Searcharxiv⌕ Search

arXiv subjects

Sibei Yang

Publications and source records attributed to Sibei Yang.

At least 91 records · Page 5Linked to original sources
arXiv2021

A Two-Weight Boundedness Criterion and Its Applications

In this article, the authors establish a general (two-weight) boundedness criterion for a pair of functions, $(F,f)$, on $\mathbb{R}^n$ in the scale of weighted Lebesgue spaces, weighted Lorentz spaces, (Lorentz--)Morrey spaces, and variable Lebesgue spaces. As applications, the authors give a unified approach to prove the (two-weight) boundedness of Calderón--Zygmund operators, Littlewood--Paley $g$-functions, Lusin area functions, Littlewood--Paley $g^\ast_λ$-functions, and fractional integral operators, in the aforementioned function spaces. Moreover, via applying the above (two-weight) boundedness criterion, the authors further obtain the (two-weight) boundedness of Riesz transforms, Littlewood--Paley $g$-functions, and fractional integral operators associated with second-order divergence elliptic operators with complex bounded measurable coefficients on $\mathbb{R}^n$ in the aforementioned function spaces.

math.AP↗
arXiv2021

ConvNets vs. Transformers: Whose Visual Representations are More Transferable?

Vision transformers have attracted much attention from computer vision researchers as they are not restricted to the spatial inductive bias of ConvNets. However, although Transformer-based backbones have achieved much progress on ImageNet classification, it is still unclear whether the learned representations are as transferable as or even more transferable than ConvNets' features. To address this point, we systematically investigate the transfer learning ability of ConvNets and vision transformers in 15 single-task and multi-task performance evaluations. Given the strong correlation between the performance of pre-trained models and transfer learning, we include 2 residual ConvNets (i.e., R-101x3 and R-152x4) and 3 Transformer-based visual backbones (i.e., ViT-B, ViT-L and Swin-B), which have close error rates on ImageNet, that indicate similar transfer learning performance on downstream datasets. We observe consistent advantages of Transformer-based backbones on 13 downstream tasks (out of 15), including but not limited to fine-grained classification, scene recognition (classification, segmentation and depth estimation), open-domain classification, face recognition, etc. More specifically, we find that two ViT models heavily rely on whole network fine-tuning to achieve performance gains while Swin Transformer does not have such a requirement. Moreover, vision transformers behave more robustly in multi-task learning, i.e., bringing more improvements when managing mutually beneficial tasks and reducing performance losses when tackling irrelevant tasks. We hope our discoveries can facilitate the exploration and exploitation of vision transformers in the future.

cs.CV↗
arXiv2020

Relationship-Embedded Representation Learning for Grounding Referring Expressions

Grounding referring expressions in images aims to locate the object instance in an image described by a referring expression. It involves a joint understanding of natural language and image content, and is essential for a range of visual tasks related to human-computer interaction. As a language-to-vision matching task, the core of this problem is to not only extract all the necessary information (i.e., objects and the relationships among them) in both the image and referring expression, but also make full use of context information to align cross-modal semantic concepts in the extracted information. Unfortunately, existing work on grounding referring expressions fails to accurately extract multi-order relationships from the referring expression and associate them with the objects and their related contexts in the image. In this paper, we propose a Cross-Modal Relationship Extractor (CMRE) to adaptively highlight objects and relationships (spatial and semantic relations) related to the given expression with a cross-modal attention mechanism, and represent the extracted information as a language-guided visual relation graph. In addition, we propose a Gated Graph Convolutional Network (GGCN) to compute multimodal semantic contexts by fusing information from different modes and propagating multimodal information in the structured relation graph. Experimental results on three common benchmark datasets show that our Cross-Modal Relationship Inference Network, which consists of CMRE and GGCN, significantly surpasses all existing state-of-the-art methods. Code is available at https://github.com/sibeiyang/sgmn/tree/master/lib/cmrin_models

