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Mengxue Yang

Publications and source records attributed to Mengxue Yang.

6 recordsLinked to original sources

ViSR-KGC: Visual Subgraph Reasoning with Vision-Language Models for Multimodal Knowledge Graph Completion

Knowledge graph completion (KGC) aims to infer missing entities or relations from incomplete graph structures, and has evolved into multimodal knowledge graph completion (MMKGC), where entities are associated with multiple modalities such as text and images. Traditional representation learning approaches follow the embedding-based paradigm and may struggle when relation-specific evidence is limited. Meanwhile, LLM-based reasoning methods typically linearize graph structures into textual prompts, which obscures structural topology and neglects vital visual information. While vision-language models (VLMs) excel at multimodal reasoning, they cannot natively interpret structured graph topology, particularly when it comes to knowledge graphs where nodes and edges carry complex semantics. To bridge this gap, we propose ViSR-KGC, a visual subgraph reasoning approach for KGC. It integrates three complementary capabilities to capture semantic correlations: identifying global topology dependencies via representation learning, analyzing local multimodal evidence using VLMs, and providing necessary commonsense knowledge inherent in pre-trained models. Based on learned multimodal embeddings, our framework first extracts a compact and query-aware subgraph from the MMKG. Then, this subgraph is transformed into a visually interpretable image using a layout strategy selected through empirical comparison. Finally, the visualized subgraph, entity images, textual descriptions, and candidate answers are combined into a unified prompt, enabling the VLM to infer the missing entity.

cs.AI

SLiNT: Structure-aware Language Model with Injection and Contrastive Training for Knowledge Graph Completion

Link prediction in knowledge graphs requires integrating structural information and semantic context to infer missing entities. While large language models offer strong generative reasoning capabilities, their limited exploitation of structural signals often results in structural sparsity and semantic ambiguity, especially under incomplete or zero-shot settings. To address these challenges, we propose SLiNT (Structure-aware Language model with Injection and coNtrastive Training), a modular framework that injects knowledge-graph-derived structural context into a frozen LLM backbone with lightweight LoRA-based adaptation for robust link prediction. Specifically, Structure-Guided Neighborhood Enhancement (SGNE) retrieves pseudo-neighbors to enrich sparse entities and mitigate missing context; Dynamic Hard Contrastive Learning (DHCL) introduces fine-grained supervision by interpolating hard positives and negatives to resolve entity-level ambiguity; and Gradient-Decoupled Dual Injection (GDDI) performs token-level structure-aware intervention while preserving the core LLM parameters. Experiments on WN18RR and FB15k-237 show that SLiNT achieves superior or competitive performance compared with both embedding-based and generation-based baselines, demonstrating the effectiveness of structure-aware representation learning for scalable knowledge graph completion.

cs.CL

(BAA)-branes from higher Teichmüller theory

Interpreting certain holomorphic Lagrangians that arise from the relative Langlands program, we construct moduli stacks underlying the generalized Slodowy categories of Collier--Sanders and $G^\mathbf{R}$-Higgs bundles over a Riemann surface. Furthermore, we extend the Cayley correspondence of Bradlow--Collier--García-Prada--Gothen--Oliveira to a morphism of Lagrangians over the Hitchin moduli stack, and initiate the study of its hyperholomorphic mirror partner under $S$-duality.

math.AG

Conformal limits in Cayley components and $Θ$-positive opers

We study Gaiotto's conformal limit for the $G^{\mathbb{R}}$-Hitchin equations, when $G^{\mathbb{R}}$ is a simple real Lie group admitting a $Θ$-positive structure. We identify a family of flat connections coming from certain solutions to the equations for which the conformal limit exists and admits the structure of an oper. We call this new class of opers appearing in the conformal limit $Θ$-positive opers. The two families involved are parameterized by the same base space. This space is a generalization of the base of Hitchin's integrable system in the case when the structure group is a split real group.

math.DG

On the generalized SO(2n,C)-opers

Since their introduction by Beilinson-Drinfeld \cite{BD,Opers1}, opers have seen several generalizations. In \cite{BSY} a higher rank analog was studied, named {generalized $B$-opers}, where the successive quotients of the oper filtration are allowed to have higher rank and the underlying holomorphic vector bundle is endowed with a bilinear form which is compatible with both the filtration and the oper connection. Since the definition didn't encompass the even orthogonal groups, we dedicate this paper to study generalized $B$-opers whose structure group is ${\rm SO}(2n,\mathbb{C})$, and show their close relationship with geometric structures on a Riemann surface.

math.AG

Generalized B-Opers

Opers were introduced by Beilinson-Drinfeld [arXiv:math.AG/0501398]. In [J. Math. Pures Appl. 82 (2003), 1-42] a higher rank analog was considered, where the successive quotients of the oper filtration are allowed to have higher rank. We dedicate this paper to introducing and studying generalized $B$-opers (where "$B$" stands for "bilinear"), obtained by endowing the underlying vector bundle with a bilinear form which is compatible with both the filtration and the connection. In particular, we study the structure of these $B$-opers, by considering the relationship of these structures with jet bundles and with geometric structures on a Riemann surface.

math.AG