arXiv subjects

Jing Yu

Publications and source records attributed to Jing Yu.

At least 37 records · Page 2Linked to original sources

arXiv2026

The list coloring number of uncrowded hypergraphs

We prove that for every fixed integer $r\geq 2$ and every $\varepsilon>0$, every sufficiently large finite uncrowded $(r+1)$-uniform hypergraph of maximum degree $Δ$ has list chromatic number at most \[ (1+\varepsilon)\left(\frac{rΔ}{\logΔ}\right)^{1/r}. \] The proof is a semi-random list-coloring nibble carried out directly on the original hypergraph. We encode the remaining coloring problem by active edge-color constraints and control all residual sizes through a binomial degree bound. After the nibble reaches a sparse terminal state, the coloring is completed by a Rosenfeld-style counting argument.

math.CO↗

arXiv2026

Trajectory-Aware Information Matching for Multi-Step Gradient Inversion in Federated Learning

Federated learning enables distributed information sharing and collaborative model training without exposing raw client data. However, shared gradients or model updates may still contain sensitive information, making federated learning vulnerable to gradient inversion attacks. Most existing gradient inversion attacks rely on simplified update observations, such as single-step gradients or endpoint-based matching. In practical FL, however, FedAvg produces an accumulated trajectory-dependent update after multiple local steps, rather than a gradient computed at a single model state.To address this issue, we propose NL-SME, a trajectory-aware information matching method for multi-step gradient inversion. NL-SME constructs a learnable nonlinear surrogate trajectory to approximate hidden local states and integrates trajectory-level information with calibrated gradient matching. For perturbed updates, NL-SME can further use an observed-update reliability-aware strategy to reduce the influence of unreliable components. Extensive experiments under diverse multi-step FedAvg settings show that NL-SME outperforms state-of-the-art gradient inversion baselines in reconstruction quality and update-matching accuracy. Additional evaluations on natural and medical images, as well as under fused-update observations and representative defense strategies, further suggest that observable multi-step updates may still retain reconstruction signals. These results reveal potential privacy leakage risks in federated information sharing. Code is available at https://anonymous.4open.science/r/NL-SME-main/README.md.

cs.LG↗

arXiv2026

Achieving $\widetilde{O}(1/ε)$ Sample Complexity for Bilinear Systems Identification under Bounded Noises

This paper studies finite-sample set-membership identification for discrete-time bilinear systems under bounded symmetric log-concave disturbances. Our analysis considers trajectory-dependent regressors and allows marginally stable dynamics with polynomial mean-square state growth. We prove that the diameter of the feasible parameter set shrinks with sample complexity $\widetilde{\mathcal O}(1/ε)$ where $ε$ is the estimation error. Simulation supports the theory and illustrates the advantage of the proposed estimator for uncertainty quantification.

cs.LG↗

arXiv2026

Strong marker sets for arbitrary generating sets of $\mathbb Z^n$

Gao and Wang proved a strong clopen marker theorem for finite generating sets of $\mathbb Z^n$ under the assumption that each generator has support of size either $1$ or $n$. We show that this support assumption can be removed. The proof is a short conjugacy argument: after a unimodular change of coordinates, any finite set of nonzero lattice vectors can be put in full-support position, allowing one to apply the theorem of Gao and Wang and conjugate the resulting marker set back.

math.CO↗

arXiv2026

Coradically graded Hopf algebras of tame corepresentation type

Let $\Bbbk$ be an algebraically closed field of characteristic $0$ and let $H$ be a finite-dimensional Hopf algebra over $\Bbbk$ with the dual Chevalley property. In this paper, we give a description of the link quiver of $H$ for different corepresentation types. Moreover, we show that $\operatorname{gr}^c(H)$ is of tame corepresentation type if and only if $\operatorname{gr}^c(H)\cong (\k\langle x,y\rangle/I)^* \times H_0$ for some special ideals $I$. Using the methods of link quivers and bosonization, we then discuss which of the above ideals occur when $(\Bbbk\langle x,y\rangle/I)^* \times H_0$ is a Hopf algebra of tame corepresentation type under certain assumptions.