cs.CV↗
arXiv2020

Graph-Structured Referring Expression Reasoning in The Wild

Grounding referring expressions aims to locate in an image an object referred to by a natural language expression. The linguistic structure of a referring expression provides a layout of reasoning over the visual contents, and it is often crucial to align and jointly understand the image and the referring expression. In this paper, we propose a scene graph guided modular network (SGMN), which performs reasoning over a semantic graph and a scene graph with neural modules under the guidance of the linguistic structure of the expression. In particular, we model the image as a structured semantic graph, and parse the expression into a language scene graph. The language scene graph not only decodes the linguistic structure of the expression, but also has a consistent representation with the image semantic graph. In addition to exploring structured solutions to grounding referring expressions, we also propose Ref-Reasoning, a large-scale real-world dataset for structured referring expression reasoning. We automatically generate referring expressions over the scene graphs of images using diverse expression templates and functional programs. This dataset is equipped with real-world visual contents as well as semantically rich expressions with different reasoning layouts. Experimental results show that our SGMN not only significantly outperforms existing state-of-the-art algorithms on the new Ref-Reasoning dataset, but also surpasses state-of-the-art structured methods on commonly used benchmark datasets. It can also provide interpretable visual evidences of reasoning. Data and code are available at https://github.com/sibeiyang/sgmn

cs.CV↗
arXiv2020

Weighted Global Regularity Estimates for Elliptic Problems with Robin Boundary Conditions in Lipschitz Domains

Let $n\ge2$ and $Ω$ be a bounded Lipschitz domain in $\mathbb{R}^n$. In this article, the authors investigate global (weighted) estimates for the gradient of solutions to Robin boundary value problems of second order elliptic equations of divergence form with real-valued, bounded, measurable coefficients in $Ω$. More precisely, let $p\in(n/(n-1),\infty)$. Using a real-variable argument, the authors obtain two necessary and sufficient conditions for $W^{1,p}$ estimates of solutions to Robin boundary value problems, respectively, in terms of a weak reverse Hölder inequality with exponent $p$ or weighted $W^{1,q}$ estimates of solutions with $q\in(n/(n-1),p]$ and some Muckenhoupt weights. As applications, the authors establish some global regularity estimates for solutions to Robin boundary value problems of second order elliptic equations of divergence form with small $\mathrm{BMO}$ coefficients, respectively, on bounded Lipschitz domains, $C^1$ domains or (semi-)convex domains, in the scale of weighted Lebesgue spaces, via some quite subtle approach which is different from the existing ones and, even when $n=3$ in case of bounded $C^1$ domains, also gives an alternative correct proof of some know result. By this and some technique from harmonic analysis, the authors further obtain the global regularity estimates, respectively, in Morrey spaces, (Musielak--)Orlicz spaces and variable Lebesgue spaces

math.AP↗
arXiv2019

Applications of Hardy Spaces Associated with Ball Quasi-Banach Function Spaces

Let $X$ be a ball quasi-Banach function space satisfying some minor assumptions. In this article, the authors establish the characterizations of $H_X(\mathbb{R}^n)$, the Hardy space associated with $X$, via the Littlewood--Paley $g$-functions and $g_λ^\ast$-functions. Moreover, the authors obtain the boundedness of Calderón--Zygmund operators on $H_X(\mathbb{R}^n)$. For the local Hardy-type space $h_X(\mathbb{R}^n)$ associated with $X$, the authors also obtain the boundedness of $S^0_{1,0}(\mathbb{R}^n)$ pseudo-differential operators on $h_X(\mathbb{R}^n)$ via first establishing the atomic characterization of $h_X(\mathbb{R}^n)$. Furthermore, the characterizations of $h_X(\mathbb{R}^n)$ by means of local molecules and local Littlewood--Paley functions are also given. The results obtained in this article have a wide range of generality and can be applied to the classical Hardy space, the weighted Hardy space, the Herz--Hardy space, the Lorentz--Hardy space, the Morrey--Hardy space, the variable Hardy space, the Orlicz-slice Hardy space and their local versions. Some special cases of these applications are even new and, particularly, in the case of the variable Hardy space, the $g_λ^\ast$-function characterization obtained in this article improves the known results via widening the range of $λ$.

