# Human-LLM Deliberation as Interactive Proof: Conditions for Verifiability Without Transparency

arXiv: https://arxiv.org/abs/2609.24895 · HTML: https://mlsanity.com/paper/2609.24895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 42 of its 59 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 30 of 42)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Sparks of Artificial General Intelligence: Early experiments with GPT-4](https://mlsanity.com/paper/2303.12712/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Language Models Don't Always Say What They Think: Unfaithful Explanations in Chain-of-Thought Prompting](https://mlsanity.com/paper/2305.04388/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Towards Faithfully Interpretable NLP Systems: How should we define and evaluate faithfulness?](https://mlsanity.com/paper/2004.03685/) (2020)
- [Weak-to-Strong Generalization: Eliciting Strong Capabilities With Weak Supervision](https://mlsanity.com/paper/2312.09390/) (2023)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [AI safety via debate](https://mlsanity.com/paper/1805.00899/) (2018)
- [Self-critiquing models for assisting human evaluators](https://mlsanity.com/paper/2206.05802/) (2022)
- [Explainability for Large Language Models: A Survey](https://mlsanity.com/paper/2309.01029/) (2023)
- [Chain-of-Verification Reduces Hallucination in Large Language Models](https://mlsanity.com/paper/2309.11495/) (2023)
- [Draft, Sketch, and Prove: Guiding Formal Theorem Provers with Informal Proofs](https://mlsanity.com/paper/2210.12283/) (2022)
- [Debating with More Persuasive LLMs Leads to More Truthful Answers](https://mlsanity.com/paper/2402.06782/) (2024)
- [When Can LLMs Actually Correct Their Own Mistakes? A Critical Survey of Self-Correction of LLMs](https://mlsanity.com/paper/2406.01297/) (2024)
- [Measuring Progress on Scalable Oversight for Large Language Models](https://mlsanity.com/paper/2211.03540/) (2022)
- [On Human Predictions with Explanations and Predictions of Machine Learning Models: A Case Study on Deception Detection](https://mlsanity.com/paper/1811.07901/) (2018)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Fact-Checking Complex Claims with Program-Guided Reasoning](https://mlsanity.com/paper/2305.12744/) (2023)
- [Supervising strong learners by amplifying weak experts](https://mlsanity.com/paper/1810.08575/) (2018)
- [Faithfulness vs. Plausibility: On the (Un)Reliability of Explanations from Large Language Models](https://mlsanity.com/paper/2402.04614/) (2024)
- [On scalable oversight with weak LLMs judging strong LLMs](https://mlsanity.com/paper/2407.04622/) (2024)
- [Prover-Verifier Games improve legibility of LLM outputs](https://mlsanity.com/paper/2407.13692/) (2024)
- [Scalable AI Safety via Doubly-Efficient Debate](https://mlsanity.com/paper/2311.14125/) (2023)

## Abstract (arXiv)

When an LLM supplies an argument a user could not produce, how can the user decide whether to accept its claim? Inspired by interactive proofs, we pair a computationally unbounded LLM prover with a resource-bounded human verifier. The verifier checks requested details without seeing the LLM's internals; passed checks accumulate evidence toward an acceptance threshold. Given task-supplied bounds on false passes and human checking errors, we prove anytime-valid soundness against adaptive provers: the probability of ever accepting a false claim is at most a chosen error level. For a true claim, acceptance within the budget has probability at least the product of per-round probabilities that the LLM responds adequately and the human checks correctly, provided the threshold is reachable in time. Each additional check guards against false claims but gives a true claim another chance to fail. Which review lengths meet both error targets depends on the verifier's effort, cognitive load, expertise, and fatigue. With equal resources, we identify conditions under which the bounds certify a review by local checks but not a one-shot check. In LLM-only simulations on GPQA Diamond and Humanity's Last Exam, whether answers accepted without revision were more accurate varied by task and model pair.