arXiv subjects

Yanping Chen

Publications and source records attributed to Yanping Chen.

At least 19 recordsLinked to original sources

arXiv2026

Sharp Variational estimates for Schrödinger equation in $\mathbb{R}^{2}$

For $p\geq2$ and $r\geq 1$, we prove the sharp strong $r$-variation estimate for solutions to the free Schrödinger equation $$ \bigl\|V^r_{[0,1]}\{e^{itΔ}f\}\bigr\|_{L^p(\mathbb R^2)} \lesssim \|f\|_{H^s(\mathbb R^2)}. $$ The estimate holds if $s> s(p,r)$ and fails if $s< s(p,r)$, where $$s(p,r)=\max\left\{ \frac{2}{r}+\frac{1}{p}-\frac12,\, \frac{2}{r}-\frac{2}{p},\, \frac{1}{p}+\frac{1}{r},\, \frac{2}{p}-\frac13,\, 1-\frac{2}{p} \right\}.$$ In particular, $s(3,\infty)=1/3$. Thus our result yields a sharp variational extension of the two-dimensional Schrödinger maximal estimate of Du, Guth, and Li [{Ann. Math.}, 186, 607--640 (2017)]. The proof employs fractal restriction estimates to eliminate the regularity loss originating from the summation in the variation norm.

math.CA↗

arXiv2026

Covariance Identification from Regression Residuals

Regression residuals are projections of the errors, not observations of them. This paper characterizes what residuals identify about the error covariance. Residualization acts on the covariance through a known linear map, and under an unrestricted covariance model the directions it destroys are exactly those generated by the column space of the regressors. A linear covariance functional is identified if and only if it does not load on these lost directions, and restricting the covariance model, for instance to diagonal or clustered form, shrinks them. The central result separates projection loss from moment-selection loss: projecting the residual covariance onto the maintained covariance structure loses no identifying information, so cross-cluster, long-lag, and long-distance residual products add no identifying directions. They can still improve conditioning, since restricting to the aligned moments squares the condition number. This equivalence relies on the orthogonal-projection geometry of OLS, and generally fails for non-orthogonal transformation. Quadratic statistics in the outcome that are free of the regression coefficients additionally identify the covariance between the fitted and residual components, but not the covariance within the span of the regressors. Because the OLS sandwich variance depends only on that block, it is not identified by any such statistic under an unrestricted covariance model; robust variance estimation draws its identification from maintained restrictions on the covariance structure.

econ.EM↗

arXiv2026

Weak type $(1,1)$ bounds for rough oscillatory singular integrals

In their seminal work, F. Ricci and E. M. Stein [Proc. Nat. Acad. Sci. USA 83, 1--3 (1986)] introduced the oscillatory singular integral \[ T_Pf(x)=\mathrm{p.v.}\int_{\mathbb{R}^n} e^{iP(x,y)}\frac{Ω(x-y)}{|x-y|^n}f(y)\,dy, \] and S. Chanillo and M. Christ [Duke Math. J. 55, 141--155 (1987)] established its weak-type $(1,1)$ inequality for smooth $Ω$. For the rough variant, however, the weak-type $(1,1)$ inequality remained a long-standing open question. In the present paper, we settle this problem: specifically, we prove that the rough oscillatory singular integral is of weak type $(1,1)$ with $Ω\in L\log^+L(\mathbb{S}^{n-1})$. Moreover, we establish weak-type $(1,1)$ bounds for the rough maximal oscillatory operator associated with $T_P$, a result of independent interest.

math.CA↗

arXiv2026

A Multi-granularity Interaction Network for Relational Triple Extraction

Relational triple extraction identifies entity relations from raw sentences without depending on entity type information. The performance of traditional methods is seriously degenerated by ``unseen'' entities, because these methods can't build contextual dependencies relevant ``unseen'' entities. This paper addresses this challenge by proposing a multi-granularity interaction network that leverages word-word, entity-relation, and head-tail interactions to capture deep semantic dependencies. By incorporating multiple iterations, the multi-granularity interaction network is effective to refine the representations corresponding to head and tail entities. It enhances the global semantic features associated with relational triples, aiding in the remediation of triples that may have been overlooked or omitted in earlier steps. Strong and consistent performance is achieved by our method on two rearranged datasets, with a significant improvement in identifying relational triples, including those involving ``unseen'' named entities. For example, our model improves F1-score by 3.1%/20.5% over previous approaches on the NYT-R/WebNLG-R datasets in the Unseen metric. Code: https://github.com/xiaocen-luo/Interaction-Network.

