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Main Authors: Williamson, Geordie, Yacobi, Oded, Zinn-Justin, Paul
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2604.11101
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author Williamson, Geordie
Yacobi, Oded
Zinn-Justin, Paul
author_facet Williamson, Geordie
Yacobi, Oded
Zinn-Justin, Paul
contents We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is particularly effective for Hadamard matrices of Goethals--Seidel type, where Fourier methods permit fast scoring and optimisation. For orders between 100 and 200, it produces large numbers of inequivalent Hadamard matrices, and for larger orders, it succeeds where local search from random initialisation fails. The largest example found by our method has order 252. In addition to these new constructions, our experiments reveal that the transformer can discover and exploit useful hidden symmetry in the search space.
format Preprint
id arxiv_https___arxiv_org_abs_2604_11101
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Generating Hadamard matrices with transformers
Williamson, Geordie
Yacobi, Oded
Zinn-Justin, Paul
Combinatorics
Machine Learning
We present a new method for constructing Hadamard matrices that combines transformer neural networks with local search in the PatternBoost framework. Our approach is designed for extremely sparse combinatorial search problems and is particularly effective for Hadamard matrices of Goethals--Seidel type, where Fourier methods permit fast scoring and optimisation. For orders between 100 and 200, it produces large numbers of inequivalent Hadamard matrices, and for larger orders, it succeeds where local search from random initialisation fails. The largest example found by our method has order 252. In addition to these new constructions, our experiments reveal that the transformer can discover and exploit useful hidden symmetry in the search space.
title Generating Hadamard matrices with transformers
topic Combinatorics
Machine Learning
url https://arxiv.org/abs/2604.11101