用Transformer发现组合数学中的映射规律，生成新算法。
From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm
- 用Transformer学习双路径数据，捕捉隐含模式
- 基于注意力机制提出新算法‘骨架映射’
- 适合组合数学与可解释机器学习研究者
代数组合学中有大量问题可归结为构造显式的组合双射。传统方法依赖人工观察数据、提出猜想并证明。但当数据规模超出人类感知范围时，传统方法失效。本文提出一种新工作流：利用机器学习发现组合双射。以成对的Dyck路径为训练数据，训练Transformer模型，通过分析其学习到的注意力模式，推导出新的zeta映射算法，称为“骨架映射”（Scaffolding Map），实现了从黑箱到可解释双射的转变。
原文摘要 · Abstract (English)
There is a large class of problems in algebraic combinatorics which can be distilled into the same challenge: construct an explicit combinatorial bijection. Traditionally, researchers have solved challenges like these by visually inspecting the data for patterns, formulating conjectures, and then proving them. But what is to be done if patterns fail to emerge until the data grows beyond human scale? In this paper, we propose a new workflow for discovering combinatorial bijections via machine learning. As a proof of concept, we train a transformer on paired Dyck paths and use its learned attention patterns to derive a new algorithmic description of the zeta map, which we call the \textit{Scaffolding Map}.
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