arXiv research

A new VAE model captures hyperspherical data better than the standard Gaussian model.

Researchers enhance hyperspherical latent representations for higher-dimensional data.

Proposes a new latent variable model for hyperspherical latent spaces.

A new method uses hyperspherical latent spaces to disentangle data with periodic structures.

Paper optimizes hyperspherical prototypes for better class separation.

Constructs hyperspheres with prescribed mean curvature in Euclidean space.

The study characterizes kernel spaces on hyperspheres, impacting cubature algorithms.

Study on hyperspheres in 4-spaces as special Riemannian manifolds.

Horospheres, hyperspheres, and hyperplanes in hyperbolic spaces are rigid in terms of mean curvature.

The study classifies product affine hyperspheres in R^n+1.

The paper finds conditions for biharmonic orbits in symmetric spaces.

Prototype networks on hyperspheres improve classification and regression.

Method learns PDE dynamics via evolving latent manifold using Ricci flow.

We show how in many cases the algebraic number of immersed hyperspheres of constant (and prescribed) curvature may be related to the Euler Characteristic of the ambient space.

Paper presents exact heat kernel on hypersphere for SVM improvements.

SphereConv improves deep learning by learning angular representations on hyperspheres.

There are considered 4-dimensional pseudo-Riemannian spaces with inner products of signature (3,1) and (2,2). The objects of investigation are space-like and time-like hyperspheres in the respective cases. These hypersurfaces are equipped with almost contact B-metric structures. The constructed manifolds are characteri…

Researchers prove constant mean curvature graphs in hyperbolic 3-space for specific domains.

Method detects anomalies on attributed graphs with few labeled instances.

We show that the natural S^1-bundle over a projective special Kaehler manifold carries the geometry of a proper affine hypersphere endowed with a Sasakian structure. The construction generalizes the geometry of the Hopf-fibration $\Sr^{2n+1} \longrightarrow \CP^n$ in the context of projective special Kaehler manifolds.…

The paper classifies $\widetilde{J}$-tangent affine hyperspheres in arbitrary dimensions.

The orthogonal trajectories of the first tangents of the curve are called the involutes of $x$. The hyperspheres which have higher order contact with a curve $x$ are known osculating hyperspheres of $x$. The centers of osculating hyperspheres form a curve which is called generalized evolute of the given curve $x$ in $n…

The study characterizes canal hypersurfaces formed by non-null curves with parallel frame in Minkowski space-time.

We describe extrinsic hyperspheres and totally geodesic hypersurfaces in manifolds with special holonomy. In particular we prove the nonexistence of extrinsic hyperspheres in quaternion-Kaehler manifolds. We develop a new approach to extrinsic hyperspheres based on the classification of special Killing forms.

We show that a space with a finite asymptotic dimension is embeddable in a non-positively curved manifold. Then we prove that if a uniformly contractible manifold X is uniformly embeddable in $\R^n$ or non-positively curved n-dimensional simply connected manifold then $X\times\R^n$ is integrally hyperspherical. If a un…

An affine hypersurface M is said to admit a pointwise symmetry, if there exists a subgroup G of Aut(T_p M) for all p in M, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator S. Here, we consider 3-dimensional indefinite affine hyperspheres, i.e. S= H Id (and thus S is…

Study examines structures on special hyperspheres in a 6-sphere.

In this paper, we explicitly construct the Calabi composition of multiple affine hyperspheres possibly including some points viewing as 0-dimensional hypersheres. Then we compute all the basic affine invariants of the composed affine hyperspheres, proving that the composed affine hypersphere is symmetric one if and onl…

Paper proposes a structured approach to improve active learning performance.

Paper proposes efficient method to calculate Fisher-Bingham distribution normalizing constant.

New method uses hyperspherical geometry to improve community detection.

Small hypersphere is unstable in both 4-harmonic and ES-4-harmonic settings.

Study classifies hypersurfaces in 4D Lorentz-Minkowski space using specific operators.

A holomorphic representation formula for special parabolic hyperspheres is given.

New minimal hypersphere found in 4-sphere solving Bernstein problem.

Upper estimate of Dirac eigenvalue linked to hyperspherical radius.

Distributions over permutations arise in applications ranging from multi-object tracking to ranking of instances. The difficulty of dealing with these distributions is caused by the size of their domain, which is factorial in the number of considered entities ($n!$). It makes the direct definition of a multinomial dist…

This paper proves the manifold hypothesis for lower embedding dimensions using osculating hyperspheres.

The paper projects unknown manifolds onto hyperspheres for efficient function approximation.

In this paper, a correspondence via duality is established between the set of locally strongly convex symmetric equiaffine hyperspheres and the set of minimal symmetric Lagrangian submanifolds in a certain complex space form. By using this correspondence theorem, we are able to provide an alternative proof of the class…

No regular algebraic hypersurfaces with non-zero constant mean curvature in Euclidean spaces are found.

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

Formulates integrals for hypersphere arrangements using cohomology and Cayley-Menger determinants.

This work optimizes alignment and uniformity of features on a hypersphere for better downstream performance.

The paper proves volume bounds for specific hyperspheres in Riemannian manifolds.

The paper studies canal hypersurfaces in Lorentz-Minkowski 4-space.

A new loss function HUG decouples and generalizes neural collapse.

The study characterizes quadrics among affine hyperspheres based on centroid collinearity of sections.