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Yuxin Dong

Yuxin Dong appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
math.DGMachine Learningmath.CVComputer Visionmath-phmath.MPeess.IVmath.APMethodologyNetworking and Internet ArchitectureQuantitative Methods

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Published work

24 published item(s)

preprint2026arXiv

Thinking in Scales: Accelerating Gigapixel Pathology Image Analysis via Adaptive Continuous Reasoning

Traditional whole slide image (WSI) analysis methods typically rely on the multiple instance learning (MIL) paradigm, which extracts patch-level features at high magnification and aggregates them for slide-level prediction. However, such exhaustive patch-level processing is computationally expensive, severely limiting the efficiency and scalability of WSI analysis. To address this challenge, we propose PathCTM (a Pathology-oriented Continuous Thought Model) that enables token-efficient scale-space continuous reasoning for gigapixel WSIs. PathCTM formulates diagnostic inference as a dynamic sequential information pursuit. It progressively transitions from low-magnification global to high-magnification local inspection, and adaptively terminates inference when sufficient evidence is gathered to effectively bound decision uncertainty. Specifically, it uses conditional computation for dynamic scale switching with attention-guided region pruning, coupled with confidence-aware early stopping. Extensive experiments demonstrate that, compared with standard MIL-based methods, PathCTM reduces the number of required image patches by 95.95% and shortens inference time by approximately 95.62%, while maintaining AUC without degradation. Code is available at https://github.com/JSGe-AI/PathCTM.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Computationally Efficient Approximations for Matrix-based Renyi's Entropy

The recently developed matrix based Renyi's entropy enables measurement of information in data simply using the eigenspectrum of symmetric positive semi definite (PSD) matrices in reproducing kernel Hilbert space, without estimation of the underlying data distribution. This intriguing property makes the new information measurement widely adopted in multiple statistical inference and learning tasks. However, the computation of such quantity involves the trace operator on a PSD matrix $G$ to power $α$(i.e., $tr(G^α)$), with a normal complexity of nearly $O(n^3)$, which severely hampers its practical usage when the number of samples (i.e., $n$) is large. In this work, we present computationally efficient approximations to this new entropy functional that can reduce its complexity to even significantly less than $O(n^2)$. To this end, we leverage the recent progress on Randomized Numerical Linear Algebra, developing Taylor, Chebyshev and Lanczos approximations to $tr(G^α)$ for arbitrary values of $α$ by converting it into matrix-vector multiplications problem. We also establish the connection between the matrix-based Renyi's entropy and PSD matrix approximation, which enables exploiting both clustering and block low-rank structure of $G$ to further reduce the computational cost. We theoretically provide approximation accuracy guarantees and illustrate the properties of different approximations. Large-scale experimental evaluations on both synthetic and real-world data corroborate our theoretical findings, showing promising speedup with negligible loss in accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Markov subsampling based Huber Criterion

Subsampling is an important technique to tackle the computational challenges brought by big data. Many subsampling procedures fall within the framework of importance sampling, which assigns high sampling probabilities to the samples appearing to have big impacts. When the noise level is high, those sampling procedures tend to pick many outliers and thus often do not perform satisfactorily in practice. To tackle this issue, we design a new Markov subsampling strategy based on Huber criterion (HMS) to construct an informative subset from the noisy full data; the constructed subset then serves as a refined working data for efficient processing. HMS is built upon a Metropolis-Hasting procedure, where the inclusion probability of each sampling unit is determined using the Huber criterion to prevent over scoring the outliers. Under mild conditions, we show that the estimator based on the subsamples selected by HMS is statistically consistent with a sub-Gaussian deviation bound. The promising performance of HMS is demonstrated by extensive studies on large scale simulations and real data examples.

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preprint2022arXiv

On subelliptic harmonic maps with potential

Let $(M,H,g_H;g)$ be a sub-Riemannian manifold and $(N,h)$ be a Riemannian manifold. For a smooth map $u: M \to N$, we consider the energy functional $E_G(u) = \frac{1}{2} \int_M[|\mathrm{d}u_H|^2-2G(u)] \mathrm{d}V_M$, where $\mathrm{d}u_H$ is the horizontal differential of $u$, $G:N\to \mathbb{R}$ is a smooth function on $N$. The critical maps of $E_G(u)$ are referred to as subelliptic harmonic maps with potential $G$. In this paper, we investigate the existence problem for subelliptic harmonic maps with potentials by a subelliptic heat flow. Assuming that the target Riemannian manifold has non-positive sectional curvature and the potential $G$ satisfies various suitable conditions, we prove some Eells-Sampson type existence results when the source manifold is either a step-$2$ sub-Riemannian manifold or a step-$r$ sub-Riemannian manifold whose sub-Riemannian structure comes from a tense Riemannian foliation.