math.QA↗

arXiv2026

Submodular flows and extreme flows on measurable spaces

The theory of submodular flows, introduced by Edmonds and Giles, is a cornerstone of combinatorial optimization, unifying network flows, matroid intersections and directed cut coverings. In this paper, we establish a measurable-space version of this framework, addressing the structural existence and duality questions raised as part of Problem~10.6 by Lovász in \textit{Submodular setfunctions on sigma-algebras, version 2}. We develop a theory of submodular flows on standard Borel spaces and establish the measurable analogues of the existence and optimality theorems. Furthermore, we introduce a measurable notion of the residual graph and characterize extreme flows by combining a base-polytope intersection condition with an acyclicity condition for the measurable residual graph, generalizing the discrete geometric intuition to the infinite-dimensional setting. Finally, we apply the theory to constrained supply-demand problems on measurable bipartite graphs and to fractional measurable orientations.

math.CO↗

arXiv2026

Borel Local Lemma: arbitrary random variables and limited exponential growth

The Lovász Local Lemma (the LLL for short) is a powerful tool in probabilistic combinatorics that is used to verify the existence of combinatorial objects with desirable properties. Recent years saw the development of various "constructive" versions of the LLL. A major success of this research direction is the Borel version of the LLL due to Csóka, Grabowski, Máthé, Pikhurko, and Tyros, which holds under a subexponential growth assumption. A drawback of their approach is that it only applies when the underlying random variables take values in a finite set. We present an alternative proof of a Borel version of the LLL that holds even if the underlying random variables are continuous and applies to dependency graphs of limited exponential growth.

math.CO↗

arXiv2026

Beyond Chunk-Local Extraction: Cross-Chunk Graph Augmentation for GraphRAG

GraphRAG extends retrieval-augmented generation by organizing corpora as explicit knowledge graphs, enabling graph-based retrieval for complex question answering. However, existing frameworks extract entities and relations within individual chunks, leaving cross-chunk relations -- those whose evidence spans multiple passages -- systematically absent from the index. Exhaustive LLM-based recovery of such relations is impractical due to the combinatorial explosion of chunk combinations. We present CrossAug, a GNN-guided CROSS-Chunk Graph AUGmentation method that enriches GraphRAG indices with cross-chunk relational structure as an offline step before query-time retrieval. CrossAug derives training supervision through self-supervised graph corruption, uses a topology-aware GNN to score subgraphs for missingness, and applies evidence-grounded LLM completion only to selected high-scoring regions. Experiments on three LLM-based GraphRAG frameworks across four multi-hop and long-document QA benchmarks demonstrate that CrossAug consistently improves performance, confirming the benefit of cross-chunk graph augmentation for retrieval-based question answering. Our code is available at https://github.com/DonFinliani/CrossAug.

cs.CL↗

arXiv2026

Asymptotic-Type Dimension Bounds through Combinatorial Approaches

We develop a probabilistic framework for large-scale dimension bounds in metric geometry, based on padded decompositions, randomized ball carving on net graphs, and the Lovász Local Lemma. For metric measure spaces with volume doubling constant $C_{\mathsf D}$, we prove the sharp bound $\mathrm{asdim}_{AN}(X)\le \mathrm{dim}_{AN}(X)\le \lfloor{\log_2 C_{\mathsf D}}\rfloor$. In particular, if $(M,g)$ is a complete Riemannian $n$-manifold with $\mathrm{Ric}_g\ge 0$, then $\mathrm{asdim}(M)\le n$, thereby settling a question of Papasoglu on manifolds with nonnegative Ricci curvature. We also show that if $(X,\mathsf{d},\mathfrak{m})$ is proper, volume noncollapsed, and has polynomial volume growth rate $ρ^V(X)$, then $\mathrm{asdim}(X)\le \lfloor{ρ^V(X)}\rfloor$. Moreover, the corresponding control function can be chosen to have polynomial growth. This extends Papasoglu's sharp asymptotic-dimension bound from graphs of polynomial growth to a metric-measure setting. As applications, we study equality in the polynomial-growth bound for universal covers of nilmanifolds, and under nonnegative Ricci curvature we relate the equality case in the volume-doubling bound to Gromov largeness, obtaining in particular a consequence for complete manifolds with positive scalar curvature.

