arXiv subjects

Xiaohui Zhang

Publications and source records attributed to Xiaohui Zhang.

At least 91 records · Page 5Linked to original sources

arXiv2021

Circular arc polygons, numerical conformal mappings, and moduli of quadrilaterals

We study numerical conformal mappings of planar Jordan domains with boundaries consisting of finitely many circular arcs and compute the moduli of quadrilaterals for these domains. Experimental error estimates are provided and, when possible, comparison to exact values or other methods are given. The main ingredients of the computation are boundary integral equations combined with the fast multipole method.

math.CV↗

arXiv2021

Impact of deep learning-based image super-resolution on binary signal detection

Deep learning-based image super-resolution (DL-SR) has shown great promise in medical imaging applications. To date, most of the proposed methods for DL-SR have only been assessed by use of traditional measures of image quality (IQ) that are commonly employed in the field of computer vision. However, the impact of these methods on objective measures of image quality that are relevant to medical imaging tasks remains largely unexplored. In this study, we investigate the impact of DL-SR methods on binary signal detection performance. Two popular DL-SR methods, the super-resolution convolutional neural network (SRCNN) and the super-resolution generative adversarial network (SRGAN), were trained by use of simulated medical image data. Binary signal-known-exactly with background-known-statistically (SKE/BKS) and signal-known-statistically with background-known-statistically (SKS/BKS) detection tasks were formulated. Numerical observers, which included a neural network-approximated ideal observer and common linear numerical observers, were employed to assess the impact of DL-SR on task performance. The impact of the complexity of the DL-SR network architectures on task-performance was quantified. In addition, the utility of DL-SR for improving the task-performance of sub-optimal observers was investigated. Our numerical experiments confirmed that, as expected, DL-SR could improve traditional measures of IQ. However, for many of the study designs considered, the DL-SR methods provided little or no improvement in task performance and could even degrade it. It was observed that DL-SR could improve the task-performance of sub-optimal observers under certain conditions. The presented study highlights the urgent need for the objective assessment of DL-SR methods and suggests avenues for improving their efficacy in medical imaging applications.

eess.IV↗

arXiv2021

On BiHom-analogue of generalized Lie algebras

In this paper, we introduce the definition of generalized BiHom-Lie algebras and generalized BiHom-Lie admissible algebras in the category ${}_H{\mathcal M}$ of left modules for any quasitriangular Hopf algebra $(H, R) $. Also, we describe the BiHom-Lie ideal structures of the BiHom-associative algebras.

math.RA↗

arXiv2020

Benchmarking LF-MMI, CTC and RNN-T Criteria for Streaming ASR

In this work, to measure the accuracy and efficiency for a latency-controlled streaming automatic speech recognition (ASR) application, we perform comprehensive evaluations on three popular training criteria: LF-MMI, CTC and RNN-T. In transcribing social media videos of 7 languages with training data 3K-14K hours, we conduct large-scale controlled experimentation across each criterion using identical datasets and encoder model architecture. We find that RNN-T has consistent wins in ASR accuracy, while CTC models excel at inference efficiency. Moreover, we selectively examine various modeling strategies for different training criteria, including modeling units, encoder architectures, pre-training, etc. Given such large-scale real-world streaming ASR application, to our best knowledge, we present the first comprehensive benchmark on these three widely used training criteria across a great many languages.

eess.AS↗

arXiv2020

More properties of Yetter-Drinfeld category over dual quasi-Hopf algebras

Let $H$ be a dual quasi-Hopf algebra. In this paper we will firstly introduce all possible categories of Yetter-Drinfeld modules over $H$, and give explicitly the monoidal and braided structure of them. Then we prove that the category $^H_H\mathcal{YD}^{fd}$ of finite-dimensional left-left Yetter-Drinfeld modules is rigid. Finally we will study the braided cocommunitivity of $H_0$ in $^H_H\mathcal{YD}$.

math.RA↗

arXiv2020

Faster, Simpler and More Accurate Hybrid ASR Systems Using Wordpieces

In this work, we first show that on the widely used LibriSpeech benchmark, our transformer-based context-dependent connectionist temporal classification (CTC) system produces state-of-the-art results. We then show that using wordpieces as modeling units combined with CTC training, we can greatly simplify the engineering pipeline compared to conventional frame-based cross-entropy training by excluding all the GMM bootstrapping, decision tree building and force alignment steps, while still achieving very competitive word-error-rate. Additionally, using wordpieces as modeling units can significantly improve runtime efficiency since we can use larger stride without losing accuracy. We further confirm these findings on two internal VideoASR datasets: German, which is similar to English as a fusional language, and Turkish, which is an agglutinative language.

