arXiv subjects

Qianyuan Zhang

Publications and source records attributed to Qianyuan Zhang.

6 recordsLinked to original sources

arXiv2026

How Order-Sensitive Are LLMs? OrderProbe for Deterministic Structural Reconstruction

Large language models (LLMs) excel at semantic understanding, yet their ability to reconstruct internal structure from scrambled inputs remains underexplored. Sentence-level restoration is difficult to evaluate automatically because scrambled sentences often admit multiple valid reorderings. We introduce OrderProbe, a deterministic benchmark for structural reconstruction using fixed four-character expressions in Chinese, Japanese, and Korean, which have a unique canonical order and thus support exact-match scoring. We further propose a diagnostic framework that evaluates models beyond recovery accuracy, including Semantic Accuracy, Logical Validity, Structural Consistency, Robustness, and Information Density. Experiments on twelve widely used LLMs show that structural reconstruction remains difficult even for frontier systems: zero-shot recovery frequently falls below 35%. We also observe a consistent gap between meaning-oriented generation and exact structural reconstruction, suggesting that structural robustness is not an automatic byproduct of semantic competence.

cs.CL↗

arXiv2026

Global dynamics and asymptotic stability for a nonlocal LANS-$α$-type system

This paper is devoted to the global dynamics of a nonlocal Lagrangian-averaged Navier-Stokes-$α$ (LANS-$α$)-type system (also known as the viscous Euler-Poincaré system) in one, two, and three spatial dimensions. In the unforced periodic setting with zero mean, we establish global well-posedness for the initial-value problem and prove that the corresponding solution semigroup is dissipative and possesses a compact global attractor consisting of the singleton $\{0\}$. Furthermore, we obtain the following global-in-time algebraic asymptotic stability estimate: \[ \|u(t,\cdot)\|_{H^3}\lesssim t^{-1/2},\qquad \forall\, t>0, \] which is derived from higher-order energy inequalities combined with a uniform Gronwall-type argument. Our results provide a complete description of the long-time behavior of the unforced periodic dynamics for this nonlocal LANS-$α$-type system.

math.AP↗

arXiv2026

Sharp well-posedness and ill-posedness of the Camassa-Holm equation in critical Triebel-Lizorkin spaces

This paper is devoted to the sharp well-posedness and ill-posedness of the Cauchy problem for the Camassa-Holm (CH) equation in critical Triebel-Lizorkin spaces $F^{1+\frac{1}{p}}_{p,q}(\mathbb{R})$ with $(p,q)\in[1,\infty)\times[1,\infty]$ or $p=q=\infty$. On the one hand, we establish the local well-posedness in the sense of Hadamard in $F^2_{1,q}(\mathbb{R})$ for $1\leq q<\infty$ via Lagrangian coordinate transformation. On the other hand, by means of smooth atomic decomposition, strong ill-posedness is then proved in $F^{1+\frac{1}{p}}_{p,q}(\mathbb{R})$ with $(p,q)\in(1,\infty)\times[1,\infty]$ or $p=q=\infty$ in the sense of norm inflation, which in particular yields the ill-posedness of CH in critical Sobolev spaces $W^{1+\frac{1}{p},p}(\mathbb{R})$ with $1<p<\infty$, and provides a new perspective on the ill-posedness of CH in $H^{\frac{3}{2}}(\mathbb{R})$.

math.AP↗

arXiv2026

Commutator estimates and their applications to the transport-type equations

In this paper, we derive new commutator estimates in the Triebel-Lizorkin spaces by employing Bony's para-product decomposition, the Nikol'skij representation, and the Fefferman-Stein vector-valued maximal function. These estimates are then applied to develop a general theory for transport equations. Although analogous results are already available in the setting of Besov spaces, the methods developed there do not carry over directly to the Triebel-Lizorkin case. Our approach works for Triebel-Lizorkin spaces and, as a byproduct, also yields the corresponding results in Besov spaces. All proofs are presented in a unified manner that applies to both scales of function spaces, thereby extending and sharpening previous results on transport equations in these frameworks. Furthermore, the general theory we obtain is widely applicable to evolution equations, including incompressible and compressible ideal fluid flows, shallow water waves, and related models. As an illustration, we consider the two-component Euler-Poincaré system. Using the theoretical framework developed herein, we establish its local well-posedness and a blow-up criterion in both sub-critical and critical Triebel-Lizorkin spaces.

math.AP↗

arXiv2026

Transport equation theory in the Triebel-Lizorkin spaces and its applications to the ideal fluid flows

In this paper, we develop a general theory for the transport equation within the framework of Triebel-Lizorkin spaces. We first derive commutator estimates in these spaces, dispensing with the conventional divergence-free condition, via the Bony paraproduct decomposition and vector-valued maximal function inequalities. Building on these estimates and combining the method of characteristics with a compactness argument, we then obtain the new a priori estimates and prove local well-posedness for the transport equation in Triebel-Lizorkin spaces. The resulting theory is applicable to a wide range of evolution equations, including models for incompressible and compressible ideal fluid flows, shallow water waves, among others. As an illustration, we consider the incompressible ideal magnetohydrodynamics (MHD) system. Employing the general transport theory developed here yields a complete local well-posedness result in the sense of Hadamard, covering both sub-critical and critical regularity regimes, and provides corresponding blow-up criteria for the ideal MHD equations in Triebel-Lizorkin spaces. Our results refine and substantially extend earlier work in this direction.

math.AP↗

arXiv2024

COMET: Benchmark for Comprehensive Biological Multi-omics Evaluation Tasks and Language Models

As key elements within the central dogma, DNA, RNA, and proteins play crucial roles in maintaining life by guaranteeing accurate genetic expression and implementation. Although research on these molecules has profoundly impacted fields like medicine, agriculture, and industry, the diversity of machine learning approaches-from traditional statistical methods to deep learning models and large language models-poses challenges for researchers in choosing the most suitable models for specific tasks, especially for cross-omics and multi-omics tasks due to the lack of comprehensive benchmarks. To address this, we introduce the first comprehensive multi-omics benchmark COMET (Benchmark for Biological COmprehensive Multi-omics Evaluation Tasks and Language Models), designed to evaluate models across single-omics, cross-omics, and multi-omics tasks. First, we curate and develop a diverse collection of downstream tasks and datasets covering key structural and functional aspects in DNA, RNA, and proteins, including tasks that span multiple omics levels. Then, we evaluate existing foundational language models for DNA, RNA, and proteins, as well as the newly proposed multi-omics method, offering valuable insights into their performance in integrating and analyzing data from different biological modalities. This benchmark aims to define critical issues in multi-omics research and guide future directions, ultimately promoting advancements in understanding biological processes through integrated and different omics data analysis.

q-bio.BM↗