Generating Hadamard matrices with transformers

ArXi:2604.11101v1 Announce Type: cross 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 $250$, it produces large numbers of inequivalent Hadamard matrices, and in harder cases it succeeds where local search from random initialisation fails.