eess.AS↗

arXiv2020

The Hom-Long dimodule category and nonlinear equations

In this paper, we construct a kind of new braided monoidal category over two Hom-Hopf algerbas $(H,α)$ and $(B,β)$ and associate it with two nonlinear equations. We first introduce the notion of an $(H,B)$-Hom-Long dimodule and show that the Hom-Long dimodule category $^{B}_{H} \Bbb L$ is an autonomous category. Second, we prove that the category $^{B}_{H} \Bbb L$ is a braided monoidal category if $(H,α)$ is quasitriangular and $(B,β)$ is coquasitriangular and get a solution of the quantum Yang-Baxter equation. Also, we show that the category $^{B}_{H} \Bbb L$ can be viewed as a subcategory of the Hom-Yetter-Drinfeld category $^{HøB}_{HøB} \Bbb {HYD}$. Finally, we obtain a solution of the Hom-Long equation from the Hom-Long dimodules.

math.RA↗

arXiv2020

On cyclic quadrilaterals in euclidean and hyperbolic geometries

Four points ordered in the positive order on the unit circle determine the vertices of a quadrilateral, which is considered either as a euclidean or as a hyperbolic quadrilateral depending on whether the lines connecting the vertices are euclidean or hyperbolic lines. In the case of hyperbolic lines, this type of quadrilaterals are called ideal quadrilaterals. Our main result gives a euclidean counterpart of an earlier result on the hyperbolic distances between the opposite sides of ideal quadrilaterals. The proof is based on computations involving hyperbolic geometry. We also found a new formula for the hyperbolic midpoint of a hyperbolic geodesic segment in the unit disk. As an application of some geometric properties, we provided a euclidean construction of the symmetrization of random four points on the unit circle with respect to a diameter which preserves the absolute cross ratio of quadruples.

math.MG↗

arXiv2020

A Gromov Hyperbolic metric and Möbius transformations

We compare a Gromov hyperbolic metric with the hyperbolic metric in the unit ball or in the upper half space, and prove sharp comparison inequalities between the Gromov hyperbolic metric and some hyperbolic type metrics. We also obtain several sharp distortion inequalities for the Gromov hyperbolic metric under some families of Möbius transformations.

math.CV↗

arXiv2020

Transformer-based Acoustic Modeling for Hybrid Speech Recognition

We propose and evaluate transformer-based acoustic models (AMs) for hybrid speech recognition. Several modeling choices are discussed in this work, including various positional embedding methods and an iterated loss to enable training deep transformers. We also present a preliminary study of using limited right context in transformer models, which makes it possible for streaming applications. We demonstrate that on the widely used Librispeech benchmark, our transformer-based AM outperforms the best published hybrid result by 19% to 26% relative when the standard n-gram language model (LM) is used. Combined with neural network LM for rescoring, our proposed approach achieves state-of-the-art results on Librispeech. Our findings are also confirmed on a much larger internal dataset.

cs.CL↗

arXiv2020

Multilingual Graphemic Hybrid ASR with Massive Data Augmentation

Towards developing high-performing ASR for low-resource languages, approaches to address the lack of resources are to make use of data from multiple languages, and to augment the training data by creating acoustic variations. In this work we present a single grapheme-based ASR model learned on 7 geographically proximal languages, using standard hybrid BLSTM-HMM acoustic models with lattice-free MMI objective. We build the single ASR grapheme set via taking the union over each language-specific grapheme set, and we find such multilingual graphemic hybrid ASR model can perform language-independent recognition on all 7 languages, and substantially outperform each monolingual ASR model. Secondly, we evaluate the efficacy of multiple data augmentation alternatives within language, as well as their complementarity with multilingual modeling. Overall, we show that the proposed multilingual graphemic hybrid ASR with various data augmentation can not only recognize any within training set languages, but also provide large ASR performance improvements.

eess.AS↗

arXiv2020

Deja-vu: Double Feature Presentation and Iterated Loss in Deep Transformer Networks

