arXiv research

New algorithm radVI improves variational inference by optimizing radial profiles.

We propose a new variational family for Bayesian neural networks. We decompose the variational posterior into two components, where the radial component captures the strength of each neuron in terms of its magnitude; while the directional component captures the statistical dependencies among the weight parameters. The …

We propose Radial Bayesian Neural Networks (BNNs): a variational approximate posterior for BNNs which scales well to large models while maintaining a distribution over weight-space with full support. Other scalable Bayesian deep learning methods, like MC dropout or deep ensembles, have discrete support-they assign zero…

The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.

K-Means and RBF networks are shown to be equivalent under certain conditions.

Stochastic gradient descent optimizes Nyström samples for kernel matrix approximation.

Study on surfaces in Heisenberg group with constant mean curvature.

An ODE variational calculation shows that an image principle curvature ratio factor can raise the lower bound, 2(Image Area), on energy of a harmonic map of a surface into Rn. In certain situations, including all radially symmetry harmonic maps, equality is achieved.

The Gauss Image Measure uniquely identifies dual convex bodies up to dilation.

The paper generalizes radial curvature bounds on manifolds.

Study examines maximal domains of radial harmonic functions across different curvature types.

The paper proves geometric and spectral alignment for deep neural networks.

Convexity properties are preserved under radial transformations in hyperbolic and spherical geometries.

The first order behavior of multivariate heavy-tailed random vectors above large radial thresholds is ruled by a limit measure in a regular variation framework. For a high dimensional vector, a reasonable assumption is that the support of this measure is concentrated on a lower dimensional subspace, meaning that certai…

The study characterizes harmonic spaces and their radial eigen-functions and vector fields.

A method to fix radius distortion in generative models on curved spaces.

No radial balanced metrics found on Kepler manifold unit ball with mild boundary conditions.

Study complete gradient Ricci solitons with zero radial Weyl curvature.

We consider smooth radial solutions to the Hamiltonian stationary equation which are defined away from the origin. We show that in dimension two all radial solutions on unbounded domains must be special Lagrangian. In contrast, for all higher dimensions there exist non-special Lagrangian radial solutions over unbounded…

New topologies for star-shaped sets without boundedness.

In recent years, total variation (TV) and Euler's elastica (EE) have been successfully applied to image processing tasks such as denoising and inpainting. This paper investigates how to extend TV and EE to the supervised learning settings on high dimensional data. The supervised learning problem can be formulated as an…

In this paper we introduce two new notions of sectional curvature for Riemannian manifolds with density. Under both notions of curvature we classify the constant curvature manifolds. We also prove generalizations of the theorems of Cartan-Hadamard, Synge, and Bonnet-Myers as well as a generalization of the (non-smooth)…

The aim of this article is to establish a Toponogov type triangle comparison theorem for Finsler manifolds, in the manner of radial curvature geometry. We consider the situation that the radial flag curvature is bounded below by the radial curvature function of a non-compact surface of revolution, the edge opposite to …

Proves conditions for radial Kaehler metrics to be Kaehler-Einstein.

Real projective structures on $n$-orbifolds are useful in understanding the space of representations of discrete groups into $\mathrm{SL}(n+1, \mathbb{R})$ or $\mathrm{PGL}(n+1, \mathbb{R})$. A recent work shows that many hyperbolic manifolds deform to manifolds with such structures not projectively equivalent to the o…

Develops a framework for generating harmonic maps from a unit ball to a sphere.

Study on gradient ρ-Einstein solitons with radially nonnegative Bach tensor.

Radial graphs with constant mean curvature found in Euclidean space.

Let us fix two different radial eigenfunctions of a hyperbolic Laplacian and assume that both of them have the same value at the origin. Both eigenvalues can be complex numbers. The main goal of this paper is to estimate the lower bound for the interval (0,T], where these two eigenfunctions must assume different values…

Study proves radial symmetry in convex cones using subharmonic functions.

We generalize the maximal diameter sphere theorem due to Toponogov by means of the radial curvature. As a corollary to our main theorem, we prove that for a complete connected Riemannian $n$-manifold $M$ having radial sectional curvature at a point bounded from below by the radial curvature function of an ellipsoid of …

We classify the radially symmetric connections in vector bundles over round spheres by proving that they are all parallel.

We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.

Study on manifolds with density using modified Hessians for curvature comparison.

Sharp inequalities for radial functions on hyperbolic spaces without boundary conditions.

It is showed that on a plane with a radial density the Four Vertex Theorem holds for the class of all simple closed curves if and only if the density is constant. But for the class of simple closed curves that are invariant under a rotation about the origin, the Four Vertex Theorem holds for every radial density.

We show that a smooth radially symmetric solution $u$ to the graphic Willmore surface equation is either a constant or the defining function of a half sphere in ${\mathbb R}^3$. In particular, radially symmetric entire Willmore graphs in ${\mathbb R}^3$ must be flat. When $u$ is a smooth radial solution over a puncture…

This paper derives radial fields on manifolds of symmetric positive definite matrices.

This paper introduces the dual Orlicz-Brunn-Minkowski theory for star sets. A radial Orlicz addition of two or more star sets is proposed and a corresponding dual Orlicz-Brunn-Minkowski inequality is established. Based on a radial Orlicz linear combination of two star sets, a formula for the dual Orlicz mixed volume is…

In this paper we are concerned with the problem of finding hypersurfaces of constant curvature and prescribed boundary in the Euclidean space, using the theory of fully nonlinear elliptic equations. We prove that if the given data admits a suitable radial graph as a subsolution, then we can find a radial graph with con…

We establish a classification of cubic minimal cones in case of the so-called radial eigencubics. Our principal result states that any radial eigencubic is either a member of the infinite family of eigencubics of Clifford type, or belongs to one of 18 exceptional families. We prove that at least 12 of the 18 families a…

In this work, we propose an iterative reconstruction scheme (ALONE - Adaptive Learning Of NEtworks) for 2D radial cine MRI based on ground truth-free unsupervised learning of shallow convolutional neural networks. The network is trained to approximate patches of the current estimate of the solution during the reconstru…

In this paper, we systematically investigate the geometry and topology of manifolds with integral radial curvature bounds, and obtain many interesting and important conclusions.

Radial-basis-function networks are traditionally defined for sets of vector-based observations. In this short paper, we reformulate such networks so that they can be applied to adjacency-matrix representations of weighted, directed graphs that represent the relationships between object pairs. We re-state the sum-of-squ…

New non-trivial Kaehler-Ricci solitons found in infinite dimensional complex space forms.

Proves resurgence properties for Habiro elements from radial limits of theta series.

Paper proves MS convergence for radially symmetric kernels with large bandwidths.

Study proves radial symmetry of solutions to certain nonlinear equations in space forms.