cs.CL↗

arXiv2026

Sparse bounds for rough non-translation-invariant Calderón-Zygmund operators

In this paper, we establish sparse bounds for singular integral operators with rough non-translation-invariant Calderón-Zygmund kernels. Our approach verifies the localized hypothesis in the sparse domination framework introduced by Conde-Alonso, Di Plinio et al. The proof refines Seeger's microlocal decomposition using a Littlewood-Paley analysis adapted to the non-translation-invariant setting. As applications, we obtain quantitative weighted estimates for Calderón-type commutators and other singular integrals with rough kernels.

math.CA↗

arXiv2026

Hausdorff-Choquet Angular Spaces and Weak-Type $(1,1)$ Bounds for Rough Maximal Operators

In the present paper, we consider the maximal operator \[ \mathcal M_Ωf(x) := \sup_{r>0}\frac{1}{r^n} \int_{|y| 2$. To our knowledge, the present paper is the first to relax this threshold for $n>2$. Finally, for the general Hausdorff--Choquet scale $\mathcal H\mathcal C_α$, we show that $α=(n-1)/2$ is the sharp exponent for uniform weak type $(1,1)$ estimates.

math.CA↗

arXiv2026

Robust Variance Estimation in Linear Regression: A Projection-Geometry Perspective

Inference in linear regression commonly treats OLS residuals as proxies for unobserved errors. This approximation can fail when the regression projection is nonlocal relative to the error-dependence structure. Residualization then shifts covariance information across observations and clusters, while conventional heteroskedasticity-consistent (HC) and cluster-robust variance estimators (CRVE) retain only diagonal or within-cluster residual moments and may therefore understate sampling uncertainty. This paper develops a projection-geometry framework for robust variance estimation. The variance of the OLS estimator is represented exactly as a Riesz functional of latent covariance blocks, and observable residual moments are linked to the target through a linear operator determined by the full regression projection. This formulation reduces variance estimation to a linear inverse problem. I propose a Riesz variance estimator that combines within- and cross-cluster residual moments. Conventional HC and CRVE emerge as restricted approximations whose validity depends on negligible projection spillovers. The estimator remains well defined when cluster-specific leverage matrices are singular and is computed by an iterative algorithm that avoids explicit matrix inversion. Simulations show substantial undercoverage by conventional methods under projection spillovers, whereas the proposed estimator restores near-nominal coverage. In an application to colonial governor promotions, the correction changes the significance of four of five reported coefficients.

econ.EM↗

arXiv2026

Task Decomposition-Guided Reranking for Adaptive Agent Skill Retrieval

Skill usage can significantly enhance the ability of modern agent systems to complete complex tasks. However, the growing scale of skill libraries makes accurate skill selection increasingly challenging. In real-world scenarios, ambiguous semantic matching often arises between a specific task requirement and multiple generic yet semantically similar candidate skills. Moreover, existing methods tend to overlook the dynamic influence of task difficulty and skill applicability when selecting the optimal target skill set. To address these issues, we propose SkillReranker, an inference-time reranking framework for adaptive skill selection. Specifically, we first perform semantic decomposition on both the task and skill sides, yielding informative subtask and execution-state descriptions as well as transition-state descriptions that characterize each skill's functionality. These descriptions are then used to construct a directed acyclic execution graph, where intermediate task states are modeled as nodes and candidate skills as edges, thereby establishing a structured task-skill correspondence. On this basis, SkillReranker determines whether each state node satisfies the split condition to identify subtask intervals. For each task interval, we employ a cross-encoder to perform comprehensive scoring over candidate skills and select the most suitable ones to form the final target skill set. Experiments on ALFWorld and ScienceWorld with three backbone LLMs show that SkillReranker effectively improves task performance, reduces environment interaction steps, and lowers token consumption compared with existing skill selection baselines.

cs.AI↗

arXiv2026

On the relationship between block spaces and Orlicz spaces

Let $1 -1$. Let $(X,d,μ)$ be an $s$-Ahlfors-regular quasi-metric measure space. Suppose that $B^{0,v}_q(X)$ is the block space which consists of all functions that admit a decomposition into $q$-blocks supported on balls. In this paper, we study the relationship between the block space $B^{0,v}_q(X)$ and the Orlicz-type space $L(\log^+\!\!L)^{1+v}(X)$. More precisely, we show that the block space $B_q^{0,v}(X)$ is a proper subspace of the Orlicz space $L(\log^+\!\!L)^{1+v}(X)$ for any fixed $1 -1$. Namely, $$B_q^{0,v}(X)\subsetneq L(\log^+\!\!L)^{1+v}(X),$$ which gives a confirmed answer to a longstanding open problem concerning the relationship between block spaces and Orlicz-type spaces on the unit sphere $\mathbb S^{n-1}$. We further show that $L(\log^+\!\!L)^{1+v}(X)$ is the smallest Orlicz-type space containing $B^{0,v}_{q}(X)$. We also introduce a generalized block space $\mathscr B_q^{0,v}(X)$ that depends only on the measure structure and show that this space is equivalent to the Orlicz space $L(\log^+\!\!L)^{1+v}(X)$ when $μ(X)<\infty$. Finally, we consider two special cases that further clarify the roles of the parameter $q$ and the logarithmic weight.

