arXiv research

In this paper we deduce a local deformation lemma for uniform embeddings in a metric covering space over a compact manifold from the deformation lemma for embeddings of a compact subspace in a manifold. This implies the local contractibility of the group of uniform homeomorphisms of such a metric covering space under t…

A local deformation property for uniform embeddings in metric manifolds (LD) is formulated and its behaviour is studied in a formal view point. It is shown that any metric manifold with a geometric group action, typical metric spaces (Euclidean space, hyperbolic space and cylinders) and for κ\leq 0 the κ-cone ends over…

Groups can embed uniformly but not act properly on contractible manifolds.

We prove effective uniformization for nearly round 2-spheres and investigate their stability.

New method detects communities in hypergraphs by embedding them into a vector space.

New learning rates for embeddings in RKHSs, even when the target is not Hilbert-Schmidt.

Let $G$ and $G'$ be simple Lie groups of equal real rank and real rank at least $2$. Let $Γ<G$ and $Λ< G'$ be non-uniform lattices. We prove a theorem that often implies that any quasi-isometric embedding of $Γ$ into $Λ$ is at bounded distance from a homomorphism. For example, any quasi-isometric embedding of $SL(n,\ma…

This work reduces model size by 86.11% for recommender systems using 4-bit quantization.

This paper refines homotopy theory for cubical sets and uniform spaces.

PCA whitening weighted by Zipfian word frequencies improves task performance.

The study examines how much data is needed for generative and vision-language models to make reliable predictions.

We prove that if $G$ is a non-uniform lattice in a rank-one semi-simple Lie group $\ne Isom(\H^2_\R)$ then $G$ is quasi-isometrically co-Hopf. This means that every quasi-isometric embedding $G\to G$ is coarsely onto and thus is a quasi-isometry.

Abstract machinery finds obstructions to uniform positive scalar curvature.

There is a word metric $d$ on countably generated free group $Γ$ such that $(Γ,d)$ does not admit a coarse uniform embedding into a Hilbert space.

If one tries to embed a metric space uniformly in Hilbert space, how close to quasi-isometric could the embedding be? We answer this question for finite dimensional CAT(0) cube complexes and for hyperbolic groups. In particular, we show that the Hilbert space compression of any hyperbolic group is 1.

Uniformizes surfaces using discrete harmonic maps and hyperbolic metrics.

We study quasi-isometric embeddings of symmetric spaces and non-uniform irreducible lattices in semisimple higher rank Lie groups. We show that any quasi-isometric embedding between symmetric spaces of the same rank can be decomposed into a product of quasi-isometric embeddings into irreducible symmetric spaces. We thu…

Paper introduces S-SSE for stable sparse subspace embedding.

Continuous MDS embeds sequences of dissimilarities in Euclidean space.

This paper proves Hölder continuity for complex Monge-Ampère equations on Kähler varieties.

Estimates spectral projections restricted to uniformly embedded submanifolds.

Researchers found 5 local fields to uniquely describe 3D director fields, related through 6 differential relations.

Graph-Relational Domain Adaptation (GRDA) adapts domains based on their graph structure.

Given a closed Riemannian manifold of dimenion less than eight, we prove a compactness result for the space of closed, embedded minimal hypersurfaces satisfying a volume bound and a uniform lower bound on the first eigenvalue of the stability operator. When the latter assumption is replaced by a uniform lower bound on …

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.

UMAP (Uniform Manifold Approximation and Projection) is a novel manifold learning technique for dimension reduction. UMAP is constructed from a theoretical framework based in Riemannian geometry and algebraic topology. The result is a practical scalable algorithm that applies to real world data. The UMAP algorithm is c…

AUASE embeds dynamic networks with stability guarantees for node comparison.

The study shows that close hypersurfaces have uniformly bounded inequalities.

The paper constructs Anosov representations for specific types of groups.

New approach to extremal hyperbolic surfaces using NEC groups.

The paper proposes a uniformity regularization scheme to improve deep neural network transferability.

We present explicit geometric decompositions of the hyperbolic complements of alternating $k$-uniform tiling links, which are alternating links whose projection graphs are $k$-uniform tilings of $S^2$, $\mathbb{E}^2$, or $\mathbb{H}^2$. A consequence of this decomposition is that the volumes of spherical alternating $k…

SymNoise improves language model fine-tuning by 6.7% over NEFTune, using symmetric noise.

Proves limit of free boundary minimal hypersurfaces inherit non-trivial Jacobi fields.

The current article stems from our study on the asymptotic behavior of holomorphic isometric embeddings of the Poincaré disk into bounded symmetric domains. As a first result we prove that any holomorphic curve exiting the boundary of a bounded symmetric domain $Ω$ must necessarily be asymptotically totally geodesic. A…

By Gromov's compactness theorem for metric spaces, every uniformly compact sequence of metric spaces admits an isometric embedding into a common compact metric space in which a subsequence converges with respect to the Hausdorff distance. Working in the class or oriented $k$-dimensional Riemannian manifolds (with bound…

We show that, up to some natural normalizations, the moduli space of singly periodic complete embedded maximal surfaces in the Lorentz-Minkowski space $ł^3=(\r^3,dx_1^2+dx_2^2-dx_3^2),$ with fundamental piece having a finite number $(n+1)$ of singularities, is a real analytic manifold of dimension $3n+4.$ The underlyin…

Let $ρ$ be a maximal representation of a uniform lattice $Γ\subset{\rm SU}(n,1)$, $n\geq 2$, in a classical Lie group of Hermitian type $H$. We prove that necessarily $H={\rm SU}(p,q)$ with $p\geq qn$ and there exists a holomorphic or antiholomorphic $ρ$-equivariant map from complex hyperbolic space to the symmetric sp…

Characterizes infinite ideal polyhedra in hyperbolic 3-space and proves their existence and rigidity.

Study linearizes 2-Wasserstein space using optimal transport maps.

New methods explain NE embeddings by identifying key variables.

Sequence feature embedding is a challenging task due to the unstructuredness of sequence, i.e., arbitrary strings of arbitrary length. Existing methods are efficient in extracting short-term dependencies but typically suffer from computation issues for the long-term. Sequence Graph Transform (SGT), a feature embedding …

This paper improves spectral embedding for multipartite networks, revealing latent subspaces and providing consistent node representations.

In this paper, we find a holomorphic Darboux chart around any immersed noncompact holomorphic Legendrian curve in a complex contact manifold $(X,ξ)$. By using such a chart, we show that every holomorphic Legendrian immersion $R\to X$ from an open Riemann surface can be approximated on relatively compact subsets by holo…

New measure helps identify better word embedding compression methods.

Improved SRHT for linear SVM classification with higher accuracy.

The paper provides generalization bounds for metric learning using neural network embeddings.

A new method estimates multi-dimensional value distributions using Hilbert space embeddings.