arXiv research

New Ricci curvature means derived from plane curvatures.

For many years, i-vector based audio embedding techniques were the dominant approach for speaker verification and speaker diarization applications. However, mirroring the rise of deep learning in various domains, neural network based audio embeddings, also known as d-vectors, have consistently demonstrated superior spe…

It is the purpose of the present paper to outline an introduction in theory of embeddings in the manifold Osc^{2}M. First, we recall the notion of 2-osculator bundle. The second section is dedicated to the notion of submanifold in the total space of the 2-osculator bundle, the manifold Osc^{2}M. A moving frame is const…

It is the purpose of the present paper to outline an introduction in theory of embeddings in the manifold Osc^{2}M. First, we recall the notion of 2-osculator bundle. The second section is dedicated to the notion of submanifold in the total space of the 2-osculator bundle, the manifold Osc^{2}M. A moving frame is const…

This paper proposes novel algorithms for speaker embedding using subjective inter-speaker similarity based on deep neural networks (DNNs). Although conventional DNN-based speaker embedding such as a $d$-vector can be applied to multi-speaker modeling in speech synthesis, it does not correlate with the subjective inter-…

A new type of End-to-End system for text-dependent speaker verification is presented in this paper. Previously, using the phonetically discriminative/speaker discriminative DNNs as feature extractors for speaker verification has shown promising results. The extracted frame-level (DNN bottleneck, posterior or d-vector) …

We present a distributionally robust formulation of a stochastic optimization problem for non-i.i.d vector autoregressive data. We use the Wasserstein distance to define robustness in the space of distributions and we show, using duality theory, that the problem is equivalent to a finite convex-concave saddle point pro…

Constructs polyhedral chains with prescribed tangent plane distributions.

In this paper, we propose a fully supervised speaker diarization approach, named unbounded interleaved-state recurrent neural networks (UIS-RNN). Given extracted speaker-discriminative embeddings (a.k.a. d-vectors) from input utterances, each individual speaker is modeled by a parameter-sharing RNN, while the RNN state…

Vector-valued neural learning has emerged as a promising direction in deep learning recently. Traditionally, training data for neural networks (NNs) are formulated as a vector of scalars; however, its performance may not be optimal since associations among adjacent scalars are not modeled. In this paper, we propose a n…

In this short note, we investigate some features of the space $\Inject{d}{m}$ of linear injective maps from $\bbR^d$ into $\bbR^m$; in particular, we discuss in detail its relationship with the Stiefel manifold $V_{m,d}$, viewed, in this context, as the set of orthonormal systems of $d$ vectors in $\bbR^m$. Finally, we…

In this paper, we propose a new pooling method called spatial pyramid encoding (SPE) to generate speaker embeddings for text-independent speaker verification. We first partition the output feature maps from a deep residual network (ResNet) into increasingly fine sub-regions and extract speaker embeddings from each sub-…

Data sets are often modeled as point clouds in $R^D$, for $D$ large. It is often assumed that the data has some interesting low-dimensional structure, for example that of a $d$-dimensional manifold $M$, with $d$ much smaller than $D$. When $M$ is simply a linear subspace, one may exploit this assumption for encoding ef…

New bounds on self-normalized martingales improve online linear regression performance.

In a previous paper, we introduced special types of fusions, so called simple-ribbon fusions on links. A knot obtained from the trivial knot by a finite sequence of simple-ribbon fusions is called a simple-ribbon knot. Every ribbon knot with <10 crossings is a simple-ribbon knot. In this paper, we give a formula for th…

Simple lifts of non-simple curves on surfaces.

The paper studies the topology and geometry of simple orbifolds, generalizing concepts from simple polytopes.

The study of orthospectrum and simple orthospectrum of hyperbolic surfaces.

3D hyperbolic spaces have endless simple paths.

Most simple braids have positive topological entropy.

The paper characterizes simple closed curves on surfaces using profinite rigidity.

Simple loop conjecture proven for certain discrete representations.

Study geodesics on spherical polyhedra, estimating their number.

We give a new proof of McShane's classification of simple cuspidal geodesics, using simple equivariant methods in the hyperbolic plane.

Study real logarithms of semi-simple matrices, focusing on differential structure.

The paper explores simple and relatively simple transformation groups and their universal coverings.

A version of Dehn's algorithm for simple diagrams on a once punctured surface representing simple diagrams on a closed surface is presented

Rotation systems can't always be drawn in surfaces.

The simple length spectrum of a Riemannian manifold is the set of lengths of its simple closed geodesics. We prove a theorem claimed by Lusternik: in any Riemannian 2-sphere whose simple length spectrum consists of only one element L, any geodesic is simple closed with length L.

The paper finds braid representatives minimizing simple walks for knots.

Geometric models for Lie algebras from simple singularities.

We characterize the kernel of the mixed ray transform on simple $2$-dimensional Riemannian manifolds, that is, on simple surfaces for tensors of any order.

Study finds counterexamples to simple loop conjecture in higher dimensions.

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tenso…

New concept of k-holes in simple drawings and convex drawings.

Proves simple type conjecture for mod 2 Seiberg-Witten invariants.

Simple knots in lens spaces fiber if their order doesn't divide certain Euclidean remainders.

We study complex spatial quartic surfaces with simple singularities up to equisingular deformations; as a first step, give a complete equisingular deformation classification of the so-called non-special simple quartic surfaces.

The paper proves rigidity of length identities for simple closed curves on hyperbolic surfaces.

In this paper we study a new combinatorial invariant of simple polytopes, which comes from toric topology. With each simple n-polytope P with m facets we can associate a moment-angle complex Z_P with a canonical action of the torus T^m. Then s(P) is the maximal dimension of a toric subgroup that acts freely on Z_P. The…

All closed geodesics are simple and non-intersecting in dimensions 3 and above.

Mirzakhani obtained the asymptotic growth, when $L\to\infty$, of the number of curves in the mapping class group orbit of some given simple curve and with length at most $L$. Years later she extended this result from simple to arbitrary curves. Here we give a short and relative low-tech argument showing how to derive t…

We characterize absence of arbitrage with simple trading strategies in a discounted market with a constant bond and several risky assets. We show that if there is a simple arbitrage, then there is a 0-admissible one or an obvious one, that is, a simple arbitrage which promises a minimal riskless gain of ε, if the inves…

Unique simple spines of homotopy 2-spheres are shown to be ambiently isotopic.

Characterizes covers using simple closed curves on surfaces.

We classify the simple sheaves microsupported along the conormal bundle of a knot. We also establish a correspondence between simple sheaves up to local systems and augmentations, explaining the underlying reason why knot contact homology representations detect augmentations.

Study on frequencies of non-simple curves in surfaces of large genus.

The length of shortest non-simple geodesics grows logarithmically with surface genus.