math.CA↗

arXiv2026

Hierarchical Prototype-based Domain Priors for Multiple Instance Learning in Multimodal Histopathology Analysis

Digital pathology has fundamentally altered diagnostic workflows by enabling the computational analysis of gigapixel Whole Slide Images (WSIs), yet effectively deciphering their complex tumor microenvironments remains a formidable challenge. Existing Multiple Instance Learning (MIL) frameworks typically treat Whole Slide Images as unstructured bags of patches, discarding critical morphological semantics and spatial geometry. This lack of inductive bias often leads to overfitting on background noise and fails to align visual features with high-level diagnostic knowledge. To overcome these limitations, we propose the Hierarchical Prototype-based Domain Priors (HPDP) framework, a unified multimodal approach for joint histopathology diagnosis and prognosis. HPDP mitigates the data-driven "black box" issue by introducing a Morphologically Anchored Prototype System (MAPS), which anchors learning to interpretable morphological clusters, and a Sinusoidal Positional Encoder (SPE) to explicitly model tissue architecture. Furthermore, we bridge the semantic gap via a Hierarchical Cross-Modal Alignment (HCMA) module, using Large Language Model (LLM)-generated descriptions to contextually refine visual representations. Extensive experiments across seven cancer cohorts demonstrate that HPDP consistently achieves state-of-the-art performance with superior robustness and interpretability.

cs.CV↗

arXiv2026

On Achievable Covert Communication Performance under CSI Estimation Error and Feedback Delay

Covert communication's effectiveness critically depends on precise channel state information (CSI). This paper investigates the impact of imperfect CSI on achievable covert communication performance in a two-hop relay system. Firstly, we introduce a two-hop covert transmission scheme utilizing channel inversion power control (CIPC) to manage opportunistic interference, eliminating the receiver's self-interference. Given that CSI estimation error (CEE) and feedback delay (FD) are the two primary factors leading to imperfect CSI, we construct a comprehensive theoretical model to accurately characterize their effects on CSI quality. With the aid of this model, we then derive closed-form solutions for detection error probability (DEP) and covert rate (CR), establishing an analytical framework to delineate the inherent relationship between CEE, FD, and covert performance. Furthermore, to mitigate the adverse effects of imperfect CSI on achievable covert performance, we investigate the joint optimization of channel inversion power and data symbol length to maximize CR under DEP constraints and propose an iterative alternating algorithm to solve the bi-dimensional non-convex optimization problem. Finally, extensive experimental results validate our theoretical framework and illustrate the impact of imperfect CSI on achievable covert performance.

cs.IT↗

arXiv2025

CAMS: Towards Compositional Zero-Shot Learning via Gated Cross-Attention and Multi-Space Disentanglement

Compositional zero-shot learning (CZSL) aims to learn the concepts of attributes and objects in seen compositions and to recognize their unseen compositions. Most Contrastive Language-Image Pre-training (CLIP)-based CZSL methods focus on disentangling attributes and objects by leveraging the global semantic representation obtained from the image encoder. However, this representation has limited representational capacity and do not allow for complete disentanglement of the two. To this end, we propose CAMS, which aims to extract semantic features from visual features and perform semantic disentanglement in multidimensional spaces, thereby improving generalization over unseen attribute-object compositions. Specifically, CAMS designs a Gated Cross-Attention that captures fine-grained semantic features from the high-level image encoding blocks of CLIP through a set of latent units, while adaptively suppressing background and other irrelevant information. Subsequently, it conducts Multi-Space Disentanglement to achieve disentanglement of attribute and object semantics. Experiments on three popular benchmarks (MIT-States, UT-Zappos, and C-GQA) demonstrate that CAMS achieves state-of-the-art performance in both closed-world and open-world settings. The code is available at https://github.com/ybyangjing/CAMS.