math.MG↗

arXiv2026

CrossCult-KIBench: A Benchmark for Cross-Cultural Knowledge Insertion in MLLMs

Multimodal Large Language Models (MLLMs), trained primarily on English-centric data, frequently generate culturally inappropriate or misaligned responses in cross-cultural settings. To mitigate this, we introduce the task of cross-cultural knowledge insertion, which focuses on adapting models to specific cultural contexts while preserving their original behavior in other cultures. To facilitate research in this area, we introduce CrossCult-KIBench, a comprehensive evaluation benchmark for assessing both the effectiveness of knowledge insertion and its unintended side effects on non-target cultures. The benchmark includes 9,800 image-grounded cases covering 49 culturally relevant visual scenarios across English, Chinese, and Arabic language-culture groups. It supports evaluation in both single-insert and sequential-insert settings. We also propose Memory-Conditioned Knowledge Insertion (MCKI) as a baseline method. MCKI retrieves relevant cultural knowledge from an external memory using frozen MLLM representations, prepending matched entries as conditional prompts when applicable. Extensive experiments on CrossCult-KIBench reveal that current approaches struggle to balance effective cultural adaptation with behavioral preservation, highlighting a key challenge in developing culturally-aware MLLMs. Our work thus underscores an important research direction for developing more culturally adaptive and responsible MLLMs.

cs.AI↗

arXiv2026

Counting degree-constrained orientations

We study the enumeration of graph orientations under local degree constraints. Given a finite graph $G = (V, E)$ and a family of admissible sets $\{\mathsf P_v \subseteq \mathbb{Z} : v \in V\}$, let $\mathcal N (G; \prod_{v \in V} \mathsf P_v)$ denote the number of orientations in which the out-degree of each vertex $v$ lies in $P_v$. We prove a general duality formula expressing $\mathcal N(G; \prod_{v \in V} \mathsf P_v)$ as a signed sum over edge subsets, involving products of coefficient sums associated with $\{\mathsf P_v\}_{v \in V}$, from a family of polynomials. Our approach employs gauge transformations, a technique rooted in statistical physics and holographic algorithms. We also present a probabilistic derivation of the same identity, interpreting the orientation-generating polynomial as the expectation of a random polynomial product. As applications, we obtain explicit formulas for the number of even orientations and for mixed Eulerian-even orientations on general graphs. Our formula generalizes a result of Borbényi and Csikvári on Eulerian orientations of graphs.

math.CO↗

arXiv2026

Hypergraph independence bounds: from maximum degree to average degree

We prove a transfer theorem for hereditary classes of $(r+1)$-uniform hypergraphs. Let $\mathcal H$ be such a class, and for $H\in\mathcal H$ write $Δ(H)$ and $d(H)$ for the maximum degree and average degree of $H$, respectively. We show that, for every nearly logarithmic function $f$ in the sense defined below, a maximum-degree lower bound for the independence number of the form \[ α(H)\ge (1-o(1))\frac{f(Δ(H))}{Δ(H)^{1/r}}|V(H)| \qquad\text{as }Δ(H)\to\infty \] for all $H\in\mathcal H$ implies the corresponding average-degree lower bound \[ α(H)\ge (1-o(1))\frac{f(d(H))}{d(H)^{1/r}}|V(H)| \qquad\text{as }d(H)\to\infty . \] We combine this transfer theorem with known coloring and fractional-coloring bounds to obtain consequences for graphs excluding a fixed cycle, graphs with bounded clique number, locally $q$-colorable graphs, and locally sparse uniform hypergraphs.

