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Microsoft Researchers Resolve KLS Conjecture via Human-Directed AI
Microsoft Research and collaborators proved the 31-year-old Kannan-Lovász-Simonovits conjecture in high-dimensional geometry using a human-directed agentic AI research workflow.
Researchers including Xinzhi Zhang from Microsoft Research announced the resolution of the Kannan-Lovász-Simonovits (KLS) conjecture, a 31-year-old problem in high-dimensional geometry and probability. The proof used a human-directed agentic workflow where AI systems explored over 100 approaches while researchers pruned and redirected searches, followed by independent expert proofs and Lean 4 machine verification.
Key takeaways
- Researchers established a dimension-free bound for the KLS conjecture using a recursive criterion refined across October 2026 paper versions.
- The human-AI workflow relied on researchers pruning agent search paths, contrasting with unguided attempts that failed under similar token budgets.
Source：Microsoft Research Read the original ↗
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