arXiv research

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…

Unsupervised domain adaptation methods aim to alleviate performance degradation caused by domain-shift by learning domain-invariant representations. Existing deep domain adaptation methods focus on holistic feature alignment by matching source and target holistic feature distributions, without considering local feature…

Local rigidity results for Bergman and Kähler Carathéodory metrics on domains.

Proves local maximizers for higher Ekeland-Hofer capacities in 4D star-shaped domains.

This paper introduces localized discrepancy theories for unsupervised domain adaptation.

Almost all local minima in neural networks are strongly convex.

In this paper we extend the local scalar curvature rigidity result in [6] to a small domain on general vacuum static spaces, which confirms the interesting dichotomy of local surjectivity and local rigidity about the scalar curvature in general in the light of the paper [10]. We obtain the local scalar curvature rigidi…

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

Study bounds derivatives of solutions to a specific equation on domains.

SCTL scales causal domain adaptation without prior knowledge.

For an admissible class of smooth compact initial data sets with boundary, we prove a comparison theorem between the Wang/Liu-Yau quasi-local mass of the boundary and the Hawking mass of strictly minimizing hulls in the Jang graphs of the domain. Using this, we prove a quasi-local Penrose inequality that involves these…

A new method tackles Bayesian inverse problems with complex PDEs.

Proper holomorphic isometries between Bergman domains are biholomorphisms.

Logifold improves ensemble machine learning by identifying fuzzy domains.

Develops a logifold structure for understanding datasets.

In this paper we propose a domain adaptation algorithm designed for graph domains. Given a source graph with many labeled nodes and a target graph with few or no labeled nodes, we aim to estimate the target labels by making use of the similarity between the characteristics of the variation of the label functions on the…

In this paper we prove a new version of the Schoenflies extension theorem for collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz homeomorphisms between collared domains with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity. Moreover, the th…

Sharp estimate for nodal domains intersecting a ball on a Riemannian manifold.

Proves smoothness of minimal surfaces near polyhedral boundaries.

We present a new and direct proof of the local Neumann isoperimetric inequality on convex domains of a Riemannian manifold with Ricci curvature bounded below.

The paper proves a conjecture about the Bergman metric of real analytic domains.

TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.

We use a locally constrained mean curvature flow to prove the isoperimetric inequality for spacelike domains in generalized Robertson-Walker spaces satisfying the null convergence condition.

We prove that the Teichmüller space $\mathscr{T}$ of a closed surface of genus $g \ge 2$ cannot be biholomorphic to any domain which is locally strictly convex at some boundary point.

Domain adaptation aims to exploit the knowledge in source domain to promote the learning tasks in target domain, which plays a critical role in real-world applications. Recently, lots of deep learning approaches based on autoencoders have achieved a significance performance in domain adaptation. However, most existing …

I prove three classification results about harmonic morphisms whose fibers have dimension one. All are valid when the domain is at least of dimension 4. (The character of this overdetermined problem is very different when the dimension of the domain is 3 or less.) The first result is a local classification for such har…

Edge devices adapt pre-trained models to local data without backpropagation.

Method approximates Lipschitz domains with smoother shapes.

This paper is a sequel to \cite{Choi} in Math. Ann. In that paper we studied the subharmonicity of Kähler-Einstein metrics on strongly pseudoconvex domains of dimension greater than or equal to $3$. In this paper, we study the variations Kähler-Einstein metrics on bounded strongly pseudoconvex domains of dimension $2$.…

A simple proof shows standard billiard for certain convex domains.

Flat minimal hypersurfaces found in wedge-shaped domains.

The assumption that training and testing samples are generated from the same distribution does not always hold for real-world machine-learning applications. The procedure of tackling this discrepancy between the training (source) and testing (target) domains is known as domain adaptation. We propose an unsupervised ver…

Backward stochastic partial differential equations of parabolic type in bounded domains are studied in the setting where the coercivity condition is not necessary satisfied and the equation can be degenerate. Some generalized solutions based on the representation theorem are suggested. In addition to problems with a st…

Study how nodal domains change on surfaces under perturbations.

We derive local $C^{2}$ estimates for complete non-compact translating solitons of the Gauss curvature flow in $\mathbb{R}^3$ which are graphs over a convex domain $Ω$. This is closely is related to deriving local $C^{1,1}$ estimates for the degenerate Monge-Ampére equation. As a result, given a weakly convex bounded d…

We prove that the Hilbert geometry of a convex domain in ${\mathbb R}^n$ has bounded local geometry, i.e., for a given radius, all balls are bilipschitz to a euclidean domain of ${\mathbb R}^n$. As a consequence, if the Hilbert geometry is also Gromov hyperbolic, then the bottom of its spectrum is strictly positive. We…

We prove local Holder continuity of quasi-n-harmonic mappings from Euclidean domains into metric spaces with non-positive curvature in the sense of Alexandrov. We also obtain global Holder continuity of such mappings from bounded Lipschitz domains.

Geometric inequalities for static convex domains in hyperbolic space proved.

Uncertainty principles such as Heisenberg's provide limits on the time-frequency concentration of a signal, and constitute an important theoretical tool for designing and evaluating linear signal transforms. Generalizations of such principles to the graph setting can inform dictionary design for graph signals, lead to …

In this paper, we propose to apply object detection methods from the vision domain on the speech recognition domain, by treating audio fragments as objects. More specifically, we present SpeechYOLO, which is inspired by the YOLO algorithm for object detection in images. The goal of SpeechYOLO is to localize boundaries …

Minimal partitions with minimal perimeter found in metric spaces.

Dimensionality reduction (DR) methods have attracted extensive attention to provide discriminative information and reduce the computational burden of the hyperspectral image (HSI) classification. However, the DR methods face many challenges due to limited training samples with high dimensional spectra. To address this …

In this paper, we propose a novel learning framework for the problem of domain transfer learning. We map the data of two domains to one single common space, and learn a classifier in this common space. Then we adapt the common classifier to the two domains by adding two adaptive functions to it respectively. In the com…

Local convolutions bias neural networks towards high-frequency adversarial examples.

New geometric conditions ensure compactness of $\bar{\partial}$-Neumann problem.

Local differential privacy (LDP) is a strong notion of privacy for individual users that often comes at the expense of a significant drop in utility. The classical definition of LDP assumes that all elements in the data domain are equally sensitive. However, in many applications, some symbols are more sensitive than ot…

Improved guarantees for misspecified kernelized bandit optimization.

We consider the action of Anosov subgroups of a semi-simple Lie group on the associated flag manifolds. A systematic approach to construct cocompact domains of discontinuity for this action was given by Kapovich, Leeb and Porti in arXiv:1306.3837. For $Δ$-Anosov representations, we prove that every cocompact domain of …