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新论文 · v1arXiv:2611.09736

Safety Is $Π_1$, Provability Is $Σ_1$: One Framework for the Hugging Face Breach and OpenAI's Mathematical Proofs

Jinho Kang, Jinsook Kim

原文摘要

OpenAI's agents breached Hugging Face in July 2026, and the same company released more than seven hundred AI-generated manuscripts of mathematical proofs in October 2026. The first event is read as a failure in security, while the second is read as a success in mathematics. We read both through the hybrid framework of our paper (Kim and Kang, 2026, arXiv:2611.01914), in which coding, proving, and learning from data are derivations by one and the same deductive mechanism, distinguished by the kinds of premises from which they are derived. Under this framework, the AI systems behind the two events ran the same loop, in which a statistical proposer produces candidate exploits or proofs and a deductive verifier settles each one by a derivation. What separates the events is the logical form of the statement wanted by each of the two domains, security and mathematics. The safety of a program is a $Π_1$ statement, for it says that no exploit exists, which is not assured by any finite list of tests that have been passed by the program. By contrast, the provability of a sentence is a $Σ_1$ statement, for it says that a proof exists, which is assured by a single instance, namely a proof that has been checked by the deductive verifier. The theorem behind both is Turing's Undecidability Theorem: the halting set is $Σ_1$ but not decidable, so its complement is $Π_1$ and not $Σ_1$, which is to say that membership has a finite witness but non-membership has none. We prove that attaching a statistical proposer to a deductive verifier does not change this undecidability result, however good the proposer is. We then discuss what does assure safety and where the residual risk goes.

cs.LG · cs.AI · cs.CR · cs.LO

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新论文 · v1arXiv:2611.01914

Machine Learning Beyond Statistical Consistency for Hybrid AI

Jinsook Kim, Jinho Kang

原文摘要

We propose a new definition of machine learning, according to which a machine learns a function when it computes the function successfully, that is, when the value it returns for each input has a proper derivation in a formal system. We extend Gödel's Representability Theorem, which equates computation with derivation, to empirical targets in two ways: the theorem is extended to the computable reals, and the data are admitted into the system as empirical definitions that record what has been observed. We prove that a machine learns a true probability if and only if two conditions are met. The Truth Condition is that its estimate converges to the true probability, which is statistical consistency. The Assurance Condition is that the machine properly derives its own convergence inside the system. Learning thus lies beyond statistical consistency, for it requires a derivation of the convergence from the record. A global assumption about the data, such as the i.i.d. assumption, does not supply such a derivation, because it leads only to a circular one, as we show for PAC learning. On the other hand, the two conditions are met for the probability of a sentence over a finite ideal corpus. A real machine can approximate a true probability only if an ideal machine can learn it precisely, that is, only in a domain that meets the two conditions. Modern AI works in such a domain, and we offer this as a clue to its success. Modern AI is hybrid as well, in two senses: First, it performs two kinds of tasks, namely probabilistic ones such as predicting the next word and deductive ones such as proving and coding. Second, it combines two parts of different kinds, a statistical proposer and a deductive verifier, for proving and coding. Our framework explains both senses of hybridity in one formal system.

cs.LG · cs.AI

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首次观测 · 记录 #1ACL Anthology · ACL 2026:acl:2026.acl-industry.54ACL Anthology · ACL 2026

From Relevance to Authority: Authority-aware Generative Retrieval in Web Search Engines

Sunkyung Lee, Jihye Back, Donghyeon Jeon, Soonhwan Kwon, Moonkwon Kim, Inho Kang, Jongwuk Lee

原文摘要

Generative information retrieval (GenIR) formulates the retrieval process as a text-to-text generation task, leveraging the vast knowledge of large language models. However, existing works primarily optimize for relevance while often overlooking document trustworthiness. This is critical in high-stakes domains like healthcare and finance, where relying solely on semantic relevance risks retrieving unreliable information. To address this, we propose an Authority-aware Generative Retriever (AuthGR), the first framework that incorporates authority into GenIR. AuthGR consists of three key components: (i) Multimodal Authority Scoring, which employs a vision-language model to quantify authority from textual and visual cues; (ii) a Three-stage Training Pipeline to progressively instill authority awareness into the retriever; and (iii) a Hybrid Ensemble Pipeline for robust deployment. Offline evaluations demonstrate that AuthGR successfully enhances both authority and accuracy, with our 3B model matching a 14B baseline. Crucially, large-scale online A/B tests and human evaluations conducted on the commercial web search platform confirm significant improvements in real-world user engagement and reliability.

cs.CL · cs.CV

Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 6: Industry Track) · 2026 · 正式发表