4 papers · 1 filter
Generating Hadamard matrices with transformers
Geordie Williamson, Oded Yacobi, Paul Zinn-Justin
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 e…
Drums of high width
Alex Davies, Prateek Gupta, Sebastien Racaniere +4
We provide a family of -dimensional prismatoids whose width grows linearly in the number of vertices. This provides a new infinite family of counter-examples to the Hirsch conje…
Advancing Geometry with AI: Multi-agent Generation of Polytopes
Grzegorz Swirszcz, Adam Zsolt Wagner, Geordie Williamson +7
Polytopes are one of the most primitive concepts underlying geometry. Discovery and study of polytopes with complex structures provides a means of advancing scientific knowledge. C…
PatternBoost: Constructions in Mathematics with a Little Help from AI
François Charton, Jordan S. Ellenberg, Adam Zsolt Wagner +1
We introduce PatternBoost, a flexible method for finding interesting constructions in mathematics. Our algorithm alternates between two phases. In the first ``local'' phase, a clas…