arXiv research

New condition ensures submanifolds are skew in small areas.

New test for conditional independence using kernel embeddings.

Condition for embedding metric spaces into curved manifolds.

given two minimal surfaces embedded in $\S3$ of genus $g$ we prove the existence of a sequence of non-congruent compact minimal surfaces embedded in $\S3$ of genus $g$ that converges in $C^{2,α}$ to a compact embedded minimal surface provided some conditions are satisfied. These conditions also imply that, if any of th…

Article provides conditions for embedding braid groups into mapping class groups.

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

Paper develops a unified framework for measuring differences between conditional distributions.

We give a solution to the equivalence and the embedding problems for smooth CR-submanifolds of complex spaces (and, more generally, for abstract CR-manifolds) in terms of complete differential systems in jet bundles satisfied by all CR-equivalences or CR-embeddings respectively (local and global). For the equivalence p…

New recursive algorithm estimates conditional kernel mean embeddings in Hilbert space.

Paper studies embedding conditions for homogeneous quandles.

We demonstrate an equivalence between reproducing kernel Hilbert space (RKHS) embeddings of conditional distributions and vector-valued regressors. This connection introduces a natural regularized loss function which the RKHS embeddings minimise, providing an intuitive understanding of the embeddings and a justificatio…

Conditional mean embeddings (CMEs) have proven themselves to be a powerful tool in many machine learning applications. They allow the efficient conditioning of probability distributions within the corresponding reproducing kernel Hilbert spaces (RKHSs) by providing a linear-algebraic relation for the kernel mean embedd…

The abstract finds conditions for creating curves of constant curvature.

The paper explores conditions for lifting maps between graphs to embeddings.

Study optimizes learning rates for conditional mean embedding estimates.

The critical catenoid is uniquely determined by certain symmetries of its boundary.

The use of deep networks to extract embeddings for speaker recognition has proven successfully. However, such embeddings are susceptible to performance degradation due to the mismatches among the training, enrollment, and test conditions. In this work, we propose an adversarial speaker verification (ASV) scheme to lear…

We present an operator-free, measure-theoretic approach to the conditional mean embedding (CME) as a random variable taking values in a reproducing kernel Hilbert space. While the kernel mean embedding of unconditional distributions has been defined rigorously, the existing operator-based approach of the conditional ve…

Conditional kernel mean embeddings form an attractive nonparametric framework for representing conditional means of functions, describing the observation processes for many complex models. However, the recovery of the original underlying function of interest whose conditional mean was observed is a challenging inferenc…

We consider existence and uniqueness of two kinds of coisotropic embeddings and deduce the existence of deformation quantizations of certain Poisson algebras of basic functions. First we show that any submanifold of a Poisson manifold satisfying a certain constant rank condition sits coisotropically inside some larger …

Neumann eigenmaps improve landmark-based diffusion map embeddings.

This paper describes a conditional neural network architecture for Mandarin Chinese polyphone disambiguation. The system is composed of a bidirectional recurrent neural network component acting as a sentence encoder to accumulate the context correlations, followed by a prediction network that maps the polyphonic charac…

New framework for manifold convolutions using toric embeddings.

We propose a novel framework for multi-task reinforcement learning (MTRL). Using a variational inference formulation, we learn policies that generalize across both changing dynamics and goals. The resulting policies are parametrized by shared parameters that allow for transfer between different dynamics and goal condit…

Classifies linear embeddings of grassmannians and ind-grassmannians.

Paper proves Chow stability implies balanced embedding.

In the following article we discuss Delaunay triangulations for a point cloud on an embedded surface in $\mathbb{R}^3$. We give sufficient conditions on the point cloud to show that the diagonal switch algorithm finds an embedded Delaunay triangulation.

Notes on embedding criteria for smooth manifolds.

We introduce $(k,l)$-regular maps, which generalize two previously studied classes of maps: affinely $k$-regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean space into which a manifold can be embedded by a $(k,l)$-regular map. The problem c…

We show that the left-monotone martingale coupling is optimal for any given performance function satisfying the martingale version of the Spence-Mirrlees condition, without assuming additional structural conditions on the marginals. We also give a new interpretation of the left monotone coupling in terms of Skorokhod e…

Given a finite or infinite planar graph all of whose faces have degree 4, we study embeddings in the plane in which all edges have length 1, that is, in which every face is a rhombus. We give a necessary and sufficient condition for the existence of such an embedding, as well as a description of the set of all such emb…

Conditional kernel mean embeddings are nonparametric models that encode conditional expectations in a reproducing kernel Hilbert space. While they provide a flexible and powerful framework for probabilistic inference, their performance is highly dependent on the choice of kernel and regularization hyperparameters. Neve…

The paper explores how semantic independence can be captured in text embeddings using partial orthogonality.

We prove some infinitesimal analogs of classical results of Menger, Schoenberg and Blumenthal giving the existence conditions for isometric embeddings of metric spaces in the finite-dimensional Euclidean spaces.

Neural-Kernel CME tackles scalability and expressiveness challenges in conditional distribution representation.

Proposes CCME framework for estimating heterogeneous treatment effects.

We study some graphs associated to a surface, called k-multicurve graphs, which interpolate between the curve complex and the pants graph. Our main result is that, under certain conditions, simplicial embeddings between multicurve graphs are induced by $π_1$-injective embeddings of the corresponding surfaces. We also p…

The paper proves the existence of capillary geodesics on Riemannian 2-disks.

Current meta-learning approaches focus on learning functional representations of relationships between variables, i.e. on estimating conditional expectations in regression. In many applications, however, we are faced with conditional distributions which cannot be meaningfully summarized using expectation only (due to e…

We describe sufficient conditions which guarantee that a finite set of mapping classes generate a right-angled Artin group quasi-isometrically embedded in the mapping class group. Moreover, under these conditions, the orbit map to Teichmuller space is a quasi-isometric embedding for both of the standard metrics. As a …

We consider mean-convex Alexandrov embedded surfaces in the round unit 3-sphere, and show under which conditions it is possible to continuously deform these preserving mean-convex Alexandrov embeddedness.

A Hilbert space embedding for probability measures has recently been proposed, with applications including dimensionality reduction, homogeneity testing, and independence testing. This embedding represents any probability measure as a mean element in a reproducing kernel Hilbert space (RKHS). A pseudometric on the spac…

The paper explores linearly free graphs and their embeddings into 3D space.

Word embeddings are a powerful approach for capturing semantic similarity among terms in a vocabulary. In this paper, we develop exponential family embeddings, a class of methods that extends the idea of word embeddings to other types of high-dimensional data. As examples, we studied neural data with real-valued observ…

Given a properly embedded graph Gamma in a ball B and a punctured sphere Sigma properly embedded in B - Gamma, we examine the conditions on Gamma that are necessary to assure that Sigma is boundary parallel.

The paper shows how coarse embeddings affect homological Dehn functions.

We show that any metric on $S^2$ with Gauss curvature $K \geq -κ$ admits a $C^{1,1}$-isometric embedding into the hyperbolic space with sectional curvature $-κ$. We also give a sufficient condition for a metric on $S^2$ to be isometrically embedded into anti-de Sitter spacetime with the prescribed cosmological time fun…

SA-REMBO adapts to nonstationary high-dimensional optimization.