OpenAI presents three claimed scientific results — The Verge
OpenAI announced three claimed scientific results in mathematics, computer science and physics. It said that groups of external experts would be involved in reviewing the computer science and physics papers, while materials on the mathematical problem were immediately released for study by researchers, The Verge reports.
Exponential Time Hypothesis
OpenAI claims that its computer science work disproves the Exponential Time Hypothesis (ETH), which was widely believed to be correct. The paper describes a deterministic algorithm capable of exactly counting the number of satisfying assignments for fixed-width CNF formulas in subexponential time and using a polynomial amount of memory. The 3-SAT case, according to the company, disproves ETH.
An independent group of scientists led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams is to verify and explain the proof. Impagliazzo and Paturi were part of the group that proposed ETH in 1999. OpenAI published a description of the work and a Lean-formalized proof on GitHub.
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Mathematics and physics
In mathematics, the company stated that its model produced a proof of the local smoothing conjecture for the Euclidean wave equation in all dimensions. According to OpenAI, this also resolves the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The company released the model's results directly so that researchers could independently examine them and prepare an explanation.
Regarding physics, OpenAI reported a mathematically rigorous proof of the existence of certain interacting quantum field theories with gauge fields and fermions in four dimensions, including for quantum chromodynamics and a unified completion of the Standard Model. The full materials on this work have not yet been released. They will be reviewed by a group led by David Gross, which is expected to include Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov.
Scientists' recommendations
The AGMAI mathematical advisory panel, created by OpenAI, recommended that AI companies not select individual people for priority access to results. Among the risks of this approach, it cited unequal access, borrowed reputation and biased selection. Instead, the panel proposed publishing results in scientific repositories, adding Lean-formalized proofs, information on task selection, and funding for experts who will analyze the obtained results.
