用Transformer+局部搜索生成大阶数哈达玛矩阵，突破传统方法极限。
Generating Hadamard matrices with transformers
- 结合Transformer与局部搜索，在模式增强框架中优化构造过程。
- 成功构造出阶数达252的哈达玛矩阵，远超传统方法上限。
- 发现搜索空间中的隐藏对称性，适用于稀疏组合优化问题。
我们提出一种新方法，将Transformer神经网络与模式增强框架中的局部搜索相结合，用于构造哈达玛矩阵。该方法针对极稀疏的组合搜索问题设计，特别适用于戈萨尔斯-塞德尔型哈达玛矩阵，其傅里叶方法支持快速评分与优化。在100至200阶之间，可生成大量非等价的哈达玛矩阵；对于更大阶数，该方法在随机初始化的局部搜索失效时仍有效。本文找到的最大实例阶数为252。此外，实验表明，Transformer能发现并利用搜索空间中的隐含对称性。
原文摘要 · Abstract (English)
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.
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