OpenAI announces three science discoveries and new academic collaboration

OpenAI says it has three more major discoveries in mathematics, computer science and physics, less than a month after releasing hundreds of manuscripts it said contained solutions to long-standing mathematics questions. This time, external experts described as shepherds are guiding the computer science and physics results, while for the math problem OpenAI says it was advised to release the AI output for researchers to work through their own explanations.

Math and physics results

OpenAI released results on GitHub today, including a proof of local smoothing for the Euclidean wave equation. The proof uses an auxiliary partial differential equation to establish Sogge's local smoothing for waves in every spatial dimension at least two, and it also yields the Kakeya maximal and dimension conjectures and Stein's spherical restriction estimates throughout the interior of the conjectured range. OpenAI says the model also produced a proof of the local smoothing conjecture in every dimension, resolving the Kakeya conjecture and Stein's restriction conjecture in all dimensions. The physics information has not been released in full, but OpenAI describes it as a mathematically rigorous existence proof of certain interacting quantum field theories containing gauge fields and fermions in four dimensions, including Quantum Chromodynamics 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 to shepherd that work.

Computer science result

The computer science result says the Exponential Time Hypothesis, which has been widely believed to be true, is false. The paper gives a deterministic algorithm that exactly counts satisfying assignments of fixed-width CNF formulas in subexponential time and polynomial space, and the case of 3-SAT refutes the hypothesis. An independent working group led by Russell Impagliazzo, Ramamohan Paturi and Ryan Williams will examine and explain the proof, and at the group's request OpenAI made the materials public immediately. The group released the AI output write-up and Lean proof on GitHub today, along with an open letter asking for input on how to examine the claim and on norms for AI-generated breakthroughs.

Debate over release practices

OpenAI admits this approach could have its own issues. An AGMAI panel of math advisers that OpenAI put together said yesterday that it recommends AI companies do not adopt practices that designate certain people to receive output first, citing unequal access, borrowed reputation and biased selection. Instead, the panel recommended that future AI labs release output on scholarly repositories, with Lean-formalized proofs, information on how problems were chosen, funding for people working on understanding the results, and other information. The open letter asks what expectations should govern early access to AI-generated results, disclosure of conflicts of interest and use of unpublished material for subsequent research; how credit should recognize both new discoveries and the work of checking, fixing, simplifying, explaining and extending them; and how to support students and researchers as methods and research directions change while preserving understanding and judgment needed to question results and develop new ideas. OpenAI is also giving $5 million to help mathematicians make sense of AI-generated research.

Context

Just a few months ago, NYU professor Hong Wang was awarded a Fields Medal by the International Mathematical Union for resolving the Kakeya conjecture in three dimensions. OpenAI's earlier October 6 release is referenced in the new math result, and the company previously released hundreds of manuscripts it said contained solutions to long-standing mathematics questions.

Sources: The Verge · Techmeme