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Neural Discovery in Mathematics: Do Machines Dream of Colored Planes?

May 29, 2025 · Our ICML 2025 Oral Paper Neural Discovery in Mathematics: Do Machines Dream of Colored Planes? introduces a novel neural network approach to tackle the famous Hadwiger-Nelson problem and related geometric coloring challenges. We reformulate the combinatorial task as a continuous optimization problem, enabling neural networks to find probabilistic colorings. This led to discovering two new 6-colorings, marking the first progress in 30 years on a key variant involving different forbidden distances and significantly expanding the known solution range.