arXiv research

Improves tensor networks for classifying medical images.

Tensor networks improve medical image classification performance.

Neural Autoregressive Distribution Estimators (NADEs) have recently been shown as successful alternatives for modeling high dimensional multimodal distributions. One issue associated with NADEs is that they rely on a particular order of factorization for $P(\mathbf{x})$. This issue has been recently addressed by a vari…

In graph instance representation learning, both the diverse graph instance sizes and the graph node orderless property have been the major obstacles that render existing representation learning models fail to work. In this paper, we will examine the effectiveness of GRAPH-BERT on graph instance representation learning,…

A new tensor network method for image classification reduces computation cost.

We consider the problem of active feature acquisition, where we sequentially select the subset of features in order to achieve the maximum prediction performance in the most cost-effective way. In this work, we formulate this active feature acquisition problem as a reinforcement learning problem, and provide a novel fr…

Convolutional neural networks (CNNs) attained a good performance in hyperspectral sensing image (HSI) classification, but CNNs consider spectra as orderless vectors. Therefore, considering the spectra as sequences, recurrent neural networks (RNNs) have been applied in HSI classification, for RNNs is skilled at dealing …

Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In…

Deep learning models have achieved huge success in numerous fields, such as computer vision and natural language processing. However, unlike such fields, it is hard to apply traditional deep learning models on the graph data due to the 'node-orderless' property. Normally, adjacency matrices will cast an artificial and …

We study locally compact contractive local groups, that is, locally compact local groups with a contractive pseudo-automorphism. We prove that if such an object is locally connected, then it is locally isomorphic to a Lie group. We also prove a related structure theorem for locally compact contractive local groups whic…

Every locally compact local group is locally isomorphic to a topological group.

Generalizing the notion of local $φ$-symmetry of Takahashi, in the present paper, we introduce the notion of local $φ$-semisymmetry of a Sasakian manifold along with its proper existence and characterization. We also study the notion of local Ricci (resp., projective, conformal) $φ$-semisymmetry of a Sasakian manifold …

Local Gradient Descent with local steps converges to the centralized model in the interpolation regime.

Positive simplicial volume implies locally symmetric space structure.

We introduce the notion of a local torus action modeled on the standard representation (for simplicity, we call it a local torus action). It is a generalization of a locally standard torus action and also an underlying structure of a locally toric Lagrangian fibration. For a local torus action, we define two invariants…

We modify previous quasi-local mass definition. The new definition provides expressions of the quasi-local energy, the quasi-local linear momentum and the quasi-local mass. And they are equal to the ADM expressions at spatial infinity. Moreover, the new quasi-local energy has the positivity property.

Localized diffusion models reduce training complexity by exploiting low-dimensional structure.

Generalizes machine learning models using localization kernels and local means.

This paper explores estimating chaotic dynamics and parameters using local ensemble Kalman filters.

We give a description of local and global moves on a class of locally planar trivalent graphs and we show that it contains $λ$-Scale calculus, therefore in particular untyped lambda calculus. Surprisingly, the beta reduction rule comes from a local "sewing" transformation of trivalent locally planar graphs.

Local mass perspective on Bayesian inference

LASE improves local network structure visualization by targeting locally low-dimensional regions.

A reflexion space is generalization of a symmetric space introduced by O. Loos. We generalize locally symmetric spaces to local reflexion spaces in the similar way. We investigate, when local reflexion spaces are equivalently given by a locally flat Cartan connection of certain type.

Non-local GNNs improve performance on disassortative graphs.

Smooth manifolds from locally homogeneous spaces.

Vaisman's theorem extended to locally reducible Kähler spaces.

Develops a new theory of localization in algebraic geometry.

Fractional porous media equations yield q-Gaussian solutions for stock price returns.

The excellent performance of representation learning of autoencoders have attracted considerable interest in various applications. However, the structure and multi-local collaborative relationships of unlabeled data are ignored in their encoding procedure that limits the capability of feature extraction. This paper pre…

Holomorphic structures on Oeljeklaus-Toma manifolds are shown to be locally homogeneous.

Investigate local Lie group structure of bisections over compact manifolds

We introduce a notion of non-local almost minimal boundaries similar to that introduced by Almgren in geometric measure theory. Extending methods developed recently for non-local minimal surfaces we prove that flat non-local almost minimal boundaries are smooth. This can be viewed as a non-local version of the Almgren-…

It is proved that every locally conformal flat Riemannian manifold all of whose Jacobi operators have constant eigenvalues along every geodesic is with constant principal Ricci curvatures. A local classification (up to an isometry) of locally conformal flat Riemannian manifold with constant Ricci eigenvalues is given i…

Flow deforms locally convex curves to curves of constant k-order width.

Improves local learning models for complex feature extraction.

A manifold is locally \emph{$k$-fold symmetric}, if for any point and any $k$-dimensional vector subspace tangent to this point there exists a local isometry such that this point is a fixed point and the differential of the isometry restricted to that $k$-dimensional vector subspace is minus the identity. We show that …

Extends Calabi operator to Riemannian locally symmetric spaces.

The notion of local equivalence relation on a topological space is generalised to that of local subgroupoid. The main result is the construction of the holonomy and monodromy groupoids of certain Lie local subgroupoids, and the formulation of a monodromy principle on the extendibility of local Lie morphisms.

Develops local curvature estimates for mean curvature flow.

Central to robot exploration and mapping is the task of persistent localization in environmental fields characterized by spatially correlated measurements. This paper presents a Gaussian process localization (GP-Localize) algorithm that, in contrast to existing works, can exploit the spatially correlated field measurem…

It is shown that the geometry of locally homogeneous multisymplectic manifolds (that is, smooth manifolds equipped with a closed nondegenerate form of degree > 1, which is locally homogeneous of degree k with respect to a local Euler field) is characterized by their automorphisms. Thus, locally homogeneous multisymplec…

In this paper, we introduce an approach for leveraging available data across multiple locales sharing the same language to 1) improve domain classification model accuracy in Spoken Language Understanding and user experience even if new locales do not have sufficient data and 2) reduce the cost of scaling the domain cla…

New method controls error in low-dimensional marginals of spatial models.

The main new notions are the notions of tangent-like spaces and local monoids. The main result is the pasage from a local monoid to its tangent-like space which is a local Leibniz algebra.

A Riemannian orbifold is a mildly singular generalization of a Riemannian manifold which is locally modeled on the quotient of a connected, open manifold under a finite group of isometries. If all of the isometries used to define the local structures of an entire orbifold are orientation preserving, we call the orbifol…

We solve Hilbert's fifth problem for local groups: every locally euclidean local group is locally isomorphic to a Lie group. Jacoby claimed a proof of this in 1957, but this proof is seriously flawed. We use methods from nonstandard analysis and model our solution after a treatment of Hilbert's fifth problem for global…

In Bayesian classification, it is important to establish a probabilistic model for each class for likelihood estimation. Most of the previous methods modeled the probability distribution in the whole sample space. However, real-world problems are usually too complex to model in the whole sample space; some fundamental …

This thesis explores GNNs, categorizing them into local and global approaches.