Microsoft researchers used AI agents to explore over a hundred paths and proved the 31-year-old KLS conjecture
Microsoft researchers used AI agents to explore about 100 research paths and completed a proof of the Kannan-Lovász-Simonovits (KLS) conjecture, which was proposed in 1995 and is 31 years old; the resulting manuscript is about 140 pages. AI was responsible for exploring candidate methods, carrying out derivations, assisting in writing the manuscript, and performing internal proof checks, while the recursive method and error bounds that completed the proof are credited to the two researchers. The conjecture can be understood as: a random walk inside a convex shape will not be trapped by narrow passages, and can efficiently explore the entire shape even in high-dimensional space.
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A math problem older than Google has been solved, with AI doing much of the searching.
Microsoft researcher proved this 31-year-old Math conjecture (Kannan-Lovász-Simonovits conjecture) after AI agents explored over 100 approaches.
A 140-page proof, more than 100 AI-explored paths now have closed a question mathematicians had been working on since 1995.
A human-directed search, with AI agents exploring roughly 100 research trajectories while a researcher cut weak directions between rounds, produced the criterion underpinning Song and Zhang’s proof of the Kannan-Lovász-Simonovits (KLS) conjecture.
The AI explored candidate approaches, carried out derivations, helped prepare the manuscript and ran internal proof checks, while the recursive method and the error bound that finished the proof are credited to the 2 researchers.
About the Kannan-Lovász-Simonovits conjecture: Picture a random walker wandering inside a convex shape: the conjecture says no secret narrow passage can trap it, so it can explore the whole shape efficiently, even in huge dimensions.