The proofs that earned EPFL professor Maryna Viazovska the Fields Medal in 2022 have reached a new milestone: their complete formalization by computer, achieved through a collaboration between mathematicians and artificial intelligence tools. In 2016, Maryna Viazovska solved the sphere packing problem in dimension 8, proving that the E lattice constitutes the densest possible arrangement. Shortly after, together with collaborators, she established an analogous result in dimension 24 using the Leech lattice. Her method provided an elegant solution to a problem studied for centuries, with close ties to applied fields such as error-correcting codes. For this major contribution, Viazovska was awarded the Fields Medal in 2022, the highest distinction in mathematics.

Neural Information Processing Systems http://nips.cc/

The line, triangular and square shapes represent the joint distribution of two, three and four variables respectively.

A matching process on a two-sided market can determine who gets which job [40, 31], school place[44],orspouse.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

These are composed into a single vector representing position by a similarity-preserving, conjunctive vector-binding operation.

First, we analyze token distributions generated across multiple prediction heads.