A Microsoft researcher and Zhao Song prove the KLS conjecture
The October proof removes dimension dependence from a 1995 bound, after a human-directed AI search helped identify the key mathematical criterion.
By Ryan Merket · Published
Primary source: Microsoft Research
Why it matters
The proof turns a widely used assumption about high-dimensional sampling into a theorem. Its AI contribution is also specific: guided exploration helped researchers find a useful criterion, while human mathematical judgment shaped and completed the proof.
A proof posted on October 4th resolves the Kannan-Lovasz-Simonovits conjecture, a 1995 problem about how efficiently random walks can explore high-dimensional probability distributions. Microsoft Research announced the result on October 21st, crediting Microsoft researcher Xinzhi Zhang and collaborator Zhao Song. Their paper establishes a bound that does not grow with the number of dimensions, the defining claim of the conjecture.…
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