OpenAI has asked a group of outside scientists, including Nobel physics laureate David Gross, to check three proofs that its AI models produced in mathematics, computer science and physics, the company said in a blog post on October 26.
OpenAI said its models disproved the Exponential Time Hypothesis (ETH), a 1999 assumption that certain computing problems cannot be solved faster than a set limit. The company said the proposed algorithm runs faster than ETH allowed but would require impractically large computing resources, so it does not resolve the P versus NP problem.
In mathematics, the models extended the local smoothing conjecture, proposed by Christopher Sogge in 1991 and previously proven only in two dimensions, to all dimensions, OpenAI said. The company also presented proofs for the Kakeya conjecture and Stein's Fourier restriction conjecture.
In physics, the models produced an existence proof for interacting quantum field theories in four-dimensional spacetime, including Yang-Mills theory, a framework describing interactions between elementary particles.
Russell Impagliazzo and Ramamohan Paturi of UC San Diego, who originally proposed ETH, along with MIT professor Ryan Williams, are reviewing the computer science result. A group led by Gross, who won the Nobel Prize in Physics in 2004, including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov, is reviewing the physics proof.
The reviewers said their involvement “should not be taken as an endorsement” of OpenAI's conclusions. OpenAI described the published material as raw research data that still needs to be understood and called the outside scientists curators of the work.
The proofs were posted on GitHub in written form and in Lean, a format that allows computer verification; the Lean version of the local smoothing proof is dated October 19, while the initial physics proofs are dated September 9 and September 18.
OpenAI also pledged $5 million to the Simons Foundation for related workshops and conferences, including one on the implications of the ETH result. Whether the proofs hold will depend on the outside reviewers' work.
