OpenAI Reports Three Science Results, Tests New Academic Review Model

For the computer science result, OpenAI said its paper proves that the Exponential Time Hypothesis is false. The paper describes a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space; OpenAI said the 3-SAT case refutes ETH. An independent working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof. At the group's request, OpenAI made the materials public immediately, and the group decided to release the AI output write-up and Lean proof on GitHub the same day. Impagliazzo and Paturi were part of the group that originally proposed ETH in 1999; Williams is an MIT professor.

OpenAI also released an open letter to the community asking for input on how to examine the claim and on setting norms for dealing with AI-generated breakthroughs.

For mathematics, OpenAI said its model produced a proof of the local smoothing conjecture in every dimension and therefore also resolved the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The proof, described as local smoothing for the Euclidean wave equation, uses an auxiliary partial differential equation to establish Sogge's local smoothing for waves in every spatial dimension of at least two. OpenAI said the result also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates throughout the interior of the conjectured range. It released the model output directly, as it did in its Oct. 6 release. The report noted that NYU professor Hong Wang received a Fields Medal a few months ago for resolving the Kakeya conjecture in three dimensions.

The physics result has not been released in full. OpenAI described it as a 'mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics (QCD) and a unified completion of the Standard Model of particle physics.' David Gross will lead a group including Michael Douglas, Arthur Jaffe, Igor Klebanov and Nikita Nekrasov that will shepherd the work, according to OpenAI.

The new approach relies on external experts whom OpenAI describes as 'shepherds' to guide the computer science and physics results. For the math problem, OpenAI said the advisers recommended releasing the AI output for researchers to work through their own explanations. The company acknowledged that the approach could have its own issues. It said the AGMAI panel of math advisers it assembled said a day earlier that 'we recommend that AI companies do not adopt' practices of designating certain people to receive output first, citing unequal access, borrowed reputation and biased selection. The panel instead recommended that future AI labs release output on scholarly repositories, with Lean-formalized proofs, information on how problems were chosen, funding for people working to understand the results and other information.

Editor's Summary OpenAI announced results in mathematics, computer science and physics, with external shepherd groups reviewing the computer science and physics claims and direct release for the math proof. The company also sought input on norms for AI-generated breakthroughs, while its own math advisers cautioned against giving select experts first access.