RESEARCH · RESEARCH · #2368
KLS conjecture proved by researchers including Xinzhi Zhang (Microsoft Research) — Oct 4, 2026
Researchers, including Xinzhi Zhang of Microsoft Research, have proved the Kannan–Lovász–Simonovits (KLS) conjecture in an Oct 4, 2026 paper, establishing a universal constant bound for flat cuts in log-concave distributions independent of dimension. The result grew from a human-directed, AI-assisted research process, was independently validated by multiple researchers, and received machine-checked formal verification.
KEY POINTS
- Researchers, including Xinzhi Zhang of Microsoft Research, have proved the Kannan–Lovász–Simonovits (KLS) conjecture in an Oct 4, 2026 paper, establishing a universal constant bound for flat cuts in log-concave distributions independent of dimension.
- The result grew from a human-directed, AI-assisted research process, was independently validated by multiple researchers, and received machine-checked formal verification.
- Proving KLS resolves a 31-year central open problem in high-dimensional geometry with direct implications for sampling, randomized algorithms, optimization, and theoretical computer science, and it showcases a validated human–AI-assisted proof workflow.
WHY IT MATTERS
Proving KLS resolves a 31-year central open problem in high-dimensional geometry with direct implications for sampling, randomized algorithms, optimization, and theoretical computer science, and it showcases a validated human–AI-assisted proof workflow.