arXiv research

Learning a good speaker embedding is important for many automatic speaker recognition tasks, including verification, identification and diarization. The embeddings learned by softmax are not discriminative enough for open-set verification tasks. Angular based embedding learning target can achieve such discriminativenes…

Proposes AE for robust PCA, improving robustness to outliers.

New method resolves ambiguity in measuring black hole merger angular momentum.

Study limits of quasi-local angular momentum at infinity of gravitating systems.

Numerical simulations show stability of Type-II singularities in noncompact hypersurfaces.

Analysis of 'big data' characterized by high-dimensionality such as word vectors and complex networks requires often their representation in a geometrical space by embedding. Recent developments in machine learning and network geometry have pointed out the hyperbolic space as a useful framework for the representation o…

Ensembling word embeddings to improve distributed word representations has shown good success for natural language processing tasks in recent years. These approaches either carry out straightforward mathematical operations over a set of vectors or use unsupervised learning to find a lower-dimensional representation. Th…

An explicit global and unique isometric embedding into hyperbolic 3-space, H^3, of an axi-symmetric 2-surface with Gaussian curvature bounded below is given. In particular, this allows the embedding into H^3 of surfaces of revolution having negative, but finite, Gaussian curvature at smooth fixed points of the U(1) iso…

The margin-based softmax loss functions greatly enhance intra-class compactness and perform well on the tasks of face recognition and object classification. Outperformance, however, depends on the careful hyperparameter selection. Moreover, the hard angle restriction also increases the risk of overfitting. In this pape…

We define quasi-local conserved quantities in general relativity by using the optimal isometric embedding in [26] to transplant Killing fields in the Minkowski spacetime back to the 2-surface of interest in a physical spacetime. To each optimal isometric embedding, a dual element of the Lie algebra of the Lorentz group…

Rotationally equivariant convolutions improve molecular property prediction.

New definitions of conserved quantities at null infinity resolve ambiguities in general relativity.

In the first half of this article, we survey the new quasi-local and total angular momentum and center of mass defined in [9] and summarize the important properties of these definitions. To compute these conserved quantities involves solving a nonlinear PDE system (the optimal isometric embedding equation), which is ra…

In this paper angular curvature measures are investigated. Our first result is a complete classification of translation-invariant angular smooth curvature measures on $\mathbb{R}^n$. Subsequently, we use this result to show that the class of angular curvature measures on a Riemannian manifold is preserved by both the p…

Recent convolutional neural networks (CNNs) have led to impressive performance but often suffer from poor calibration. They tend to be overconfident, with the model confidence not always reflecting the underlying true ambiguity and hardness. In this paper, we propose angular visual hardness (AVH), a score given by the …

Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.

New method constructs axial vector fields and defines quasi-local spin-angular momentum.

Study proves inequality linking black hole properties and angular momentum.

Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.

The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.

Formulae track evolution of angular momentum and center of mass at null infinity.

We examine a class of embeddings based on structured random matrices with orthogonal rows which can be applied in many machine learning applications including dimensionality reduction and kernel approximation. For both the Johnson-Lindenstrauss transform and the angular kernel, we show that we can select matrices yield…

New definition of angular momentum avoids supertranslation ambiguity.

This is a follow-up of our paper \cite{KS-Kerr1} on the construction of general covariant modulated (GCM) spheres in perturbations of Kerr, which we expect to play a central role in establishing their nonlinear stability. We reformulate the main results of that paper using a canonical definition of $\ell=1$ modes on a …

The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.

For manifold learning, it is assumed that high-dimensional sample/data points are embedded on a low-dimensional manifold. Usually, distances among samples are computed to capture an underlying data structure. Here we propose a metric according to angular changes along a geodesic line, thereby reflecting the underlying …

New memory effect discovered in gravitational wave behavior.

We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-Ó Murchadha-Regge-T…

Generative models improve angular variable simulation in high dimensions.

We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …

We investigate deep neural network performance in the textindependent speaker recognition task. We demonstrate that using angular softmax activation at the last classification layer of a classification neural network instead of a simple softmax activation allows to train a more generalized discriminative speaker embedd…

New method uses neural networks for accurate angle estimation in noisy conditions.

This paper presents a study on power grid disturbance classification by Deep Learning (DL). A real synchrophasor set composing of three different types of disturbance events from the Frequency Monitoring Network (FNET) is used. An image embedding technique called Gramian Angular Field is applied to transform each time …

We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which …

Study reformulates Finsler metrizability problems using geodesic invariance.

AngularGrad optimizes CNNs by considering gradient direction, improving convergence.

In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…

We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…

Investigates physical properties on surfaces of rotation using Clairaut's theorem.

AGCA approximates angular variation on the unit sphere, reducing extremal dependence problems to eigenanalysis.

We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…

A framework visualizes embedding spaces of neural survival analysis models using anchor directions.

Jets from boosted heavy particles have a typical angular scale which can be used to distinguish them from QCD jets. We introduce a machine learning strategy for jet substructure analysis using a spectral function on the angular scale. The angular spectrum allows us to scan energy deposits over the angle between a pair …

We develop and study quaternionic and octonionic analogies of Cartan angular and Toledo invariants that are well known in the complex hyperbolic space. Using such invariants we study quasifuchsian deformations (including bendings) of quaternionic and octonionic hyperbolic manifolds.

A universal geometric inequality for bodies relating energy, size, angular momentum, and charge is naturally implied by Bekenstein's entropy bounds. We establish versions of this inequality for axisymmetric bodies satisfying appropriate energy conditions, thus lending credence to the most general form of Bekenstein's b…

Model place cells as spatial embeddings for efficient path planning and cognitive map construction.

Polyhedra can mimic constant curvature surfaces, even with self-intersections.

The angular power spectrum characterizes neural network complexity.