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Microsoft Research says it proved the 31-year-old KLS conjecture with AI-assisted search

2 articles2 sourcessince Oct 21Last article 1h ago ·

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Microsoft Research says Xinzhi Zhang and a co-author proved the Kannan–Lovász–Simonovits (KLS) conjecture, a question about cuts in high-dimensional probability distributions.

The proof bounds the gap between flat and curved cuts by a constant that does not depend on the number of dimensions.

The authors say AI agents explored candidate approaches under human direction. Independent proofs and a Lean 4 formalization were released afterward, according to the same report.

A later Microsoft Research post on X describes the result as removing a major barrier to understanding the efficiency of randomized algorithms. That post does not add new technical detail.

Written by AI from the articles below · updated Oct 21, 12:40 PM ET

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Latest developmentOct 21, 12:11 PM ET
Microsoft Research resolves the KLS conjecture on high-dimensional computation

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The articles in this story. Times are ET.

Oct 21
  1. Microsoft ResearchOfficial
    Microsoft Research resolves the KLS conjecture on high-dimensional computation

    AIMicrosoft Research says new research resolves the KLS conjecture, a decades-old question about the challenges of high-dimensional computation. The result removes a major barrier to understanding the efficiency of randomized algorithms used across science and computing.

    Video from @MSFTResearch's post
  2. Microsoft ResearchOfficialPick
    Microsoft Research resolves the 31-year-old KLS conjecture in high-dimensional geometry

    AIMicrosoft Research says researchers, including Xinzhi Zhang, proved the KLS conjecture, which concerns cuts in high-dimensional probability distributions. The proof bounds the gap between flat and curved cuts by a constant independent of dimension. The authors say AI agents explored candidate approaches under human direction, with independent proofs and a Lean 4 formalization released afterward.

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