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preprint2022arXiv

Optimal Randomized Approximations for Matrix based Renyi's Entropy

The Matrix-based Renyi's entropy enables us to directly measure information quantities from given data without the costly probability density estimation of underlying distributions, thus has been widely adopted in numerous statistical learning and inference tasks. However, exactly calculating this new information quantity requires access to the eigenspectrum of a semi-positive definite (SPD) matrix $A$ which grows linearly with the number of samples $n$, resulting in a $O(n^3)$ time complexity that is prohibitive for large-scale applications. To address this issue, this paper takes advantage of stochastic trace approximations for matrix-based Renyi's entropy with arbitrary $α\in R^+$ orders, lowering the complexity by converting the entropy approximation to a matrix-vector multiplication problem. Specifically, we develop random approximations for integer order $α$ cases and polynomial series approximations (Taylor and Chebyshev) for non-integer $α$ cases, leading to a $O(n^2sm)$ overall time complexity, where $s,m \ll n$ denote the number of vector queries and the polynomial order respectively. We theoretically establish statistical guarantees for all approximation algorithms and give explicit order of s and m with respect to the approximation error $\varepsilon$, showing optimal convergence rate for both parameters up to a logarithmic factor. Large-scale simulations and real-world applications validate the effectiveness of the developed approximations, demonstrating remarkable speedup with negligible loss in accuracy.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Regularized Modal Regression on Markov-dependent Observations: A Theoretical Assessment

Modal regression, a widely used regression protocol, has been extensively investigated in statistical and machine learning communities due to its robustness to outliers and heavy-tailed noises. Understanding modal regression's theoretical behavior can be fundamental in learning theory. Despite significant progress in characterizing its statistical property, the majority of the results are based on the assumption that samples are independent and identical distributed (i.i.d.), which is too restrictive for real-world applications. This paper concerns the statistical property of regularized modal regression (RMR) within an important dependence structure - Markov dependent. Specifically, we establish the upper bound for RMR estimator under moderate conditions and give an explicit learning rate. Our results show that the Markov dependence impacts on the generalization error in the way that sample size would be discounted by a multiplicative factor depending on the spectral gap of underlying Markov chain. This result shed a new light on characterizing the theoretical underpinning for robust regression.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

OpenHI2 -- Open source histopathological image platform

Transition from conventional to digital pathology requires a new category of biomedical informatic infrastructure which could facilitate delicate pathological routine. Pathological diagnoses are sensitive to many external factors and is known to be subjective. Only systems that can meet strict requirements in pathology would be able to run along pathological routines and eventually digitized the study area, and the developed platform should comply with existing pathological routines and international standards. Currently, there are a number of available software tools which can perform histopathological tasks including virtual slide viewing, annotating, and basic image analysis, however, none of them can serve as a digital platform for pathology. Here we describe OpenHI2, an enhanced version Open Histopathological Image platform which is capable of supporting all basic pathological tasks and file formats; ready to be deployed in medical institutions on a standard server environment or cloud computing infrastructure. In this paper, we also describe the development decisions for the platform and propose solutions to overcome technical challenges so that OpenHI2 could be used as a platform for histopathological images. Further addition can be made to the platform since each component is modularized and fully documented. OpenHI2 is free, open-source, and available at https://gitlab.com/BioAI/OpenHI.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Schwarz type lemmas for generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds

In this paper, we consider some generalized holomorphic maps between pseudo-Hermitian manifolds and Hermitian manifolds. By Bochner formulas and comparison theorems, we establish related Schwarz type results. As corollaries, Liouville theorem and little Picard theorem for basic CR functions are deduced. Finally, we study CR Carathéodory pseudodistance on CR manifolds.

