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arXiv · 2606.29075

Learning Unions of Intersecting Affine Modules in One Dimension with Queries

Eva González·Montserrat Hermo·Anthony Lin
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Abstract

We study the exact learnability of finite unions of intersecting affine modules in one dimension. An affine module is a set of the form $a+\sum_{j=1}^{s}b_j \mathbb{Z}$, where $a,b_1,\ldots,b_s\in\mathbb{N}$. We say that a set definable as a finite union of affine modules is a union of intersecting affine modules if it admits a representation in which all modules have a non-empty intersection. We show that this class is efficiently exactly learnable using equivalence and subset queries. Moreover, subset queries can be replaced with membership queries when a common element is known. Our algorithm requires at most $k\log(2|x_\ell|)+2k$ counterexamples, where $k$ is the number of affine modules in the smallest representation and $x_\ell$ is the largest counterexample. This implies polynomial-time learnability in the binary representation.

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Eva González, Montserrat Hermo, Anthony Lin. 2026-06-27. Learning Unions of Intersecting Affine Modules in One Dimension with Queries. https://doi.org/10.1145/3815436.3815448

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