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Xinzhi Zhang and Zhao Song Report KLS Conjecture Proof Using Human-Directed AI

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Microsoft Research’s Xinzhi Zhang and collaborator Zhao Song report proving the 31-year-old Kannan–Lovász–Simonovits (KLS) conjecture, establishing a universal bound independent of dimension for log-concave distributions. According to Microsoft Research, the researchers directed AI agents through more than 100 candidate approaches, then developed recursive refinements to complete the proof. Their argument showed that the small errors introduced at each stage shrink quickly enough for the total to remain bounded by a universal constant. Microsoft Research also described independent proofs and a subsequent Lean 4 formalization that combined the authors’ key criterion with additional research.

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Latest development10/22 00:00 (UTC+8)
Microsoft Research and Collaborator Resolve the KLS Conjecture With Human-Directed AIMicrosoft Research

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10/22
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    Microsoft Research and Collaborator Resolve the KLS Conjecture With Human-Directed AI

    Microsoft Research’s Xinzhi Zhang and collaborator Zhao Song report proving the 31-year-old KLS conjecture, establishing a universal bound independent of dimension for log-concave distributions. Researchers directed AI agents through more than 100 candidate approaches, then developed recursive refinements that completed the proof. The account describes independent proofs and a subsequent Lean 4 formalization combining their key criterion with additional research.

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