刘抒睿

项目

计算机科学与人工智能 —— 系统、智能体与应用机器学习。

数学相关研究请见论文。

智能体记忆 / 自主研究 / 测试时学习

  1. Automated Conjecture Resolution with Formal Verification. Haocheng Ju*, Guoxiong Gao*, Jiedong Jiang*, Bin Wu*, Zeming Sun*, Shurui Liu*, Leheng Chen, Yutong Wang, Yuefeng Wang, Zichen Wang, Wanyi He, Peihao Wu, Liang Xiao, Ruochuan Liu, Bryan Dai, Bin Dong. [Arxiv] [Rethlas] [Archon].

    Abstract

    Recent advances in large language models have significantly improved their ability to perform mathematical reasoning, extending from elementary problem solving to increasingly capable performance on research-level problems. However, reliably solving and verifying such problems remains challenging due to the inherent ambiguity of natural language reasoning. In this paper, we propose an automated framework that integrates natural language reasoning with formal verification to tackle research-level mathematical problems. Our framework consists of two components: an informal reasoning agent, Rethlas, and a formal verification agent, Archon. Rethlas combines reasoning primitives with our theorem search engine, Matlas, to explore solution strategies and construct candidate proofs. Archon, equipped with LeanSearch, translates informal arguments into formalized Lean 4 projects through task decomposition, iterative refinement, and automated proof synthesis, ensuring machine-checkable correctness. Using this framework, we resolve an open problem in commutative algebra and formally verify the resulting proof in Lean 4 with essentially no human involvement. Additional case studies illustrate the capabilities of Rethlas in informal mathematical reasoning and discovery, as well as the ability of Archon to formalize research-level proofs in Lean 4. Our experiments demonstrate that strong theorem retrieval tools enable the discovery and application of cross-domain mathematical techniques, while the formal agent can autonomously fill nontrivial gaps in informal arguments. More broadly, our work illustrates a promising paradigm for mathematical research in which informal and formal reasoning systems, equipped with theorem retrieval tools, operate in tandem to produce verifiable results, reduce human effort, and support human-AI collaborative mathematical research.

  2. Danus: Orchestrating Mathematical Reasoning Agents with Fact-Graph Memory. Jihao Liu, Guoxiong Gao, Zeming Sun, Bin Wu, Shurui Liu, Jiedong Jiang, Haocheng Ju, Leheng Chen, Ronnie Cheng, Xiping Zhang, Bin Dong. [Arxiv] [Danus] [my talk at Cursor].

    Abstract

    Recent LLM-based mathematical reasoning agents have begun to tackle research-level problems and, in several cases, have contributed to the resolution of open problems. However, scaling and orchestrating such agents effectively remains challenging, due to the difficulty of coordinating parallel proof search while keeping intermediate claims organized and reliable. In this paper, we propose Danus, an orchestration system for research-level mathematical reasoning centered on a shared fact graph as a global memory-management mechanism. Danus consists of a main agent that performs planning and coordination, multiple worker agents that carry out proof search in parallel, and a stateless verifier that checks proposed mathematical claims before they are admitted into the fact graph. Each verified fact is stored together with its proof and logical dependencies, allowing the system to build long arguments incrementally while keeping the shared proof state organized. The main agent periodically summarizes the evolving proof state, redirects workers across promising directions, and supports interaction with human mathematicians through progress reports. We evaluate Danus through six research-level case studies in algebraic geometry, singularity theory, and combinatorics, illustrating how the fact-graph memory mechanism enables Danus to construct long, detailed mathematical proofs. Our results suggest that fact-graph-based orchestration provides an effective route toward scaling mathematical reasoning agents for long-horizon research problems. Danus is open source at https://github.com/frenzymath/Danus.

* 同等贡献。

Lean 项目

  1. Formalization of $p$-adic representation theory，进行中，网页，依赖图。Shurui Liu, Zhuoni Chi, Stepan Kazanin.
  2. VeriBench: An End-to-End Formal Verification Benchmark for AI Coding Agents in Lean 4. Brando Miranda, Srivatsava Daruru, Ethan S. Hersch, Zhanke Zhou, Allen Nie, Daneshvar Amrollahi, Leni Aniva, Iddah Mlauzi, Kirill Acharya, Elyas Obbad, Dilara Soylu, Weston Kirk, Zixiao Jolene Wang, Kai Fronsdal, Ying Li, Donald Poindexter Jr., Rakshit Kaushik, Shurui Liu, Yegor Denisov-Blanch, Steven Dillmann, Simon Obstbaum, Santiago Cuellar, John Sarracino, Rylan Schaeffer, Mo Tiwari, Donghyun Lee, Bo Han, Sanmi Koyejo. 已作为海报被 ICML 2026 DL4C 与 AI4MATH workshop 接收。
    TL;DR

    VeriBench introduces a benchmark for evaluating language models on end-to-end Lean 4 code verification, showing current models struggle while self-optimizing agents demonstrate meaningful progress toward provably correct software generation.

课程项目

  1. Dynamic Ledger: Retrieval-Augmented Structured Memory for Test-Time Learning，Jerry Gu*, Shurui Liu*, Sabrina Yen-Ko*，导师 Mirac Suzgun，网页。CS224N 2025 winter。