# Probabilistic Guarantees for Reducing Contextual Hallucinations in LLMs

arXiv: https://arxiv.org/abs/2601.00641 · HTML: https://mlsanity.com/paper/2601.00641/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 26 references that are in the map.
- First posted on arXiv 2 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [G-Eval: NLG Evaluation using GPT-4 with Better Human Alignment](https://mlsanity.com/paper/2303.16634/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [On Faithfulness and Factuality in Abstractive Summarization](https://mlsanity.com/paper/2005.00661/) (2020)
- [SummEval: Re-evaluating Summarization Evaluation](https://mlsanity.com/paper/2007.12626/) (2020)
- [Evaluating the Factual Consistency of Abstractive Text Summarization](https://mlsanity.com/paper/1910.12840/) (2019)
- [Entity-Based Knowledge Conflicts in Question Answering](https://mlsanity.com/paper/2109.05052/) (2021)
- [Trusting Your Evidence: Hallucinate Less with Context-aware Decoding](https://mlsanity.com/paper/2305.14739/) (2023)
- [AlignScore: Evaluating Factual Consistency with a Unified Alignment Function](https://mlsanity.com/paper/2305.16739/) (2023)
- [Unleashing the Emergent Cognitive Synergy in Large Language Models: A Task-Solving Agent through Multi-Persona Self-Collaboration](https://mlsanity.com/paper/2307.05300/) (2023)
- [Why Language Models Hallucinate](https://mlsanity.com/paper/2509.04664/) (2025)
- [LM vs LM: Detecting Factual Errors via Cross Examination](https://mlsanity.com/paper/2305.13281/) (2023)
- [Evaluating Correctness and Faithfulness of Instruction-Following Models for Question Answering](https://mlsanity.com/paper/2307.16877/) (2023)
- [BooookScore: A systematic exploration of book-length summarization in the era of LLMs](https://mlsanity.com/paper/2310.00785/) (2023)
- [ChatGPT as a Factual Inconsistency Evaluator for Text Summarization](https://mlsanity.com/paper/2303.15621/) (2023)
- [FABLES: Evaluating faithfulness and content selection in book-length summarization](https://mlsanity.com/paper/2404.01261/) (2024)
- [Multi-Dimensional Evaluation of Text Summarization with In-Context Learning](https://mlsanity.com/paper/2306.01200/) (2023)
- [LLMs as Factual Reasoners: Insights from Existing Benchmarks and Beyond](https://mlsanity.com/paper/2305.14540/) (2023)
- [Faithfulness-Aware Decoding Strategies for Abstractive Summarization](https://mlsanity.com/paper/2303.03278/) (2023)
- [RefChecker: Reference-based Fine-grained Hallucination Checker and Benchmark for Large Language Models](https://mlsanity.com/paper/2405.14486/) (2024)
- [KL-Divergence Guided Temperature Sampling](https://mlsanity.com/paper/2306.01286/) (2023)
- [VeriFastScore: Speeding up long-form factuality evaluation](https://mlsanity.com/paper/2505.16973/) (2025)
- [Towards Long Context Hallucination Detection](https://mlsanity.com/paper/2504.19457/) (2025)

## Abstract (arXiv)

Large language models (LLMs) frequently produce contextual hallucinations, where generated content contradicts or ignores information explicitly stated in the prompt. Such errors are particularly problematic in deterministic automation workflows, where inputs are fixed and correctness is unambiguous. We introduce a simple and model-agnostic framework that provides explicit probabilistic guarantees for reducing hallucinations in this setting. We formalize the notion of a specific task, defined by a fixed input and a deterministic correctness criterion, and show that issuing the same prompt in independent context windows yields an exponential reduction in the probability that all model outputs are incorrect. To identify a correct answer among repeated runs, we incorporate an LLM-as-a-judge and prove that the probability that the judged pipeline fails decays at a rate determined by the judge's true- and false-positive probabilities. When the judge is imperfect, we strengthen it through majority vote over independent judge calls, obtaining ensemble-level error rates that decrease exponentially in the number of votes. This yields an explicit bound on the probability that the pipeline selects a hallucinated answer. Experiments on controlled extraction tasks with synthetic noisy judges match these predictions exactly: pipeline failure decreases exponentially with the number of repetitions, and hallucination-selection decreases exponentially with the number of judges in the ensemble. Together, these results provide a lightweight, modular, and theoretically grounded method for driving hallucination probabilities arbitrarily low in fixed-input LLM workflows-without modifying model weights, decoding strategies, or prompt engineering.