arXiv：cs.AI· Junyi Zhang, Jinxi Yu, Eric Hanchen Jiang, Jiachen Lu, Zhi Zhang, Xinjie He, Hyunsik Chae, Ethan Ji, Alexander K Taylor, Vigyan Sahai, Yiwen Kou, Kai-Wei Chang, Raghu Meka, Nanyun Peng, Amit Sahai, Terence Tao, Wei Wang·· 5 小时前AI 评分67
数学研究智能体 Ansatz 提出 Continual Graph Memory 并求解多个开放数学问题
Continual Graph Memory for Mathematical Research Agents
AI 导读
UCLA 等机构与 Terence Tao 等合作者发布论文，提出数学研究智能体 Ansatz，核心是 Continual Graph Memory，一种基于图、可演化、跨问题的数学研究记忆系统，统一组织证明搜索中的事实、计划、反例等中间结果，并通过依赖感知检索、证据敏感的策展和带范围召回实现知识复用。
正文
Authors:Junyi Zhang, Jinxi Yu, Eric Hanchen Jiang, Jiachen Lu, Zhi Zhang, Xinjie He, Hyunsik Chae, Ethan Ji, Alexander K Taylor, Vigyan Sahai, Yiwen Kou, Kai-Wei Chang, Raghu Meka, Nanyun Peng, Amit Sahai, Terence Tao, Wei Wang
Abstract:Using frontier agent harnesses to tackle mathematical research problems has emerged as an effective means of advancing mathematics. However, solving frontier problems in mathematics may require a massive number of agents working in parallel for extended periods to construct proofs, thereby generating an enormous volume of intermediate proof results. Organizing these intermediate results throughout a long-horizon proof-search process and reusing knowledge gained from prior explorations remain major challenges. We present Ansatz, a mathematical research agent built around Continual Graph Memory, a graph-based, evolvable, cross-problem mathematical research memory system that explicitly organizes the entire proof search process and reuses information from exploration trajectories of previous problems. Specifically, we develop a unified graph memory that represents all intermediate exploration results, including facts, plans, and counterexamples, together with edges that explicitly represent the relationships among them; dependency-aware retrieval supplies precisely targeted local context; an evidence-sensitive curator updates the research frontier and distills lessons from prior attempts; and scoped recall surfaces earlier statements and negative findings for local re-proving rather than uncritical reuse. Experiments cover runs across all ten First Proof Second Batch problems, together with four component studies. Ansatz reports closure on all ten research tasks, demonstrating its ability to sustain and resume long-horizon mathematical search. Beyond these problems, Ansatz also produces solutions to the Jamison caterpillar conjecture and Erdős Problems 289, 348, and 488 without human intervention, and makes partial progress on several open problems, illustrating its strong ability to solve open mathematical research problems.
| Subjects: | Artificial Intelligence (cs.AI); Computation and Language (cs.CL) |
| Cite as: | arXiv:2610.02945 [cs.AI] |
| (or arXiv:2610.02945v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2610.02945 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Eric Jiang [view email]
[v1]
Fri, 2 Oct 2026 07:38:09 UTC (1,271 KB)
来源：arXiv：cs.AI · arxiv.org