arXiv research

We discuss dense embeddings of surface groups and fully residually free groups in topological groups. We show that a compact topological group contains a nonabelian dense free group of finite rank if and only if it contains a dense surface group. Also, we obtain a characterization of those Lie groups which admit a dens…

Sharp criteria found for dense eigenvalues in Riemannian manifolds.

In this paper are given examples of tori T^2 embedded in S^3 with all their asymptotic lines dense.

In this paper are given examples of tori T2 embedded in R3 with all their principal lines dense. These examples are obtained by stereographic projection of deformations of the Clifford torus in S3.

ViCE uses superpixels to enhance self-supervised learning for better dense visual embeddings.

Paper finds a disc with finite area and dense boundary in a ball.

The square-peg problem is solved using configuration spaces and multijet transversality.

The paper constructs complete holomorphic immersions in complex spaces.

The purpose of this paper is to present, for all $n\ge 3$, very simple examples of continuous maps $f:M^{n-1} \to M^{n}$ from closed $(n-1)$-manifolds $M^{n-1}$ into closed $n$-manifold $M^n$ such that even though the singular set $S(f)$ of $f$ is countable and dense, the map $f$ can nevertheless be approximated by an …

NetSMF efficiently embeds large networks by sparse matrix factorization.

New method uses product embeddings to predict bundle success.

We prove that every proper $n$-dimensional length metric space admits an "approximate isometric embedding" into Lorentzian space $\mathbb{R}^{3n+6,1}$. By an "approximate isometric embedding" we mean an embedding which preserves the energy functional on a prescribed set of geodesics connecting a dense set of points.

SOLAR improves search efficiency and accuracy with sparse, orthogonal embeddings.

In this paper, we prove (1): for any closed contact three-manifold with a $C^\infty$-generic contact form, the union of periodic Reeb orbits is dense, (2): for any closed surface with a $C^\infty$-generic Riemannian metric, the union of closed geodesics is dense. The key observation is $C^\infty$-closing lemma for 3D R…

New techniques enforce sparseness in recurrent models, reducing memory usage.

A dense amalgam connects boundaries of groups split by finite subgroups.

A new deep metric learning method pulls embeddings towards dense clusters to improve classification accuracy.

The Nash-Kuiper Theorem states that the collection of $C^1$-isometric embeddings from a Riemannian manifold $M^n$ into $\mathbb{E}^N$ is $C^0$-dense within the collection of all smooth 1-Lipschitz embeddings provided that $n < N$. This result is now known to be a consequence of Gromov's more general $h$-principle. Ther…

Survey of word embedding techniques for NLP.

The paper studies PCA of probability measures with varying sample sizes and finds optimal convergence rates.

A new method uses sinusoidal functions to represent timestamps as dense vectors for improving irregularly sampled time series learning.

For most metrics, many minimal hypersurfaces densely cover a manifold.

Study on stable Hamiltonian topology finds non-density of certain structures.

We prove analogues for Cartan geometries of Gromov's major theorems on automorphisms of rigid geometric structures. The starting point is a Frobenius theorem, which says that infinitesimal automorphisms of sufficiently high order integrate to local automorphisms. Consequences include a stratification theorem describing…

The study constructs a dense orbit in the universal commensurability augmented Teichmüller space.

We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclid…

Extracts object-centric frames from unlabeled images.

New examples of embeddings defy Anosov representation limits.

Let $M$ be a projective toric manifold. We prove two results concerning respectively Kaehler-Einstein submanifolds of M and symplectic embeddings of the standard euclidean ball in M. Both results use the well-known fact that M contains an open dense subset biholomorphic to C^n.

We create interpretable word embeddings through sparse coding.

Paper proposes efficient inner product approximation for hybrid sparse and dense vectors.

Local deformations of solutions to open PDEs can be extended globally if derivatives are constant along a subset.

This work proposes a method to learn sparse representations that are more efficient for large-scale data retrieval.

Let $G$ be a simply connected, solvable Lie group and $Γ$ a lattice in $G$. The deformation space $\mathcal{D}(Γ,G)$ is the orbit space associated to the action of $\Aut(G)$ on the space $\mathcal{X}(Γ,G)$ of all lattice embeddings of $Γ$ into $G$. Our main result generalises the classical rigidity theorems of Mal'tsev…

New subgroup found in Lie groups with unusual properties.

Constructs equivariant embeddings of Hermitian symmetric spaces into tangent spaces.

We present a method for training multi-label, massively multi-class image classification models, that is faster and more accurate than supervision via a sigmoid cross-entropy loss (logistic regression). Our method consists in embedding high-dimensional sparse labels onto a lower-dimensional dense sphere of unit-normed …

Very recently Ben Andrews and Haizhong Li showed that every embedded cmc torus in the three dimensional sphere is axially symmetric. There is a two-parametric family of axially symmetric cmc surfaces; more precisely, for every real number H and every C > 2 (H+\sqrt{1+H^2}) there is an axially symmetry surface Σ_{H,C} w…

In the curve complex for a surface, a handlebody set is the set of loops that bound properly embedded disks in a given handlebody bounded by the surface. A boundary set is the set of non-separating loops in the curve complex that bound two-sided, properly embedded surfaces. For a Heegaard splitting, the distance betwee…

This note optimizes distributions using kernel mean embeddings with a new parameterization.

A new method reduces embedding size for efficient recommendation systems.

DCE learns customer embeddings from digital activity and financial context.

Minimal products of spherical immersions are studied with geometric and dynamical properties.

FCA2VEC embeds formal concept analysis data for large datasets.

The study finds infinitely many semi-arithmetic Riemann surfaces with dense systoles and distinct invariant trace fields.

We prove the existence of a minimal (all leaves dense) foliation of codimension one, on every closed manifold of dimension at least 4 whose Euler characteristic is null, in every homotopy class of hyperplanes distributions, in every homotopy class of Haefliger structures, in every differentiability class, under the obv…

Constructs examples of domains divided by groups in dimensions 3 and above.

Proves optimal regularity for sphere minimizers in 3-sphere.