Deep acoustic models typically receive features in the first layer of the network, and process increasingly abstract representations in the subsequent layers. Here, we propose to feed the input features at multiple depths in the acoustic model. As our motivation is to allow acoustic models to re-examine their input features in light of partial hypotheses we introduce intermediate model heads and loss function. We study this architecture in the context of deep Transformer networks, and we use an attention mechanism over both the previous layer activations and the input features. To train this model's intermediate output hypothesis, we apply the objective function at each layer right before feature re-use. We find that the use of such iterated loss significantly improves performance by itself, as well as enabling input feature re-use. We present results on both Librispeech, and a large scale video dataset, with relative improvements of 10 - 20% for Librispeech and 3.2 - 13% for videos.

cs.CL↗

arXiv2020

On split regular Hom-Leibniz-Rinehart algebras

In this paper, we introduce the notion of the Hom-Leibniz-Rinehart algebra as an algebraic analogue of Hom-Leibniz algebroid, and prove that such an arbitrary split regular Hom-Leibniz-Rinehart algebra $L$ is of the form $L=U+\sum_γI_γ$ with $U$ a subspace of a maximal abelian subalgebra $H$ and any $I_γ$, a well described ideal of $L$, satisfying $[I_γ, I_δ]= 0$ if $[γ]\neq [δ]$. In the sequel, we develop techniques of connections of roots and weights for split Hom-Leibniz-Rinehart algebras respectively. Finally, we study the structures of tight split regular Hom-Leibniz-Rinehart algebras.

math.RA↗

arXiv2019

Drinfel'd double for monoidal Hom-Hopf algebras

In this paper we mainly construct bicrossproduct for finite-dimensional monoidal Hom-Hopf algebra $(H,α)$, generalizing the Majid's bicrossproduct. Naturally the Hom-type bicrossproduct leads to Drinfel'd double $(H^{op}\bowtie H^{\ast}, α\otimes (α^{-1})^\ast)$ with a quasitriangular structure $R$ satisfying the quantum Hom-Yang-Baxter equations.

math.RA↗

arXiv2019

Representations and deformations of Hom-Lie-Yamaguti superalgebras

Let $(L, α)$ be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notions of generalized derivations and representations of $(L, α)$ and present some properties. Finally, we investigate the deformations of $(L, α)$ by choosing some suitable cohomology.

math.RA↗

arXiv2019

On 3-Hom-Lie-Rinehart algebras

We introduce the notion of 3-Hom-Lie-Rinehart algebra and systematically describe a cohomology complex by considering coefficient modules. Furthermore, we consider extensions of a 3-Hom-Lie-Rinehart algebra and characterize the first cohomology space in terms of the group of automorphisms of an $A$-split abelian extension and the equivalence classes of $A$-split abelian extensions. Finally, we study formal deformations of 3-Hom-Lie-Rinehart algebras.

math.RA↗

arXiv2019

From Senones to Chenones: Tied Context-Dependent Graphemes for Hybrid Speech Recognition

There is an implicit assumption that traditional hybrid approaches for automatic speech recognition (ASR) cannot directly model graphemes and need to rely on phonetic lexicons to get competitive performance, especially on English which has poor grapheme-phoneme correspondence. In this work, we show for the first time that, on English, hybrid ASR systems can in fact model graphemes effectively by leveraging tied context-dependent graphemes, i.e., chenones. Our chenone-based systems significantly outperform equivalent senone baselines by 4.5% to 11.1% relative on three different English datasets. Our results on Librispeech are state-of-the-art compared to other hybrid approaches and competitive with previously published end-to-end numbers. Further analysis shows that chenones can better utilize powerful acoustic models and large training data, and require context- and position-dependent modeling to work well. Chenone-based systems also outperform senone baselines on proper noun and rare word recognition, an area where the latter is traditionally thought to have an advantage. Our work provides an alternative for end-to-end ASR and establishes that hybrid systems can be improved by dropping the reliance on phonetic knowledge.

eess.AS↗

arXiv2019

Topological Graphic Passwords And Their Matchings Towards Cryptography

Graphical passwords (GPWs) are convenient for mobile equipments with touch screen. Topological graphic passwords (Topsnut-gpws) can be saved in computer by classical matrices and run quickly than the existing GPWs. We research Topsnut-gpws by the matching of view, since they have many advantages. We discuss: configuration matching partition, coloring/labelling matching partition, set matching partition, matching chain, etc. And, we introduce new graph labellings for enriching Topsnut-matchings and show that these labellings can be realized for trees or spanning trees of networks. In theoretical works we explore Graph Labelling Analysis, and show that every graph admits our extremal labellings and set-type labellings in graph theory. Many of the graph labellings mentioned are related with problems of set matching partitions to number theory, and yield new objects and new problems to graph theory.

cs.CR↗