arXiv research

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.

Paper proves a theorem about constant mean curvature surfaces in isotropic 3-space.

In this paper, we study factorable surfaces in a 3-dimensional isotropic space. We classify such surfaces with constant isotropic Gaussian (K) and mean curvature (H). We provide a non-existence result related with the surfaces satisfying H/K=const. Several examples are also illustrated.

In this paper, we study the rotational surfaces in the isotropic 3-space I^3. satisfying Weingarten conditions in terms of the relative curvature K (analogue of the Gaussian curvature) and the isotropic mean curvature H. In particular, we classify such surfaces of linear Weingarten type in I^3.

Study proves only origin-centered spheres solve certain curvature problems.

New blurring diffusion models bridge heat dissipation and denoising.

Paper calculates KL divergence for isotropic Gaussian-Markov fields.

The paper develops efficient algorithms for variational inference with mixtures of isotropic Gaussians.

The isotropic 3-space I^3 which is one of the Cayley--Klein spaces is obtained from the Euclidean space by substituting the usual Euclidean distance with the isotropic distance. In the present paper, we give several classifications on the surfaces in I^3 with the constant relative curvature (analogue of the Gaussian cu…

In this work, we are interested in the differential geometry of surfaces in simply isotropic $\mathbb{I}^3$ and pseudo-isotropic $\mathbb{I}_{\mathrm{p}}^3$ spaces, which consists of the study of $\mathbb{R}^3$ equipped with a degenerate metric such as $\mathrm{d}s^2=\mathrm{d}x^2\pm\mathrm{d}y^2$. The investigation is…

We study invariant surfaces generated by one-parameter subgroups of simply and pseudo isotropic rigid motions. Basically, the simply and pseudo isotropic geometries are the study of a three-dimensional space equipped with a rank 2 metric of index zero and one, respectively. We show that the one-parameter subgroups of i…

Proposes Gaussian process priors on graph sets with geometric structure.

Developed a new concept of isometric surfaces in isotropic space.

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…

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

In this study, we deal with the local structure of curves and surfaces immersed in a pseudo-isotropic space I_{p}^{3} that is a particular Cayley-Klein space. We provide the formulas of curvature, torsion and Frenet trihedron in order for spacelike and timelike curves. The causal character of all admissible surfaces in…

In this paper, we study the problem of finding the affine factorable surfaces in a 3-dimensional isotropic space with prescribed Gaussian (K) and mean (H) curvature. Because the absolute figure two different types of these surfaces appear by permutation of coordinates. We firstly classify the affine factorable surfaces…

SGD learns neural networks with a complexity measure called leap.

Study on Gaussian random fields' singularities on manifolds.

Randomized smoothing, using just a simple isotropic Gaussian distribution, has been shown to produce good robustness guarantees against $\ell_2$-norm bounded adversaries. In this work, we show that extending the smoothing technique to defend against other attack models can be challenging, especially in the high-dimensi…

A scalable factorized Gaussian process VAE for faster inference.

The paper proves uniqueness of solutions to curvature problems using various methods.

The paper examines Randers metrics with isotropic scalar curvature properties.

Gradient span algorithms show consistent progress in high dimensions.

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

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.

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

Study on InstaHide's security, linking to phase retrieval problem.

Study isotropic Riemannian maps and helices along them.

Bayesian framework for sphere regression using Gaussian fields.

Projection pursuit model improves Gaussian process regression for high-dimensional data.

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…

Stochastic gradient descent converges to universal limits in high dimensions.

While several papers have investigated computationally and statistically efficient methods for learning Gaussian mixtures, precise minimax bounds for their statistical performance as well as fundamental limits in high-dimensional settings are not well-understood. In this paper, we provide precise information theoretic …

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.

Novel Hilbert space Gaussian process improves sequential design accuracy and efficiency.

Spinor representation in isotropic space via Laguerre geometry.

The paper studies hanging chains and surfaces in degenerate geometries.

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

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 $\mathbb{C}^m$.

LeJEPA provides a scalable, theory-driven approach to self-supervised learning.