arXiv subjects

Mingqi Yan

Publications and source records attributed to Mingqi Yan.

3 recordsLinked to original sources

arXiv2025

LemmaHead: RAG Assisted Proof Generation Using Large Language Models

Developing the logic necessary to solve mathematical problems or write mathematical proofs is one of the more difficult objectives for large language models (LLMS). Currently, the most popular methods in literature consists of fine-tuning the model on written mathematical content such as academic publications and textbooks, so that the model can learn to emulate the style of mathematical writing. In this project, we explore the effectiveness of using retrieval augmented generation (RAG) to address gaps in the mathematical reasoning of LLMs. We develop LemmaHead, a RAG knowledge base that supplements queries to the model with relevant mathematical context, with particular focus on context from published textbooks. To measure our model's performance in mathematical reasoning, our testing paradigm focuses on the task of automated theorem proving via generating proofs to a given mathematical claim in the Lean formal language.

cs.LG↗

arXiv2025

Stochastic bubble dynamics in phase-separated scalar active matter

In ABP systems, phase separation is accompanied by the emergence of vapor bubbles within liquid domains. Using large-scale particle-based simulations, we study the stochastic dynamics of these bubbles and find that most nucleate, grow, and dissolve within liquid domains. We show that their area dynamics can be described by a Langevin equation with a constant negative drift and noise proportional to the perimeter, fully characterizing bubble area and lifetime statistics. Additionally, we develop a lattice gas model that captures the morphological properties, including the decrease in bubble asphericity with increasing area. These findings provide new insights into phase separation in active matter and highlight limitations in current continuum theories.

cond-mat.soft↗

arXiv2018

Raman evidence for dimerization and Mott collapse in $α$-RuCl$_3$ under pressures

We perform Raman spectroscopy studies on $α$-RuCl$_3$ at room temperature to explore its phase transitions of magnetism and chemical bonding under pressures. The Raman measurements resolve two critical pressures, about $p_1=1.1$~GPa and $p_2=1.7$~GPa, involving very different intertwining behaviors between the structural and magnetic excitations. With increasing pressures, a stacking order phase transition of $α$-RuCl$_3$ layers develops at $p_1=1.1$~GPa, indicated by the new Raman phonon modes and the modest Raman magnetic susceptibility adjustment. The abnormal softening and splitting of the Ru in-plane Raman mode provide direct evidence of the in-plane dimerization of the Ru-Ru bonds at $p_2=1.7$~GPa. The Raman susceptibility is greatly enhanced with pressure increasing and sharply suppressed after the dimerization. We propose that the system undergoes Mott collapse at $p_2=1.7$~GPa and turns into a dimerized correlated band insulator. Our studies demonstrate competitions between Kitaev physics, magnetism, and chemical bondings in Kitaev compounds.

cond-mat.str-el↗