AI 中文总结
本研究提出LANTERN流水线，利用语言模型内部表示自动发现数学序列间的新联系，在OEIS上验证了62对关系，其中4对为全新发现，整个过程耗时不到8小时。
AI 中文摘要
语言模型现在可以证明定理，但人们仍然决定要研究哪些问题。我们探究模型的内部表示是否有助于识别有前景的数学联系。我们开发了LANTERN，一个快速且成本高效的流水线，它使用基于预训练模型激活的分类器对候选关系进行排序，随后进行分阶段过滤、假设生成、可执行验证和分析检查。应用于在线整数序列百科全书（OEIS）时，LANTERN在10,000个频繁引用的序列中排名了5000万对，并产生了62对已验证的关系，这些关系在OEIS中不存在交叉引用。内容筛选保留了13个值得呈现的关系；其中九个具有信息性或洞察性，包括四个据我们所知完全新颖的关系：它们既不出现在OEIS中，也不出现在我们针对性的文献搜索中。整个端到端过程，包括分类器训练、候选排序、过滤和验证，耗时不到8小时。
英文摘要
Language models can now prove theorems, but people still decide which problems to pursue. We ask whether a model's internal representations can help identify promising mathematical connections. We develop LANTERN, a fast, cost-efficient pipeline that uses a classifier over pretrained-model activations to rank candidate relations, followed by staged filtering, hypothesis generation, executable verification, and analytical checking. Applied to the On-Line Encyclopedia of Integer Sequences (OEIS), LANTERN ranked 50 million pairs among 10,000 frequently referenced sequences and produced 62 verified relations between pairs without an existing OEIS cross-reference. A content screen retained 13 relations worth presenting; nine of these are informative or insightful, including four which are entirely novel to the best of our knowledge: none appears in the OEIS or in our targeted literature search. The entire end-to-end process including classifier training, candidate ranking, filtering and verification took under 8 hours.
