arXiv subjects

Yiran Lin

Publications and source records attributed to Yiran Lin.

6 recordsLinked to original sources

arXiv2026

Verication-driven closed-loop multi-agent large language modelframework for code-compliant structural design

Multi-agent large language model(LLM)systems are applied to structural design,yet most use one-shot generation and cannot verify their output,leaving themill-suited to safety-critical tasks.Rather than trusting LLM self-correction,thisframework injects feedback from an external physics-based verier into a closedrepair loop.The framework couples a three-layernite-element verication systemwith a dual-node loop.Node 1 turns code violations into hard repair constraints,Node 2 turns a four-dimensional quality score into safety-rst soft constraints,and a retrieval-augmented code base makes every violation traceable to a clause.Overve structure types and 44 cases,code compliance rises from 56.8%to 98.6%and the composite score from 63.8 to 71.4(p<0.000001),using about 5.8%lessmaterial.Removing either node degrades performance,and compliance does notchange detectably across the two backbone LLMs tested,indicating that it ishere attributed to the external verier rather than the model.The framework,the 44-case benchmark and all experiment scripts are released as open source forreplicability.

cs.SE↗

arXiv2026

Holomorphic curves in compact quotients of SL(2,C)

We prove that every discrete faithful representation of the surfcae group into SL(2,C) is the monodromy of a holomorphic connection on the trivial rank-2 vector bundle over a Riemann surface. As an application, we answer the question posed by Ghys and Huckleberry-Winkelmann (known as the Margulis' problem) by proving that every compact quotient of SL(2,C) contains a holomorphic curve of genus at least two. The main tools we use are the Non-Abelian Hodge correspondence, the WKB analysis, and the Morgan-Shalen compactification.

math.GT↗

arXiv2026

Can Vision Language Models Be Adaptive in Mathematics Education? A Learner Model-based Rubric Study

Adaptive learning refers to educational technologies that track learners' learning progress and adapt the instructional process based on individual learners' learning performance. It is increasingly recognized as critical for developing an effective learning support tool. Vision language models (VLMs) have seen adoption in mathematics education, and students have been using them as learning aids for personalized instruction. However, it is unknown whether VLMs have the ability to adapt to different learner profiles when providing mathematical instructions. Current VLMs lack a systematic evaluation framework for this adaptivity to different learner profiles in mathematics tutoring tasks. To address this gap, we draw on the learner model from the adaptive learning framework (Shute and Towle, 2018) and propose a learner model-based rubric. Our rubric formalizes adaptivity assessment into three aspects: cognitive aspects, motivational aspects, and complexity. We also evaluate two additional dimensions of VLM responses: correctness (of answers and solutions) and quality (of the response itself). Our experimental results show measurable differences in adaptivity across models and also reveal that current VLMs struggle to consistently produce learner model-based instructional responses, especially when receiving limited learner information.

cs.CL↗

arXiv2026

Caratheodory metrics on Teichmuller spaces

Let $S$ be an arbitrary Riemann surface whose Teichm\"uller space $T(S)$ has dimension at least two. A long standing problem is to determine whether the Carath\'eodory metric $d_C$ agrees with the Teichm\"uller metric $d_T$ on $T(S)$. It was shown that $d_C\ne d_T$ when $S$ is a closed surface of genus at least two. In this paper we study the general case, and prove that $d_C\ne d_T$ on $T(S)$ except possibly on the following seven Teichm\"uller spaces: $T^1_{0,0}$, $T^1_{0,1}$, $T^2_{0,0}$, $T^1_{0,2}$, $T^2_{0,1}$, $T^3_{0,0}$, and $T^3_{0,1}$.

math.GT↗

arXiv2025

Lefschetz theorems, Hodge-Riemann relations and Ample vector bundles

We introduce a new Hermitian metric on the cohomology ring of compact K\"ahlerian manifolds with a pair $(v,w)$ satisfying certain Hodge-Riemann relations. An Hermitian metric on the exterior algebra of the cotangent bundle is also defined and we establish the corresponding theory of harmonic forms, relating the global metric and local metric. This generalizes the classical Hodge theory. As an immediate application we give a new proof of Dinh-Nguyen's theorem on the Hodge-Riemann relations for mixed K\"ahler classes. We give several other applications to the Lefschetz property and Hodge-Riemann relations of Chern classes of ample vector bundles.

math.AG↗

arXiv2025

THiNK: Can Large Language Models Think-aloud?

Assessing higher-order thinking skills in large language models (LLMs) remains a fundamental challenge, especially in tasks that go beyond surface-level accuracy. In this work, we propose THiNK (Testing Higher-order Notion of Knowledge), a multi-agent, feedback-driven evaluation framework grounded in Bloom's Taxonomy. THiNK frames reasoning assessment as an iterative task of problem generation, critique, and revision, encouraging LLMs to think-aloud through step-by-step reflection and refinement. This enables a systematic evaluation of both lower-order (e.g., remember, understand) and higher-order (e.g., evaluate, create) thinking skills. We apply THiNK to seven state-of-the-art LLMs and perform a detailed cognitive analysis of their outputs. Results reveal that while models reliably perform lower-order categories well, they struggle with applying knowledge in realistic contexts and exhibit limited abstraction. Structured feedback loops significantly improve reasoning performance, particularly in higher-order thinking. Qualitative evaluations further confirm that THiNK-guided outputs better align with domain logic and problem structure. The code of our framework provides a scalable methodology for probing and enhancing LLM reasoning, offering new directions for evaluation grounded in learning science, which is available at our GitHub repository.

cs.CL↗