math.CO↗

arXiv2026

Ti-Audio: The First Multi-Dialectal End-to-End Speech LLM for Tibetan

Recent advances in Speech Large Language Models (Speech-LLMs) have made significant progress, greatly enhancing multimodal interaction capabilities.However, their application in low-resource and dialect-diverse environments still faces challenges. The severe scarcity of Tibetan data, coupled with the phonetic differences among its major dialects (Ü-Tsang, Amdo, and Kham), is a prime example of this challenge. This paper proposes Ti-Audio, the first multi-dialectal end-to-end Speech-LLM for Tibetan. To efficiently align speech and text, we introduce a Dynamic Q-Former Adapter that extracts essential acoustic features from variable-length speech, ensuring stable cross-modal alignment even with limited data. At the data level, we leverage mutual assistance among related dialects to alleviate data scarcity and employ a temperature-based sampling strategy to maximize this synergy. Experimental results demonstrate that Ti-Audio achieves state-of-the-art performance on Tibetan benchmarks for automatic speech recognition and speech translation. Our work validates the effectiveness of cross-dialectal cooperation and provides a scalable paradigm for the development of Speech-LLM in low-resource scenarios.

cs.SD↗

arXiv2026

A2-DIDM: Privacy-preserving Accumulator-enabled Auditing for Distributed Identity of DNN Model

Recent booming development of Generative Artificial Intelligence (GenAI) has facilitated model commercialization to reinforce the model performance, including licensing or trading Deep Neural Network (DNN) models. However, DNN model trading may violate the benefit of the model owner due to unauthorized replications or misuse of the model. Model identity auditing is a challenging issue in protecting DNN model ownership, and verifying the integrity and ownership of models is one of the critical obstacles. In this paper, we focus on the above issue and propose an \underline{A}ccumulator-enabled \underline{A}uditing for \underline{D}ecentralized \underline{Id}entity of DNN \underline{M}odel (A2-DIDM) that utilizes blockchain and zero-knowledge techniques to protect data and function privacy while ensuring the lightweight on-chain ownership verification. The proposed model presents a scheme of identity records via configuring model weight checkpoints with zero-knowledge proofs, which incorporates predicates to capture incremental state changes in model weight checkpoints. Our scheme ensures both computational integrity and programmability in DNN training process so that the uniqueness of the weight checkpoint sequence in a DNN model is preserved. %to ensure the correctness of model identity auditing, so that the uniqueness of the weight checkpoint sequence in a DNN model is preserved. A2-DIDM also addresses privacy protections in decentralized identity. We systematically analyze the security and robustness of our proposed model and further evaluate the effectiveness and usability of auditing DNN model identities. The code is available at https://github.com/xtx123456/A2-DIDM.git.

