Agentic Computational Algebra：用 AI 智能体求解计算代数问题
Agentic Computational Algebra
AI 导读
一篇 arXiv 论文提出以计算代数问题评测 AI 智能体发现和利用问题结构、降低计算成本的能力，并在三类设置下实验：独立求解、用持久记忆求解在线相关实例流、为已知问题族编译可复用快速求解器。实验显示智能体可在固定预算内扩大可解系统范围，但推理开销有时抵消收益；记忆能降低重复求解成本但可能保留次优策略；编译可产生更快的求解器但前期成本高昂。
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