arXiv subjects

Tianyang Sun

Publications and source records attributed to Tianyang Sun.

8 recordsLinked to original sources

arXiv2026

The Bondal-Orlov Localization Conjecture Holds for Threefolds

Let $X$ be a noetherian scheme with the resolution property, and let $p:Y\to X$ be a projective morphism. Suppose that $R^{i}p_{*}=0$ for $i>2$ and that $ \mathcal {O}_{X}\longrightarrow Rp_{*}\mathcal {O}_{Y} $ is an isomorphism. We show that derived pushforward induces an equivalence \[ D^{b}(Y)/\operatorname{Ker}(Rp_{*})\simeq D^{b}(X). \] As an application, we prove a characteristic-free form of the Bondal--Orlov localization conjecture for quasi-projective threefolds.

math.AG↗

arXiv2026

Finite quotients of sousperfectoid adic spaces need not be adic

For every prime $p$ and every perfectoid field $K$ of characteristic $p$, we construct a geometrically normal sousperfectoid affinoid adic space with a $C_p$-action whose quotient in the category of $v$-ringed spaces is not adic. The source is stably uniform and sheafy, while a cofinal sequence of rational neighborhoods at a fixed point acquires new degree-one invariant sections that do not descend by completed rational localization. Consequently, finite quotient stability for affinoid perfectoid spaces does not extend to sousperfectoid spaces.

math.AG↗

arXiv2026

Sharp asymptotics for the tree-completion time in cylindrical Hastings--Levitov$(0)$

Let $\mathrm{CHL}_N$ be the cylindrical Hastings--Levitov aggregation process with parameter $0$ on a cylinder of width $N$ with particles of fixed size $\lambda>0$, and let $\omega_{N,\lambda}$ be its tree-completion time --- the last time at which a new tree is born on the base circle. Chen, Procaccia and Zong proved the sharp upper bound $\mathbb{E}[\omega_{N,\lambda}]\le(1+\varepsilon)(\log N)/(2\lambda)$ and conjectured the matching limit. Here we prove the matching lower bound, and therefore \[ \lim_{N\to\infty}\frac{\mathbb{E}[\omega_{N,\lambda}]}{\log N}=\frac{1}{2\lambda} \qquad\text{for every fixed }\lambda>0 . \]

math.PR↗

arXiv2026

Power-law and log-periodic degree tails for a family of probability generating function equations arising in evolving networks

For a fixed integer $j\ge1$ and $0<p<1$, we study the probability generating function (pgf) equation \[ (1+2p)\,g(x)=2p\,x^{j}+g\bigl(x-px+px^{2}\bigr),\qquad 0\le x\le1 , \] which governs the limiting degree distribution $\{p_k\}$ of a family of evolving network models. The cases $j=1$ and $j=2$ are the treelike fast-growth model of Feng and Hu and the homogeneous evolving network of Feng, Li and Hu. We prove that for every $j$ the equation has a unique pgf solution, of mean $2j$, and we determine its coefficient tail exactly: \[ p_k=k^{-1-\rho}\,\Psi_j(\log_\lambda k)+o\bigl(k^{-1-\rho}\bigr), \] where $\lambda=1+p$, $\rho=\log(1+2p)/\log(1+p)$ is independent of $j$, and $\Psi_j$ is continuous, strictly positive and $1$-periodic, with explicit Fourier coefficients. This resolves two conjectures of Feng and coauthors: (1) the power-law order $p_k=\Theta(k^{-1-\rho})$ and (2) its refinement to the multiplicatively periodic form $p_k\sim\Psi_j(\log_\lambda k)\,k^{-1-\rho}$. The periodic factor is genuinely non-constant for $p$ near $1$, and, for the two network models, for all $p$ outside a discrete set. Consequently, $p_k$ is asymptotic to no constant multiple of $k^{-1-\rho}$. Our method is a self-contained local analysis of the supercritical Galton-Watson process with offspring law $1+\mathrm{Bernoulli}(p)$, inspected at an independent geometric time. This time-changed process solves the equation observed by Feng and coauthors. The main results of this paper were obtained by the multi-agent system Eureka and have subsequently been verified by the authors.

math.PR↗

arXiv2026

HiEdit: Lifelong Model Editing with Hierarchical Reinforcement Learning

Lifelong model editing (LME) aims to sequentially rectify outdated or inaccurate knowledge in deployed LLMs while minimizing side effects on unrelated inputs. However, existing approaches typically apply parameter perturbations to a static and dense set of LLM layers for all editing instances. This practice is counter-intuitive, as we hypothesize that different pieces of knowledge are stored in distinct layers of the model. Neglecting this layer-wise specificity can impede adaptability in integrating new knowledge and result in catastrophic forgetting for both general and previously edited knowledge. To address this, we propose HiEdit, a hierarchical reinforcement learning framework that adaptively identifies the most knowledge-relevant layers for each editing instance. By enabling dynamic, instance-aware layer selection and incorporating an intrinsic reward for sparsity, HiEdit achieves precise, localized updates. Experiments on various LLMs show that HiEdit boosts the performance of the competitive RLEdit by an average of 8.48% with perturbing only half of the layers per edit. Our code is available at: https://github.com/yangfanww/hiedit.