math.CA↗
arXiv2019

Dynamic Graph Attention for Referring Expression Comprehension

Referring expression comprehension aims to locate the object instance described by a natural language referring expression in an image. This task is compositional and inherently requires visual reasoning on top of the relationships among the objects in the image. Meanwhile, the visual reasoning process is guided by the linguistic structure of the referring expression. However, existing approaches treat the objects in isolation or only explore the first-order relationships between objects without being aligned with the potential complexity of the expression. Thus it is hard for them to adapt to the grounding of complex referring expressions. In this paper, we explore the problem of referring expression comprehension from the perspective of language-driven visual reasoning, and propose a dynamic graph attention network to perform multi-step reasoning by modeling both the relationships among the objects in the image and the linguistic structure of the expression. In particular, we construct a graph for the image with the nodes and edges corresponding to the objects and their relationships respectively, propose a differential analyzer to predict a language-guided visual reasoning process, and perform stepwise reasoning on top of the graph to update the compound object representation at every node. Experimental results demonstrate that the proposed method can not only significantly surpass all existing state-of-the-art algorithms across three common benchmark datasets, but also generate interpretable visual evidences for stepwisely locating the objects referred to in complex language descriptions.

cs.CV↗
arXiv2019

Non-Local Context Encoder: Robust Biomedical Image Segmentation against Adversarial Attacks

Recent progress in biomedical image segmentation based on deep convolutional neural networks (CNNs) has drawn much attention. However, its vulnerability towards adversarial samples cannot be overlooked. This paper is the first one that discovers that all the CNN-based state-of-the-art biomedical image segmentation models are sensitive to adversarial perturbations. This limits the deployment of these methods in safety-critical biomedical fields. In this paper, we discover that global spatial dependencies and global contextual information in a biomedical image can be exploited to defend against adversarial attacks. To this end, non-local context encoder (NLCE) is proposed to model short- and long range spatial dependencies and encode global contexts for strengthening feature activations by channel-wise attention. The NLCE modules enhance the robustness and accuracy of the non-local context encoding network (NLCEN), which learns robust enhanced pyramid feature representations with NLCE modules, and then integrates the information across different levels. Experiments on both lung and skin lesion segmentation datasets have demonstrated that NLCEN outperforms any other state-of-the-art biomedical image segmentation methods against adversarial attacks. In addition, NLCE modules can be applied to improve the robustness of other CNN-based biomedical image segmentation methods.

cs.CV↗
arXiv2018

New Characterizations of Musielak-Orlicz-Sobolev Spaces via Sharp Ball Averaging Functions

In this article, the authors establish a new characterization of the Musielak--Orlicz--Sobolev space on $\mathbb{R}^n$, which includes the classical Orlicz--Sobolev space, the weighted Sobolev space and the variable exponent Sobolev space as special cases, in terms of sharp ball averaging functions. Even in a special case, namely, the variable exponent Sobolev space, the obtained result in this article improves the corresponding result obtained by P. Hästö and A. M. Ribeiro [Commun. Contemp. Math. 19 (2017), 1650022, 13 pp] via weakening the assumption $f\in L^1(\mathbb R^n)$ into $f\in L_{\mathrm{loc}}^1(\mathbb R^n)$, which was conjectured to be true by Hästö and Ribeiro in the aforementioned same article.

math.CA↗
arXiv2018

Atomic and Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators on Spaces of Homogeneous Type