cs.CR↗

arXiv2026

MinerU2.5-Pro: Pushing the Limits of Data-Centric Document Parsing at Scale

Current document parsing methods advance primarily through model architecture innovation, while systematic engineering of training data remains underexplored. Yet state-of-the-art models spanning diverse architectures and parameter scales exhibit highly consistent failure patterns on the same set of hard samples, suggesting that the performance bottleneck stems from shared deficiencies in training data rather than from architectural differences. Building on this finding, we present MinerU2.5-Pro, which advances the state of the art purely through data engineering and training strategy design while retaining the 1.2B-parameter architecture of MinerU2.5 unchanged. At its core is a Data Engine co-designed around coverage, informativeness, and annotation accuracy: Diversity-and-Difficulty-Aware Sampling expands training data from under 10M to 65.5M samples while mitigating distribution shift; Cross-Model Consistency Verification leverages output consensus among heterogeneous models to assess sample difficulty and generate reliable annotations; the Judge-and-Refine pipeline improves annotation quality for hard samples through render-then-verify iterative correction. A three-stage progressive training strategy--large-scale pre-training, hard sample fine-tuning, and GRPO alignment--sequentially exploits these data at different quality tiers. On the evaluation front, we rectify element-matching biases in OmniDocBench v1.5 and introduce a Hard subset, establishing the more discriminative OmniDocBench v1.6 protocol. Without any architectural modification, MinerU2.5-Pro achieves 95.69 on OmniDocBench v1.6, improving over the same-architecture baseline by 2.71 points and surpassing all existing methods, including those based on models with over 200x more parameters.

cs.CV↗

arXiv2026

Hausdorff measure of the free boundary for the $p$-obstacle problem with subcritical exponents

This paper investigates a class of $p$-obstacle problems with subcritical exponents having the form \begin{align} \mathrm{div}\left( a(x)|\nabla u|^{p-2}\nabla u\right) =m_1χ_{\{u>0\}}-m_2u^{λ-1}χ_{\{u>0\}} \ \text{in}\ Ω,\notag \end{align} where $Ω$ is a smooth bounded domain in $ \mathbb{R}^N (N \geq 2)$, $m_1,m_2$ are positive constants, the coefficient function $a \in C^2(Ω)$ has a positive lower bound, and $2 \leq p < λ<p^*:= \frac{Np}{N-p}$ when $p<N$ and $N \geq 3$, or $2\leq p < λ<+\infty$ when $ N = 2$. By using the mountain-pass lemma, combined with the penalty method, we first establish the existence of non-negative weak solutions. Then, using the De Giorgi-Nash iteration, we prove the $L^\infty$ bound and local $C^{1,α}$ continuity for the solutions. In addition, we prove local porosity of the free boundary based on the optimal growth and non-degeneracy of solutions near the free boundary. Furthermore, by means of Lebesgue measure estimates for gradient level sets, we show that at least one solution corresponds the free boundary having locally finite $(N-1)$-dimensional Hausdorff measure.

math.AP↗

arXiv2026

Simple Yetter-Drinfeld modules over Generalized Liu algebras

Let $H$ be a generalized Liu algebra over an algebraically closed field $k$ of characteristic zero. We prove that all simple Yetter-Drinfeld modules over $H$ are finite-dimensional and present an explicit classification of these modules. Moreover, we completely determine which of them admit a finite-dimensional Nichols algebra.

math.QA↗

arXiv2026

ProAPO: Progressively Automatic Prompt Optimization for Visual Classification

Vision-language models (VLMs) have made significant progress in image classification by training with large-scale paired image-text data. Their performances largely depend on the prompt quality. While recent methods show that visual descriptions generated by large language models (LLMs) enhance the generalization of VLMs, class-specific prompts may be inaccurate or lack discrimination due to the hallucination in LLMs. In this paper, we aim to find visually discriminative prompts for fine-grained categories with minimal supervision and no human-in-the-loop. An evolution-based algorithm is proposed to progressively optimize language prompts from task-specific templates to class-specific descriptions. Unlike optimizing templates, the search space shows an explosion in class-specific candidate prompts. This increases prompt generation costs, iterative times, and the overfitting problem. To this end, we first introduce several simple yet effective edit-based and evolution-based operations to generate diverse candidate prompts by one-time query of LLMs. Then, two sampling strategies are proposed to find a better initial search point and reduce traversed categories, saving iteration costs. Moreover, we apply a novel fitness score with entropy constraints to mitigate overfitting. In a challenging one-shot image classification setting, our method outperforms existing textual prompt-based methods and improves LLM-generated description methods across 13 datasets. Meanwhile, we demonstrate that our optimal prompts improve adapter-based methods and transfer effectively across different backbones.

cs.CV↗