0 citations0 reviewsNo code linkedOpen access
preprint2019arXiv

Gradient estimate and Liouville theorems for p-harmonic maps

In this paper, we first obtain an $L^q$ gradient estimate for $p$-harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this $L^q$ gradient estimate, we get a corresponding Liouville type result for $p$-harmonic maps. Secondly, using these general results, we give various geometric applications to $p$-harmonic maps from complete manifolds with nonnegative Ricci curvature to manifolds with various upper bound on sectional curvature, under appropriate controlled images.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

$L^2$ curvature pinching theorems and vanishing theorems on complete Riemannian manifolds

In this paper, by using monotonicity formulas for vector bundle-valued $p$-forms satisfying the conservation law, we first obtain general $L^2$ global rigidity theorems for locally conformally flat (LCF) manifolds with constant scalar curvature, under curvature pinching conditions. Secondly, we prove vanishing results for $L^2$ and some non-$L^2$ harmonic $p$-forms on LCF manifolds, by assuming that the underlying manifolds satisfy pointwise or integral curvature conditions. Moreover, by a Theorem of Li-Tam for harmonic functions, we show that the underlying manifold must have only one end. Finally, we obtain Liouville theorems for $p$-harmonic functions on LCF manifolds under pointwise Ricci curvature conditions.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Liouville Theorems for critical points of the p-Ginzburg-Landau type functional

In this paper, we consider the smooth map from a Riemannian manifold to the standard Euclidean space and the p-Ginzburg-Landau energy. Under suitable curvature conditions on the domain manifold, some Liouville type theorems are established by assuming either growth conditions of the p-Ginzburg-Landau energy or an asymptotic condition at the infinity for the maps. In the end of paper, we obtain the unique constant solution of the constant Dirichlet boundary value problems on starlike domains.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

On the p-pseudoharmonic map heat flow

In this paper, we consider the heat flow for p-pseudoharmonic maps from a closed Sasakian manifold M into a compact Riemannian manifold N. We prove global existence and asymptotic convergence of the solution for the p-pseudoharmonic map heat flow, provided that the sectional curvature of the target manifold N is nonpositive. Moreover, without the curvature assumption on the target manifold, we obtain global existence and asymptotic convergence of the p-pseudoharmonic map heat flow as well when its initial p-energy is sufficiently small.

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preprint2015arXiv

Biharmonic submanifolds of pseudo-Riemannian manifolds

In this paper, we derived biharmonic equations for pseudo-Riemannian submanifolds of pseudo-Riemannian manifolds which includes the biharmonic equations for submanifolds of Riemannian manifolds as a special case. As applications, we proved that a pseudo-umbilical biharmonic pseudo-Riemannian submanifold of a pseudo-Riemannian manifold has constant mean curvature, we completed the classifications of biharmonic pseudo-Riemannian hypersurfaces with at most two distinct principal curvatures, which were used to give four construction methods to produce proper biharmonic pseudo-Riemannian submanifolds from minimal submanifolds. We also made some comparison study between biharmonic hypersurfaces of Riemannian space forms and the space-like biharmonic hypersurfaces of pseudo-Riemannian space forms.

0 citations0 reviewsNo code linkedOpen access
preprint2014arXiv

Rigidity Theorems for Complete Sasakian Manifolds with Constant Pseudo-Hermitian Scalar Curvature

The orthogonal decomposition of the Webster curvature provides us a way to characterize some canonical metrics on a pseudo-Hermitian manifold. We derive some subelliptic differential inequalities from the Weitzenböck formulas for the traceless pseudo-Hermitian Ricci tensor and the Chern-Moser tensor of Sasakian manifolds with constant pseudo-Hermitian scalar curvature and Sasakian pseudo-Einstein manifolds respectively. By means of either subelliptic estimates or maximum principle, some rigidity theorems are established to characterize Sasakian pseudo-Einstein manifolds among Sasakian manifolds with constant pseudo-Hermitian scalar curvature and Sasakian space forms among Sasakian pseudo-Einstein manifolds respectively.

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preprint2014arXiv

Rigidity theorems of complete Kähler-Einstein manifolds and complex space forms

We derive some elliptic differential inequalities from the Weitzenböck formulas for the traceless Ricci tensor of a Kähler manifold with constant scalar curvature and the Bochner tensor of a Kähler-Einstein manifold respectively. Using elliptic estimates and maximum principle, some $L^p$ and $L^\infty $ pinching results are established to characterize Kähler-Einstein manifolds among Kähler manifolds with constant scalar curvature, and others are given to characterize complex space forms among Kähler-Einstein manifolds. Finally, these pinching results may be combined to characterize complex space forms among Kähler manifolds with constant scalar curvature.

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preprint2014arXiv

Unstability of pseudoharmonic maps between pseudo-Hermitian manifolds

In this paper, we derive the second variation formula of pseudoharmonic maps into any pseudo-Hermitian manifolds. When the target manifold is an isometric embedded CR manifold in complex Euclidean space or a pseudo-Hermitian immersed submanifold in Heisenberg group, we give some conditions on Weingarten maps to obtain some unstability of pseudoharmonic maps between these pseudo-Hermitian manifolds.

