Séminaire Lotharingien de Combinatoire, 95B.95 (2026), 12 pp.
Xiaoyu Huang, Blake Jackson and Kyu-Hwan Lee
From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm
Abstract.
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 scaffolding map.
Received: November 15, 2025.
Accepted: February 15, 2026.
Final version: April 1, 2026.
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