编码理论的编码智能体
Coding Agents for Coding Theory
- Stanford University（斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究使用LLM编码智能体结合对称性约束，解决编码理论中DNA条形码的编辑距离搜索问题，将已知最优码从114提升至120，并改进十二个下界，同时揭示了中间结果未复核导致错误结论的教训。
AI中文摘要：
我们花了五周时间，使用一个LLM编码智能体解决编码理论中的开放问题：寻找大的四字母单词集合，例如DNA条形码，这些单词在编辑距离上保持足够远的间隔。智能体编写了验证器和搜索代码；人类选择问题并设定验证协议。将搜索限制在具有规定对称性的码上，这是一种经典技术，使问题规模缩小了约四倍，并将已知最好的长度为6、最小编辑距离为3的码从114个单词提高到120个单词（$E_4(6,3) \geq 120$）。同样的流程在长度6至9、距离3至6的范围内进一步改进了十二个下界。我们也给予了失败同等的篇幅。我们自己的搜索在116处停止，并记录了最后一个对称类在112处达到上限；第二个智能体会话使用更好的算子运行相同的搜索，找到了120。后来关于该方法无法推广到长度7的结论是错误的，原因相同，而更早的一个实例花费了三周时间。每次，一个中间结果被记录下来，从未重新检查，并被当作排除进一步搜索的事实。按照我们的协议检查最终输出，并不能发现此类错误。
英文摘要：
We spent five weeks using an LLM coding agent on open problems in coding theory: finding large sets of four-letter words, such as DNA barcodes, that stay far apart in edit distance. The agent wrote the verifiers and search code; a human chose the problem and set the verification protocol. Restricting the search to codes with a prescribed symmetry, a classical technique, shrank the problem about fourfold and raised the best known code of length 6 and minimum edit distance 3 from 114 to 120 words ($E_4(6,3) \geq 120$). The same pipeline improved twelve further lower bounds at lengths 6 to 9 and distances 3 to 6. We give the failures equal space. Our own search stopped at 116 and recorded the last symmetry class as topping out at 112; a second agent session, running the same search with a better operator, found the 120. A later verdict that the method did not carry over to length 7 was wrong for the same reason, and an earlier instance cost three weeks. Each time, an intermediate result was written down, never rechecked, and treated as a fact that ruled out further search. Checking final outputs, as our protocol required, does not catch such errors.