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preprint2012arXiv

Monotonicity formulae, vanishing theorems and some geometric applications

Using the stress energy tensor, we establish some monotonicity formulae for vector bundle-valued p-forms satisfying the conservation law, provided that the base Riemannian (resp. Kähler) manifolds poss some real (resp. complex) p-exhaustion functions. Vanishing theorems follow immediately from the monotonicity formulae under suitable growth conditions on the energy of the p-forms. As an application, we establish a monotonicity formula for the Ricci form of a Kähler manifold of constant scalar curvature and then get a growth condition to derive the Ricci flatness of the Kähler manifold. In particular, when the curvature does not change sign, the Kähler manifold is isometrically biholomorphic to C^m. Another application is to deduce the monotonicity formulae for volumes of minimal submanifolds in some outer spaces with suitable exhaustion functions. In this way, we recapture the classical volume monotonicity formulae of minimal submanifolds in Euclidean spaces. We also apply the vanishing theorems to Bernstein type problem of submanifolds in Euclidean spaces with parallel mean curvature. In particular, we may obtain Bernstein type results for minimal submanifolds, especially for minimal real Kähler submanifolds under weaker conditions.

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preprint2011arXiv

Liouville theorems for F-harmonic maps and their applications

We prove several Liouville theorems for F-harmonic maps from some complete Riemannian manifolds by assuming some conditions on the Hessian of the distance function, the degrees of F(t) and the asymptotic behavior of the map at infinity. In particular, the results can be applied to F-harmonic maps from some pinched manifolds, and can deduce a Bernstein type result for an entire minimal graph.

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preprint2011arXiv

Monotonicity Formulae and Holomorphicity of Harmonic Maps between Kähler manifolds

In this paper, we introduce the stress-energy tensors of the partial energies E'(f) and E"(f) of maps between Kaehler manifolds. Assuming the domain manifolds poss some special exhaustion functions, we use these stress-energy tensors to establish some monotonicity formulae of the partial energies of pluriharmonic maps into any Kaehler manifolds and harmonic maps into Kaehler manifolds with strongly semi-negative curvature respectively. These monotonicity inequalities enable us to derive some holomorphicity and Liouville type results for these pluriharmonic maps and harmonic maps. We also use the stress-energy tensors to investigate the holomorphic extension problem of CR maps.

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preprint2010arXiv

On Vanishing Theorems For Vector Bundle Valued p-Forms And Their Applications

Let $F: [0, \infty) \to [0, \infty)$ be a strictly increasing $C^2$ function with $F(0)=0$. We unify the concepts of $F$-harmonic maps, minimal hypersurfaces, maximal spacelike hypersurfaces, and Yang-Mills Fields, and introduce $F$-Yang-Mills fields, $F$-degree, $F$-lower degree, and generalized Yang-Mills-Born-Infeld fields (with the plus sign or with the minus sign) on manifolds. When $F(t)=t, \frac 1p(2t)^{\frac p2}, \sqrt{1+2t} -1,$ and $1-\sqrt{1-2t},$ the $F$-Yang-Mills field becomes an ordinary Yang-Mills field, $p$-Yang-Mills field, a generalized Yang-Mills-Born-Infeld field with the plus sign, and a generalized Yang-Mills-Born-Infeld field with the minus sign on a manifold respectively. We also introduce the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) and derive the first variational formula of the $E_{F,g}-$energy functional (resp. $F$-Yang-Mills functional) with applications. In a more general frame, we use a unified method to study the stress-energy tensors that arise from calculating the rate of change of various functionals when the metric of the domain or base manifold is changed. These stress-energy tensors, linked to $F$-conservation laws yield monotonicity formulae. A "macroscopic" version of these monotonicity inequalities enables us to derive some Liouville type results and vanishing theorems for $p-$forms with values in vector bundles, and to investigate constant Dirichlet boundary value problems for 1-forms. In particular, we obtain Liouville theorems for $F-$harmonic maps (e.g. $p$-harmonic maps), and $F-$Yang-Mills fields (e.g. generalized Yang-Mills-Born-Infeld fields on manifolds). We also obtain generalized Chern type results for constant mean curvature type equations for $p-$forms on $\Bbb{R}^m$ and on manifolds $M$ with the global doubling property by a different approach. The case $p=0$ and $M=\mathbb{R}^m$ is due to Chern.

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