OpenAIの数学論文3本が撤回、符号ミス1つで連鎖的に崩れた理由

We expanded these evaluations after performance on our existing mathematical evaluations saturated. ／ The vast majority of results were obtained with the same procedure using an unreleased internal OpenAI model. On average, each result used three hours of ChatGPT Pro thinking compute with that model. Over the course of the evaluation, the model was posed approximately 4,000 problems. — 成果を生んだ手順と計算量に関する記述より

Less than 24 hours after OpenAI posted over 700 preprints describing major math results by an internal AI model, the company has withdrawn three of the manuscripts for errors. — 撤回を伝えた記事の冒頭より

In “Algebraicity of Weil classes on split abelian eightfolds” a sign error invalidates a stabilization-trace cancellation argument and the construction used by two dependent papers. As a result, we have withdrawn the following three manuscripts: ／ Algebraicity of Weil classes on split abelian eightfolds ／ Algebraicity of Kuga–Satake Correspondences for K3 Surfaces ／ The rational Hodge conjecture for products of K3 surfaces ／ The withdrawn papers now carry notices explaining the gap and linking to the archived manuscripts. — 10月7日の撤回に関する記述より

The proof relies on an adaptation of the flawed stabilization-trace construction in Algebraicity of Weil classes on split abelian eightfolds. ／ The resulting gap leaves this paper's claimed rational Hodge theorem for products of projective K3 surfaces unproved. ／ This withdrawal concerns the proof; it does not assert that the mathematical statement is false. — 撤回の理由と位置づけに関する記述より

This withdrawal concerns the proof; it does not assert that the mathematical statement is false. — 撤回の位置づけに関する記述より

That an error cascaded into three of the OpenAI manuscripts is not surprising, said Alex Townsend, an associate professor of mathematics at Cornell University in Ithaca. He suspects there will be more errors found, he said. ／ A spokesperson for OpenAI told us the company identified the errors during an audit. — Townsend 准教授のコメントと OpenAI 広報の説明より

For any updated papers, previously published editions remain accessible through the version notes in their README. ／ We have revised 14 other manuscripts with proof repairs, corrected statements, clearer hypotheses and dependencies, and one correction to an obsolete citation. ／ Also, as a consequence of these fixes we updated 13 additional manuscripts to cite the revised editions of companion papers. ／ We have added an additional 6 formalizations and 5 other additions covering supporting results. This brings the total percentage of top-line results formalized to 300 / 719 = ~42%. — 改訂・引用更新・形式化の追加に関する記述より

This collection includes results at different stages of verification. Not all have accompanying Lean formalizations. We will continue to update this repository with Lean formalizations as we obtain them. ／ Some of the unformalized results could have issues. We will endeavor to fix any such issues quickly. — 検証の段階と未形式化の結果に関する記述より

AGMAI’s advisory role should not be interpreted as a judgment of the impact of these results or an endorsement of the process by which OpenAI obtained them. ／ This release is the beginning, not the completion, of the process of human understanding and the incorporation of the work into mathematical knowledge. ／ it is ultimately up to the mathematical community to assess the extent to which our recommendations were followed successfully, and whether there are others we should suggest. — 助言の位置づけと評価の主体に関する記述より

The OpenAI spokesperson told us the company’s collaborators at the Advisory Group on Mathematics and Artificial Intelligence recommended releasing the results without waiting for “full formalization,” and that roughly 50% of the results were released unconfirmed. — OpenAI 広報による公開の経緯の説明より

“Where errors are identified, we will work to correct them promptly and withdraw papers if no fixes can be found. ／ Andrew Sutherland, a senior research scientist in the department of mathematics at the Massachusetts Institute of Technology, said he appreciated OpenAI acting quickly after finding the errors, calling it “the responsible thing to do.” ／ However, Sutherland emphasized that many mathematicians are “unhappy with how OpenAI has behaved up to this point,” especially in its handling of the Sept. 8 announcement an AI system had solved the Navier-Stokes problem ／ “I think the withdrawals and corrections will be viewed positively by the mathematics community, but it will take a lot more than that to earn back the trust they have lost,” Sutherland told us. ／ “Releasing over 700 files at once is not a demonstration of scholarship, but a demonstration of power. We urge mathematicians to discontinue their work with OpenAI and to return to a vision of science that centers human understanding.” — OpenAI 広報、Sutherland 氏、Association for Human Mathematics の発言より

"Math 1.0" placed a premium on being the first to solve an open problem, even if the solution was not initially well understood. Now that this goal has been optimized to the point of unsustainability, "Math 2.0" will need to decenter the role of raw problem solving and value mathematical progress more holistically - for instance by elevating the role of exposition, but also that of community building and opening up new directions of study. ／ I believe that AI can contribute positively in all of these directions as well; but it will require more imagination and ambition than the "Math 1.0" mindset of simply pointing one's favorite AI agent at some set of open problems and asking for a solution. — 「Math 1.0」と「Math 2.0」の対比に関する投稿より