Let $\mathcal{X}$ be a metric space with doubling measure and $L$ a non-negative self-adjoint operator on $L^2(\mathcal{X})$ whose heat kernels satisfy the Gaussian upper bound estimates. Assume that the growth function $φ:\ \mathcal{X}\times[0,\infty) \to[0,\infty)$ satisfies that $φ(x,\cdot)$ is an Orlicz function and $φ(\cdot,t)\in {\mathbb A}_{\infty}(\mathcal{X})$ (the class of uniformly Muckenhoupt weights). Let $H_{φ,\,L}(\mathcal{X})$ be the Musielak-Orlicz-Hardy space defined via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors characterize the space $H_{φ,\,L}(\mathcal{X})$ by means of atoms, non-tangential and radial maximal functions associated with $L$. In particular, when $μ(\mathcal{X})<\infty$, the local non-tangential and radial maximal function characterizations of $H_{φ,\,L}(\mathcal{X})$ are obtained. As applications, the authors obtain various maximal function and the atomic characterizations of the "geometric" Musielak-Orlicz-Hardy spaces $H_{φ,\,r}(Ω)$ and $H_{φ,\,z}(Ω)$ on the strongly Lipschitz domain $Ω$ in $\mathbb{R}^n$ associated with second-order self-adjoint elliptic operators with the Dirichlet and the Neumann boundary conditions; even when $φ(x,t):=t$ for any $x\in\mathbb{R}^n$ and $t\in[0,\infty)$, the equivalent characterizations of $H_{φ,\,z}(Ω)$ given in this article improve the known results via removing the assumption that $Ω$ is unbounded.

math.CA↗
arXiv2018

Multi-Evidence Filtering and Fusion for Multi-Label Classification, Object Detection and Semantic Segmentation Based on Weakly Supervised Learning

Supervised object detection and semantic segmentation require object or even pixel level annotations. When there exist image level labels only, it is challenging for weakly supervised algorithms to achieve accurate predictions. The accuracy achieved by top weakly supervised algorithms is still significantly lower than their fully supervised counterparts. In this paper, we propose a novel weakly supervised curriculum learning pipeline for multi-label object recognition, detection and semantic segmentation. In this pipeline, we first obtain intermediate object localization and pixel labeling results for the training images, and then use such results to train task-specific deep networks in a fully supervised manner. The entire process consists of four stages, including object localization in the training images, filtering and fusing object instances, pixel labeling for the training images, and task-specific network training. To obtain clean object instances in the training images, we propose a novel algorithm for filtering, fusing and classifying object instances collected from multiple solution mechanisms. In this algorithm, we incorporate both metric learning and density-based clustering to filter detected object instances. Experiments show that our weakly supervised pipeline achieves state-of-the-art results in multi-label image classification as well as weakly supervised object detection and very competitive results in weakly supervised semantic segmentation on MS-COCO, PASCAL VOC 2007 and PASCAL VOC 2012.

cs.CV↗
arXiv2016

Maximal Function Characterizations of Musielak-Orlicz-Hardy Spaces Associated to Non-negative Self-adjoint Operators Satisfying Gaussian Estimates

Let $L$ be a non-negative self-adjoint operator on $L^2(\mathbb{R}^n)$ whose heat kernels have the Gaussian upper bound estimates. Assume that the growth function $φ:\,\mathbb{R}^n\times[0,\infty) \to[0,\infty)$ satisfies that $φ(x,\cdot)$ is an Orlicz function and $φ(\cdot,t)\in {\mathbb A}_{\infty}(\mathbb{R}^n)$ (the class of uniformly Muckenhoupt weights). Let $H_{φ,\,L}(\mathbb{R}^n)$ be the Musielak-Orlicz-Hardy space introduced via the Lusin area function associated with the heat semigroup of $L$. In this article, the authors obtain several maximal function characterizations of the space $H_{φ,\,L}(\mathbb{R}^n)$, which, especially, answer an open question of L. Song and L. Yan under an additional mild assumption satisfied by Schrödinger operators on $\mathbb{R}^n$ with non-negative potentials belonging to the reverse Hölder class, and second-order divergence form elliptic operators on $\mathbb{R}^n$ with bounded measurable real coefficients.

math.CA↗
arXiv2016

Gradient Estimates via Rearrangements for Solutions of Some Schrödinger Equations

