BootLoops：一个由LLM驱动的精确定量科学工具包
BootLoops: an LLM-driven toolkit for exact quantitative science
- Harvard University（哈佛大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
BootLoops是一个由LLM驱动的工具包，汇集粒子物理、实验数学等领域的精确计算方法，用于计算多圈费曼积分、贝叶斯证据等，并推广到其他科学领域。
AI中文摘要：
定量科学中的许多工作涉及困难的数学计算：例如费曼积分、进化树的证据或调控统计量。这些计算通常通过蒙特卡洛或启发式搜索来估计，或者在浮点运算中执行而不跟踪舍入误差。精确方法往往存在，但通常出现在与问题相距甚远的领域。对撞机物理中的约化方法也适用于贝叶斯证据，而数值分析中的区间算术可以解决调控阈值问题，但很少有人同时了解这两个领域。大型语言模型了解这两个领域以及所有其他领域，并且有了可运行的程序，它可以将一种方法从一个领域带到另一个领域。BootLoops就是这样一个程序池：包含来自粒子物理的积分约化、微分方程和高精度求值，来自实验数学的整数关系拟合、精确枚举和球算术，所有这些都在一个工具包中，任何智能体式大型语言模型都可以操作和扩展。这些工具可以通过自举方法而非直接积分来计算多圈费曼积分，涵盖出现的函数类，包括多对数、椭圆函数以及K3曲面和Calabi-Yau流形的周期。它们还可以将贝叶斯证据积分计算为精确有理数，以完备性证明枚举有限配置空间，显示何时所寻求的闭式解不可能存在，并以保证的数字重做浮点计算。在实践中，这将数学、计算机科学和物理学的工具应用于基因组学、统计学、生态学和其他领域的问题。该工具包及其文档位于此https URL。
英文摘要：
Much of quantitative science involves difficult mathematical computations: a Feynman integral, evidence for an evolutionary tree, or a regulatory statistic. These are often estimated by Monte Carlo or heuristic search, or computed in floating point without tracking rounding error. Exact methods often exist, but in a field far from the problem. The reduction methods of collider physics also work on a Bayesian evidence, and a regulatory threshold can be settled with interval arithmetic from numerical analysis, but few people know both fields. A large language model knows both, and every other field, and with working programs in hand it can carry a method from one to another. BootLoops is a pool of such programs: integral reduction, differential equations and high-precision evaluation from particle physics, integer-relation fitting from experimental mathematics, exact enumeration, and ball arithmetic, in one toolkit that any agentic large language model can operate and extend. These tools can compute multi-loop Feynman integrals by bootstrap methods rather than direct integration, across the function classes that arise, including polylogarithms, elliptic functions, and periods of K3 surfaces and Calabi-Yau manifolds. They can also evaluate Bayesian evidence integrals as exact rational numbers, enumerate finite configuration spaces with proof of completeness, show when a sought closed form cannot exist, and redo floating-point calculations with guaranteed digits. In practice this brings the tools of mathematics, computer science and physics to problems in genomics, statistics, ecology and other fields. The toolkit and its documentation are at https://bootloops.ai.