cs.CL↗

arXiv2025

AgriEval: A Comprehensive Chinese Agricultural Benchmark for Large Language Models

In the agricultural domain, the deployment of large language models (LLMs) is hindered by the lack of training data and evaluation benchmarks. To mitigate this issue, we propose AgriEval, the first comprehensive Chinese agricultural benchmark with three main characteristics: (1) Comprehensive Capability Evaluation. AgriEval covers six major agriculture categories and 29 subcategories within agriculture, addressing four core cognitive scenarios: memorization, understanding, inference, and generation. (2) High-Quality Data. The dataset is curated from university-level examinations and assignments, providing a natural and robust benchmark for assessing the capacity of LLMs to apply knowledge and make expert-like decisions. (3) Diverse Formats and Extensive Scale. AgriEval comprises 14,697 multiple-choice questions and 2,167 open-ended question-and-answer questions, establishing it as the most extensive agricultural benchmark available to date. We also present comprehensive experimental results over 51 open-source and commercial LLMs. The experimental results reveal that most existing LLMs struggle to achieve 60% accuracy, underscoring the developmental potential in agricultural LLMs. Additionally, we conduct extensive experiments to investigate factors influencing model performance and propose strategies for enhancement. AgriEval is available at https://github.com/YanPioneer/AgriEval/.

cs.CL↗

arXiv2023

Hunting imaging biomarkers in pulmonary fibrosis: Benchmarks of the AIIB23 challenge

Airway-related quantitative imaging biomarkers are crucial for examination, diagnosis, and prognosis in pulmonary diseases. However, the manual delineation of airway trees remains prohibitively time-consuming. While significant efforts have been made towards enhancing airway modelling, current public-available datasets concentrate on lung diseases with moderate morphological variations. The intricate honeycombing patterns present in the lung tissues of fibrotic lung disease patients exacerbate the challenges, often leading to various prediction errors. To address this issue, the 'Airway-Informed Quantitative CT Imaging Biomarker for Fibrotic Lung Disease 2023' (AIIB23) competition was organized in conjunction with the official 2023 International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI). The airway structures were meticulously annotated by three experienced radiologists. Competitors were encouraged to develop automatic airway segmentation models with high robustness and generalization abilities, followed by exploring the most correlated QIB of mortality prediction. A training set of 120 high-resolution computerised tomography (HRCT) scans were publicly released with expert annotations and mortality status. The online validation set incorporated 52 HRCT scans from patients with fibrotic lung disease and the offline test set included 140 cases from fibrosis and COVID-19 patients. The results have shown that the capacity of extracting airway trees from patients with fibrotic lung disease could be enhanced by introducing voxel-wise weighted general union loss and continuity loss. In addition to the competitive image biomarkers for prognosis, a strong airway-derived biomarker (Hazard ratio>1.5, p<0.0001) was revealed for survival prognostication compared with existing clinical measurements, clinician assessment and AI-based biomarkers.

eess.IV↗

arXiv2023

Classifying solutions of ${\rm SU}(n+1)$ Toda system around a singular source

Consider a positive integer $n$ and $\gamma_1>-1,\cdots,\gamma_n>-1$. Let $D=\{z\in {\Bbb C}:|z|<1\}$, and let $(a_{ij})_{n\times n}$ denote the Cartan matrix of $\frak{su}(n+1)$. Utilizing the ordinary differential equation of $(n+1)$th order around a singular source of ${\rm SU}(n+1)$ Toda system, as discovered by Lin-Wei-Ye ({\it Invent Math}, {\bf 190}(1):169-207, 2012), we precisely characterize a solution $(u_1,\cdots, u_n)$ to the ${\rm SU}(n+1)$ Toda system \begin{equation*} \begin{cases} \frac{\partial^2 u_i}{\partial z\partial \bar z}+\sum_{j=1}^n a_{ij} e^{u_j}&=\pi \gamma _i\delta _0\,\,{\rm on}\,\, D\\ \frac{\sqrt{-1}}{2}\,\int_{D\backslash \{0\}} e^{u_{i} }{\rm d}z\wedge {\rm d}\bar z &< \infty \end{cases} \quad \text{for all}\quad i=1,\cdots, n \end{equation*} using $(n+1)$ holomorphic functions that satisfy the normalized condition. Additionally, we demonstrate that for each $1\leq i\leq n$, $0$ represents the cone singularity with angle $2\pi(1+\gamma_i)$ for the metric $e^{u_i}|{\rm d}z|^2$ on $D\backslash\{0\}$, which can be locally characterized by $(n-1)$ non-vanishing holomorphic functions at $0$.

math.AP↗