cs.CV↗

arXiv2025

A Reasoning Paradigm for Named Entity Recognition

Generative LLMs typically improve Named Entity Recognition (NER) performance through instruction tuning. They excel at generating entities by semantic pattern matching but lack an explicit, verifiable reasoning mechanism. This "cognitive shortcutting" leads to suboptimal performance and brittle generalization, especially in zero-shot and lowresource scenarios where reasoning from limited contextual cues is crucial. To address this issue, a reasoning framework is proposed for NER, which shifts the extraction paradigm from implicit pattern matching to explicit reasoning. This framework consists of three stages: Chain of Thought (CoT) generation, CoT tuning, and reasoning enhancement. First, a dataset annotated with NER-oriented CoTs is generated, which contain task-relevant reasoning chains. Then, they are used to tune the NER model to generate coherent rationales before deriving the final answer. Finally, a reasoning enhancement stage is implemented to optimize the reasoning process using a comprehensive reward signal. This stage ensures explicit and verifiable extractions. Experiments show that ReasoningNER demonstrates impressive cognitive ability in the NER task, achieving competitive performance. In zero-shot settings, it achieves state-of-the-art (SOTA) performance, outperforming GPT-4 by 12.3 percentage points on the F1 score. Analytical results also demonstrate its great potential to advance research in reasoningoriented information extraction. Our codes are available at https://github.com/HuiResearch/ReasoningIE.

cs.CL↗

arXiv2025

Sparse domination for singular integral operators and their commutators in Dunkl setting with applications

In this paper, we establish sparse dominations for the Dunkl-Calderón-Zygmund operators and their commutators in the Dunkl setting. As applications, we first define the Dunkl-Muckenhoupt $A_p$ weight and obtain the weighted bounds for the Dunkl-Calderón-Zygmund operators, as well as the two-weight bounds for their commutators. Moreover, we also obtain the boundedness of the Dunkl-Calderón-Zygmund operators on the extrapolation space of a family of Banach function spaces.

math.CA↗

arXiv2025

The fractional Riesz transform and their commutator in Dunkl setting

In this paper, we study the boundedness of the fractional Riesz transforms in the Dunkl setting. Moreover, we establish the necessary and sufficient conditions for the boundedness of their commutator with respect to the central BMO space associated with Euclidean metric and the BMO space associated with Dunkl metric, respectively. Based on this, we further characterize the compactness of the commutator in terms of the corresponding types of VMO spaces.

math.CA↗

arXiv2024

A priori and a posteriori error estimates of a really pressure-robust virtual element method for the incompressible Brinkman problem

This paper presents both a priori and a posteriori error analyses for a really pressure-robust virtual element method to approximate the incompressible Brinkman problem. We construct a divergence-preserving reconstruction operator using the Raviart-Thomas element for the discretization on the right-hand side. The optimal priori error estimates are carried out, which imply the velocity error in the energy norm is independent of both the continuous pressure and the viscosity. Taking advantage of the virtual element method's ability to handle more general polygonal meshes, we implement effective mesh refinement strategies and develop a residual-type a posteriori error estimator. This estimator is proven to provide global upper and local lower bounds for the discretization error. Finally, some numerical experiments demonstrate the robustness, accuracy, reliability and efficiency of the method.

math.NA↗

arXiv2024

A Bi-consolidating Model for Joint Relational Triple Extraction

Current methods to extract relational triples directly make a prediction based on a possible entity pair in a raw sentence without depending on entity recognition. The task suffers from a serious semantic overlapping problem, in which several relation triples may share one or two entities in a sentence. In this paper, based on a two-dimensional sentence representation, a bi-consolidating model is proposed to address this problem by simultaneously reinforcing the local and global semantic features relevant to a relation triple. This model consists of a local consolidation component and a global consolidation component. The first component uses a pixel difference convolution to enhance semantic information of a possible triple representation from adjacent regions and mitigate noise in neighbouring neighbours. The second component strengthens the triple representation based a channel attention and a spatial attention, which has the advantage to learn remote semantic dependencies in a sentence. They are helpful to improve the performance of both entity identification and relation type classification in relation triple extraction. After evaluated on several publish datasets, the bi-consolidating model achieves competitive performance. Analytical experiments demonstrate the effectiveness of our model for relational triple extraction and give motivation for other natural language processing tasks.

cs.CL↗

arXiv2024

Calderón's commutator on Stratified Lie groups

Motivated by the recent work of Gimperlein and Goffeng on Calderón's commutator on compact Heisenberg type manifolds and the related weak Schatten class estimates, we establish the characterisation of $L^p$ boundedness for Calderon's commutator on stratified Lie groups. We further study related weak Schatten class estimates for second order commutators on two step stratified Lie groups, which include the Heisenberg groups. This latter result is obtained using double operator integral techniques which are novel in this area.

math.FA↗