arXiv cs.AI· Ryan A. Anderson, Matthew Trager, Ben Bowman, Wei Xia, Stefano Soatto·· 1 天前AI 评分31
用 AI 智能体求解计算代数问题：Agentic Computational Algebra 研究
Agentic Computational Algebra
AI 导读
研究提出用计算代数问题评估 AI 智能体发现并复用结构以降低计算成本的能力，问题答案可独立验证、结构难度可系统调控。实验显示智能体能在固定预算内扩展可解系统范围，但推理开销有时会超过节省的计算量；持久记忆可降低重复求解成本却可能保留次优策略；编译可复用求解器速度更快但前期成本高。
正文 · 原文
Abstract:We explore the use of AI agents for solving computational problems in algebra. For the problems we consider, the main challenge is not correctness but \emph{time}: general-purpose algorithms are guaranteed to provide correct solutions but can be prohibitively slow, while reformulations that exploit special structure often allow solving a problem much faster. We propose to use this setting to evaluate how effectively agents discover and exploit structure within and across tasks to reduce computational costs. More broadly, computational algebra supplies infinitely many problems with independently verifiable answers and systematically controllable structure and difficulty. To illustrate these possibilities, we use benchmark families of systems with controlled shared structure and evaluate agents in three settings: solving independent instances, solving online streams of related instances using persistent memory, and compiling a fast reusable solver for a known problem family. Our experiments show that (i) agents can extend the range of systems solvable within a fixed budget, although reasoning overhead can sometimes outweigh computational savings; (ii) memory can reduce the cost of repeated solving but may preserve suboptimal strategies; (iii) compilation produces faster reusable solvers but at substantial upfront cost. Overall, computational algebra offers concrete, measurable targets for improving how agents discover and reuse structure.
| Subjects: | Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Symbolic Computation (cs.SC) |
| Cite as: | arXiv:2611.16073 [cs.LG] |
| (or arXiv:2611.16073v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2611.16073 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Ryan Anderson [view email]
[v1]
Wed, 11 Nov 2026 22:32:22 UTC (60 KB)
来源：arXiv cs.AI · arxiv.org