AI attention, diffusion, and magnetic fields are all the same math

This paper shows that three different mathematical tools used in AI and physics — transformers, diffusion maps, and magnetic Laplacians — are actually different versions of the same underlying geometry. It means that these tools, previously seen as separate, can now be understood and potentially combined using a single mathematical framework.

For years, researchers have developed separate mathematical approaches for different problems in AI and physics. This paper suggests that these distinct methods are just different ways of looking at the same fundamental structure. This could lead to new ways of building AI models or understanding complex physical systems by applying insights from one area to another.