跳转至

文章背景与核心概要

本文介绍了 Discovery Loop（发现循环），这是一个轻量级系统，它利用大语言模型（LLM）来迭代演化和改进优化算法。该系统在 Packomania 圆堆积基准测试（目标是在单位正方形内最大化 \(N\) 个可变半径圆的半径之和）上进行了测试，成功超越了 \(N\) 在 \(101\) 到 \(114\) 之间 10 个数值的先前已知最优解。

在短短 15 次迭代中，该系统以仅 27.72 美元的极低 LLM 支出，实现了比现有纪录高出 2.4% 至 5.4% 的提升，相关结果已被 Packomania 官方正式收录。本研究详细阐述了 Discovery Loop 的运作机制、包含自适应平台检测在内的成本效益动力学，以及实现自动化科学发现民主化的更广泛潜力。

LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28

LLM-Guided Program Evolution for Circle Packing: Breaking 10 Packomania Records for $28

Summary

Summary

This paper introduces Discovery Loop, a lightweight system that leverages large language models (LLMs) to iteratively evolve and improve optimization algorithms. Tested on the Packomania circle-packing benchmark—which aims to maximize the sum of radii of \(N\) variable-radius circles inside a unit square—the system successfully surpassed the previously best-known solutions for 10 values of \(N\) (\(101\) to \(114\)).

This paper introduces Discovery Loop, a lightweight system that leverages large language models (LLMs) to iteratively evolve and improve optimization algorithms. Tested on the Packomania circle-packing benchmark—which aims to maximize the sum of radii of \(N\) variable-radius circles inside a unit square—the system successfully surpassed the previously best-known solutions for 10 values of \(N\) (\(101\) to \(114\)).

Achieving a 2.4% to 5.4% improvement over existing records within just 15 iterations and at an exceptionally low LLM expenditure of $27.72, the results have since been officially accepted by Packomania. The study highlights the mechanics of the Discovery Loop, cost-efficiency dynamics including adaptive plateau detection, and the broader potential of democratizing automated scientific discovery.

Achieving a 2.4% to 5.4% improvement over existing records within just 15 iterations and at an exceptionally low LLM expenditure of $27.72, the results have since been officially accepted by Packomania. The study highlights the mechanics of the Discovery Loop, cost-efficiency dynamics including adaptive plateau detection, and the broader potential of democratizing automated scientific discovery.

Paper Metadata

Paper Metadata

  • arXiv Identifier: arXiv:2609.05093 [cs.AI]
  • Author: Wes Sander
  • Submitted: September 4, 2026
  • Primary Subject: Artificial Intelligence (cs.AI)
  • MSC Classes: 52C15, 90C59, 68T20
  • ACM Classes: I.2.8; G.1.6
  • DOI: 10.48550/arXiv.2609.05093
  • arXiv Identifier: arXiv:2609.05093 [cs.AI]
  • Author: Wes Sander
  • Submitted: September 4, 2026
  • Primary Subject: Artificial Intelligence (cs.AI)
  • MSC Classes: 52C15, 90C59, 68T20
  • ACM Classes: I.2.8; G.1.6
  • DOI: 10.48550/arXiv.2609.05093

Abstract

Abstract

We present Discovery Loop, a lightweight system that uses a large language model (LLM) to iteratively evolve optimization algorithms. Starting from a simple seed solver, the LLM proposes algorithmic improvements guided by a scoreboard of results and a history of prior ideas. Each candidate is evaluated against an independent verifier; improvements are kept and failures discarded.

Applied to the Packomania circle-packing benchmark (maximize the sum of radii of \(N\) variable-radius circles in the unit square), the system improved the best known solutions for 10 values of \(N\) in the range 101–114, with gains of 2.4%–5.4% over prior records, all within 15 iterations and at a total LLM cost of $27.72. These results have been independently accepted by Packomania. We describe the method, analyze cost-efficiency dynamics including an adaptive plateau-detection mechanism, and discuss implications for democratizing automated scientific discovery.