generalized normal distribution manifold has constant α-Gaussian curvature, and p-dimensional statistical manifolds are α-flat.
Researchers study the geometric properties of a specific type of stable processes.
problem Understanding the information geometry of tempered stable processes.
method Derivation of α-divergence, Fisher information matrices, and α-connections.
result Obtained Fisher information matrices and α-connections for statistical manifolds.
A new method for faster optimization on statistical manifolds.
problem Slow convergence of first-order methods in manifold optimization.
method Dual Riemannian Newton method on manifolds with dual connections.
result Local quadratic convergence of the dual Riemannian Newton method.
This report concerns the problem of dimensionality reduction through information geometric methods on statistical manifolds. While there has been considerable work recently presented regarding dimensionality reduction for the purposes of learning tasks such as classification, clustering, and visualization, these method…
Entropy data replaces classical charts for smooth manifolds.
problem Establishing smooth structures on topological manifolds.
method Using entropy data to define admissible coordinate functions and reconstruct smooth atlases.
result Entropy-smooth structures are equivalent to classical smooth structures and stable under perturbations.
Constructing exponential families from statistical manifolds.
problem The central problem of constructing exponential families from statistical manifolds.
method Constructive approach proving every compact statistical manifold admits a foliation of Hessian manifolds.
result Compact orientable leaves are either finite quotients of flat torus or mapping torus with periodic monodromy.
Study angle structures on pseudo 3-manifolds, proving existence for some cases.
problem Determining if hyperbolic 3-manifolds can have angle structures.
method Examined triangulated pseudo 3-manifolds with area-curvature angle structures, establishing sufficient and necessary conditions.
result Compact hyperbolic 3-manifolds with totally geodesic boundary can have angle structures.
An Information-Theoretic Route to Isoperimetric Inequalities via Heat Flow and Entropy Dissipationmath.DG
New method uses entropy dissipation to prove isoperimetric inequalities.
problem Proving isoperimetric inequalities in geometric settings.
method Information-theoretic approach based on entropy dissipation under heat flow.
result New proof of Euclidean isoperimetric inequality with sharp constant.
CuBAS selects informative data points based on curvature for better classification.
problem Lack of efficient sampling strategies for maximizing dataset informativeness.
method Information-geometric framework using curvature scores to select labeled data.
result Consistent and statistically significant improvements over random and uncertainty-based sampling.
We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to some lower dimensional Euclidean space, as many manifold learning methods have b…
Adaptive sampling improves graph diffusion models by maintaining uniform information speed.
problem Standard diffusion models overlook non-homogeneous dynamics on complex manifolds.
method Information-geometric framework using Fisher-Rao metric and Drift Variation Score (DVS).
result DVS solver ensures uniform rate of distributional change, improving structural fidelity and efficiency.
The paper projects unknown manifolds onto hyperspheres for efficient function approximation.
problem Function approximation from data on unknown manifolds with added errors.
method Projects unknown manifold onto hypersphere and uses localized spherical polynomial kernels.
result Optimal rates of approximation for rough functions are given.
Survey of linking information geometry and optimal transport.
problem Connecting two geometric frameworks for probability measures.
method Exploration of interactions and links between information geometry and optimal transport.
result Outstanding questions for both disciplines.
We use the information metric to investigate the moduli space of a U(1) instanton on (anti)self-dual manifolds, finding an geometry similar to that for the moduli space of a Yang-Mills instanton on flat space. We discuss our results from the perspective of gauge/gravity duality.
We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such …
Inference for normal and Monte Carlo distributions using minimum relative entropy.
problem Inference from partial information on expectations and covariances.
method Minimum relative entropy sub-manifolds, analytical formulas, Monte Carlo simulations.
result Improved numerical implementation for inference from partial information.
Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary preliminaries on information geometry and holonomy groups, it is presented that the corresponding Riemannian holonomy group of the -dimension…
This research smooths out fluid equations to avoid sudden shocks.
problem Formation of shock singularities in compressible fluid equations.
method Information geometric regularization of unidimensional pressureless Euler equations.
result Smooth global solutions without artificial viscosity.
Bi-forms extend contrast functions to handle torsion in information geometry.
problem Insufficient contrast-based approaches for geometric structures with torsion.
method Introducing contrast bi-forms, a generalization of contrast functions.
result Bi-forms provide a unified framework for statistical potentials.
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We derive also the information geometry of the 3-manifold of McKay bivariate gamma dist…
We formulate the Riemannian calculus of the probability set embedded with -Wasserstein metric. This is an initial work of transport information geometry. Our investigation starts with the probability simplex (probability manifold) supported on vertices of a finite graph. The main idea is to embed the probability m…
GeoIB uses information geometry to control compression in deep learning models.
problem The indirect and biased nature of traditional IB implementations in deep learning.
method GeoIB uses Fisher-Rao and Jacobian-Frobenius terms to control information compression directly.
result GeoIB achieves better trade-off between accuracy and compression than traditional IB methods.
MALI aligns distinct domains using labeled data.
problem Aligning multi-domain data for machine learning.
method MALI learns manifold structure via diffusion and uses labeled data to guide alignment.
result MALI outperforms state-of-the-art methods across multiple datasets.
Statistical Einstein manifolds of exponential families with group-invariant potential functionsmath-ph
The paper classifies statistical Einstein manifolds in exponential families.
problem Classifying statistical Einstein manifolds in exponential families.
method Deriving partial differential equations for potential functions, obtaining special and group-invariant solutions.
result Special and group-invariant solutions of the equations for potential functions of exponential families.
Paper proves algebraic structure of a specific Frobenius manifold.
problem Understanding the algebraic properties of a specific Frobenius manifold.
method Proves decomposition into symmetric submanifolds over ideals.
result Decomposes the fourth Frobenius manifold into symmetric submanifolds.
We construct an infinite-dimensional information manifold based on exponential Orlicz spaces without using the notion of exponential convergence. We then show that convex mixtures of probability densities lie on the same connected component of this manifold, and characterize the class of densities for which this mixtur…
Topology-based information retrieval improves query accuracy.
problem Query accuracy in databases with complex structures.
method Dilation-invariant comparative measures of persistent homology.
result Topology-based retrieval outperforms standard methods.
We address the following problem: given two smooth densities on a manifold, find an optimal diffeomorphism that transforms one density into the other. Our framework builds on connections between the Fisher-Rao information metric on the space of probability densities and right-invariant metrics on the infinite-dimension…
Researchers derive asymptotic expansions for thermoelastic operators on manifolds.
problem Determining precise geometric information from thermoelastic spectra.
method Asymptotic expansions with Dirichlet and Neumann boundary conditions.
result Explicit calculation of first two coefficients for volumes.
Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the Hellinger divergence. When equipping a statistical manifold with the KL divergence, th…
Revisits information metric as pseudo metric on observables, with applications to conditional independence.
problem Clarifying the nature of information metric on manifolds of observables.
method Characterizes geodesics and applies Pythagorean theorem to conditional independence.
result Illustrates computation of information metric on Diabetes dataset.
The paper explores geometry of probability measures and barycenter maps.
problem Understanding the space of probability measures and their barycenter.
method Information geometry, Fisher metric, dualistic structures, divergences, geodesics.
result Recent developments in the geometry of probability measures and barycenter.
On the Optimal Representation Efficiency of Barlow Twins: An Information-Geometric Interpretationcs.LG
This paper analyzes Barlow Twins' representation efficiency using information-geometric methods.
problem Understanding and comparing the efficiency of self-supervised learning methods.
method Introduces an information-geometric framework to quantify representation efficiency and applies it to Barlow Twins.
result Proves that Barlow Twins achieves optimal representation efficiency (η=1).