arXiv subjects

Yiran Lin

Publications and source records attributed to Yiran Lin.

8 recordsLinked to original sources

arXiv2026

Decoding spatial and semantic information from large-scale visual cortical activity for natural-movie reconstruction

Reconstructing natural visual experience from cortical population activity is a central challenge in neural decoding, particularly for calcium imaging, where signals are noisy, temporally filtered, and paired neural-video data are limited. Here we present Ca2REAL (Calcium Activity to Reconstruct Events, Appearance, and Layout), a neural-to-video framework that conditions a pretrained video diffusion model through separate layout and semantic controls derived from calcium activity. Using measured responses from 7,863 V1 neurons in one mouse, Ca2REAL reconstructed held-out natural-movie clips with 81.4% all-pairs stimulus-identification accuracy, with its clearest gains over deterministic baselines in perceptual and semantic measures. We further evaluated the framework in a stimulus-aligned virtual population of 116,705 neurons assembled from encoding-model-predicted responses across 11 independently recorded datasets. Perturbation and ablation analyses showed that reconstruction depends on distributed, stimulus-specific population structure, with layout and semantic pathways providing complementary spatial and identity information. Temporal analyses further showed improved preservation of semantic dynamics across reconstructed clips. These results show that large-scale cortical population activity constrains the spatial, semantic, and temporal structure of natural visual experience, providing a generative framework for high-fidelity neural reconstruction of dynamic visual scenes.

cs.CV↗

arXiv2026

Exploring AI Peer in Collaborative Mathematics Learning

Artificial intelligence (AI) agents are increasingly explored as collaborative learning partners in mathematics education, yet it remains unclear what makes an AI recognizable as a peer. This study examines how domain experts perceive and interact with an adaptive LLM-based peer agent combining a Big Five-informed persona with motivational state modulation for collaborative mathematics problem solving. Through thematic analysis of expert interviews, we identify conditions shaping peer perceptions, including emotional safety, shared control, and collaborative reasoning. Participants primarily judged the AI through its social behavior rather than mathematical capabilities. The AI was perceived more as a peer when it created a non-judgmental space, engaged in tentative reasoning, displayed appropriate imperfection, and respected participants' pace. Conversely, blind agreement and over-instruction reduced trust and shifted perceptions toward a tutor role. Based on these findings, we propose human-centered design dimensions for AI peer agents to guide future peer-oriented learning systems.

cs.HC↗

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 Teichmüller space $T(S)$ has dimension at least two. A long standing problem is to determine whether the Carathéodory metric $d_C$ agrees with the Teichmüller 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 Teichmüller 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 Kählerian 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 Kähler 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↗