arXiv research

New spectral mixture representation for isotropic kernels simplifies random Fourier features.

The paper provides consistency results for KDE on manifolds with irregular kernels.

The paper studies hanging chains and surfaces in degenerate geometries.

Isotropic kernels' performance is analyzed across different tasks with and without invariants.

By adapting a technique of Molchanov, we obtain the heat kernel asymptotics at the sub-Riemannian cut locus, when the cut points are reached by an $r$-dimensional parametric family of optimal geodesics. We apply these results to the bi-Heisenberg group, that is, a nilpotent left-invariant sub-Rieman\-nian structure on …

We introduce the notion of an isotropic quantum state associated with a Bohr-Sommerfeld manifold in the context of Berezin-Toeplitz quantization of general prequantized symplectic manifolds, and we study its semi-classical properties using the off-diagonal expansion of the Bergman kernel. We then show how these results…

Proposes Gaussian process priors on graph sets with geometric structure.

We study learning problems in which the conditional distribution of the output given the input varies as a function of additional task variables. In varying-coefficient models with Gaussian process priors, a Gaussian process generates the functional relationship between the task variables and the parameters of this con…

Generative models use kernel smoothing for conditioning on small example sets.

Strictly proper kernel scores are well-known tool in probabilistic forecasting, while characteristic kernels have been extensively investigated in the machine learning literature. We first show that both notions coincide, so that insights from one part of the literature can be used in the other. We then show that the m…

Deep kernel processes unify various models using Gram matrices and kernel functions.

Study on kernel tests for high-dimensional data, focusing on MMD and CLT.

The geometric approach to diffeomorphic image registration known as "large deformation by diffeomorphic metric mapping" (LDDMM) is based on a left action of diffeomorphisms on images, and a right-invariant metric on a diffeomorphism group, usually defined using a reproducing kernel. We explore the use of left-invariant…

Proposes a new CNN for meshes that can handle orientation.

Study on KRR with power-law data, showing better sample complexity.

The paper examines Randers metrics with isotropic scalar curvature properties.

RFFNet scales kernel methods to large datasets by learning kernel relevance.

This work investigates how gradient-based learning performs with structured data, revealing issues and improvements.

Paper establishes a relation between Berwald scalar curvature and S-curvature.

Unified analysis of kernel-based and locally adaptive bandit optimization methods.

In this paper, we find a condition on $(α, β)$-metrics under which the notions of isotropic S-curvature, weakly isotropic S-curvature and isotropic mean Berwald curvature are equivalent.

Study physical work done by isotropic vector forces along isotropic curves.

The paper defines conditions for Gaussian process sample path regularity.

Study isotropic Riemannian maps and helices along them.

DNNs improve SIMP method but not spatially invariant, study shows.

We study two types of isotropic planes: weakly isotropic and strongly isotropic planes. We prove that a Riemannian manifold of indefinite metric is conformally flat if and only if its curvature tensor vanishes on all the strongly isotropic planes. We specialize the plane axiom for Riemannian manifolds of indefinite met…

Study isotropic curves on complex quadric with geometric relations.

In this paper, we construct a new class of Finsler manifolds called generalized isotropic Berwald manifolds which is an extension of the class of isotropic Berwald manifolds. We prove that every generalized isotropic Berwald manifold is a generalized Douglas-Weyl manifold. On a compact generalized isotropic Berwald man…

Constructs a moment map flow for isotropic maps on surfaces.

The paper studies Lipschitz bounds for integral kernels under differentiability assumptions.

Spinor representation in isotropic space via Laguerre geometry.

We create real-time geodesic rendering for non-isotropic geometries.

Developed a new concept of isometric surfaces in isotropic space.

Paper shows isotropic $E$- and $S$-curvatures are equivalent in warped Finsler metrics.

In this paper we will show that a Lagrangian, Lorentzian surface $M^2_1$ in a complex pseudo space form $\widetilde M^2_1 (4c)$ is pseudo-isotropic if and only if $M$ is minimal. Next we will obtain a complete classification of all Lagrangian, Lorentzian surfaces which are lightlike pseudo-isotropic but not pseudo-isot…

The paper studies Kropina metrics with a specific curvature property.

New approach uses isotropic geometry to solve Euclidean problems.

We show that for $m>n\geq 2$, there are at least two exact isotropic $n$-tori in $\mathbb{C}^m$ which are not Hamiltonian isotopic in $\mathbb{C}^m$, even though they are smoothly isotopic as isotropic $n$-tori. We apply this discovery to obtain more distinct non-exact isotropic tori in $\mathbb{C}^m$.

The paper analyzes learning curves for kernel ridge regression with dot-product kernels.

Study classifies zero mean curvature surfaces with planar curvature lines.

The study of Laguerre isotropic hypersurfaces with rigidity and isoparametric properties.

This paper aims to provide a description of totally isotropic Willmore two-spheres and their adjoint transforms. We first recall the isotropic harmonic maps which are introduced by Hélein, Xia-Shen and Ma for the study of Willmore surfaces. Then we derive a description of the normalized potential (some Lie algebra valu…

Study surfaces with constant ratio of principal curvatures in Euclidean and isotropic geometries.

This work extends holomorphic surface representations to isotropic space.

We classify translation surfaces in isotropic geometry with arbitrary constant isotropic Gaussian and mean curvature under the condition that at least one of translating curves lies in a plane.

Polynomial networks converge to Gaussian processes at a rate of O(n^(-1/2)).

Paper classifies Randers metrics based on Ricci curvature properties.

The study finds compact vacuum static spaces with positive isotropic curvature are spheres or products of a circle and sphere.