In this article, by applying the well known method for dealing with $p$-Laplace type elliptic boundary value problems, the authors establish a sharp estimate for the decreasing rearrangement of the gradient of solutions to the Dirichlet and the Neumann boundary value problems of a class of Schrödinger equations, under the weak regularity assumption on the boundary of domains. As applications, gradient estimates of these solutions in Lebesgue spaces and Lorentz spaces are obtained.

math.AP↗
arXiv2016

Global Boundedness of the Gradient for a Class of Schrödinger Equations

In this paper, via applying the method developed by A. Cianchi and V. Maz'ya, the author obtains the global boundedness of the gradient for solutions to Dirichlet and Neumann problems of a class of Schrödinger equations under the minimal assumptions for integrability on the data and regularity on the boundary of the domain. Moreover, the case of arbitrary bounded semi-convex domains is also considered.

math.AP↗
arXiv2014

Riesz Transform Characterizations of Musielak-Orlicz-Hardy Spaces

Let $φ$ be a Musielak-Orlicz function satisfying that, for any $(x,\,t)\in\mathbb{R}^n\times(0,\,\infty)$, $φ(\cdot,\,t)$ belongs to the Muckenhoupt weight class $A_\infty (\mathbb{R}^n)$ with the critical weight exponent $q(φ)\in[1,\,\infty)$ and $φ(x,\,\cdot)$ is an Orlicz function with $0 \frac{n-1}{n}$, and via all the Riesz transforms with the order not more than $m\in\mathbb{N}$ when $\frac{i(φ)}{q(φ)}>\frac{n-1}{n+m-1}$. Moreover, the authors also establish the Riesz transform characterizations of $H_φ(\mathbb{R}^n)$, respectively, by means of the higher order Riesz transforms defined via the homogenous harmonic polynomials or the odd order Riesz transforms. Even if when $φ(x,t):=tw(x)$ for all $x\in{\mathbb R}^n$ and $t\in [0,\infty)$, these results also widen the range of weights in the known Riesz characterization of the classical weighted Hardy space $H^1_w({\mathbb R}^n)$ obtained by R. L. Wheeden from $w\in A_1({\mathbb R}^n)$ into $w\in A_\infty({\mathbb R}^n)$ with the sharp range $q(w)\in [1,\frac n{n-1})$, where $q(w)$ denotes the critical index of the weight $w$.

math.CA↗
arXiv2014

Introduction to Clustering Algorithms and Applications

Data clustering is the process of identifying natural groupings or clusters within multidimensional data based on some similarity measure. Clustering is a fundamental process in many different disciplines. Hence, researchers from different fields are actively working on the clustering problem. This paper provides an overview of the different representative clustering methods. In addition, application of clustering in different field is briefly introduced.

cs.LG↗
arXiv2014

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their Applications

Lusin Area Function and Molecular Characterizations of Musielak-Orlicz Hardy Spaces and Their ApplicationsLet $φ: \mathbb R^n\times [0,\infty)\to[0,\infty)$ be a growth function such that $φ(x,\cdot)$ is nondecreasing, $φ(x,0)=0$, $φ(x,t)>0$ when $t>0$, $\lim_{t\to\infty}φ(x,t)=\infty$, and $φ(\cdot,t)$ is a Muckenhoupt $A_\infty(\mathbb{R}^n)$ weight uniformly in $t$. In this paper, the authors establish the Lusin area function and the molecular characterizations of the Musielak-Orlicz Hardy space $H_φ(\mathbb{R}^n)$ introduced by Luong Dang Ky via the grand maximal function. As an application, the authors obtain the $φ$-Carleson measure characterization of the Musielak-Orlicz ${\mathop\mathrm{BMO}}$-type space $\mathop\mathrm{BMO}_φ(\mathbb{R}^n)$, which was proved to be the dual space of $H_φ(\mathbb{R}^n)$ by Luong Dang Ky.

math.CA↗