[Paper] Probabilistic Guarantees for Reducing Contextual Hallucinations in LLMs

Source: arXiv - 2601.00641v1

Overview

Large language models (LLMs) are great at generating text, but they often “hallucinate” – they produce answers that contradict or ignore the facts supplied in the prompt. This is a serious issue for deterministic automation pipelines where the input is fixed and the correct answer is unambiguous. The paper proposes a lightweight, model‑agnostic framework that gives probabilistic guarantees on how much hallucination can be reduced simply by repeating the same prompt and using an LLM‑based judge to pick the right answer.

Key Contributions

• Formal definition of a deterministic task (fixed input + exact correctness criterion) and a proof that independent repetitions of the same prompt reduce the joint error probability exponentially.
• LLM‑as‑judge pipeline: a second LLM evaluates the multiple generated answers; the authors derive a bound on the failure probability based on the judge’s true‑positive and false‑positive rates.
• Ensemble voting for imperfect judges: showing that majority voting over several independent judge calls drives the overall error down exponentially with the number of votes.
• Empirical validation on synthetic extraction tasks that match the theoretical predictions to the last decimal place.
• Model‑agnostic, zero‑training solution: works with any off‑the‑shelf LLM, no need to fine‑tune, modify decoding, or craft elaborate prompts.

Methodology

1. Task Formalization – The authors treat a “task” as a tuple (input, correctness predicate). The predicate can be evaluated automatically (e.g., does the answer contain a specific string?).
2. Repeated Generation – The same prompt is sent to the LLM k times, each in an independent context window, producing k candidate answers. Because each call is statistically independent, the chance that all k answers are wrong drops as (p^k) where p is the single‑run error rate.
3. LLM‑as‑Judge – A second LLM receives each candidate answer plus the original prompt and decides “correct/incorrect”. The judge itself has a true‑positive rate t and a false‑positive rate f.
4. Selection Strategy – The pipeline picks the answer with the highest judge confidence (or the majority vote among judges). The authors derive the overall failure probability as a function of t, f, k (generation repetitions), and j (judge repetitions).
5. Ensemble Voting for Judges – When the judge is noisy, they repeat the judging step j times and take a majority vote, which again yields an exponential decay in error with j.
6. Experiments – Synthetic extraction tasks (e.g., “return the value of field X from JSON”) with deliberately noisy judges were used to verify that the observed failure rates follow the derived exponential curves.

Results & Findings

The empirical curves overlay the theoretical predictions almost perfectly, confirming that the independence assumptions hold in practice for the tested LLMs (GPT‑3.5‑turbo and Claude‑2).

Practical Implications

• Deterministic automation – Data extraction, code generation, or configuration synthesis pipelines can now be hardened against hallucinations without touching the model internals.
• Cost‑effective reliability – Instead of expensive fine‑tuning, developers can trade a modest increase in API calls for provable error reductions, which is attractive for latency‑tolerant batch jobs.
• Modular architecture – The generation and judging stages can be swapped independently (e.g., use a cheaper LLM for generation and a more accurate one for judging).
• Safety‑critical systems – In contexts like contract analysis or medical report summarization, the exponential decay guarantees give auditors a quantifiable risk metric.
• Tooling integration – The approach maps cleanly onto existing orchestration frameworks (Airflow, Prefect) by adding “repeat‑N” and “judge‑ensemble” tasks.

Limitations & Future Work

• Independence assumption – The theory relies on generation calls being statistically independent; caching or deterministic temperature settings could violate this.
• Judge quality dependence – If the judge’s false‑positive rate is high, many repetitions are needed, which may offset cost benefits.
• Scope of tasks – The experiments focus on extraction‑style tasks with a clear correctness predicate; extending to open‑ended generation (e.g., creative writing) remains open.
• Latency – Repeating calls linearly increases response time; future work could explore parallelism or adaptive stopping criteria.
• Real‑world noisy judges – The paper uses synthetic noisy judges; evaluating on human‑in‑the‑loop or domain‑specific judges would strengthen practical confidence.

Overall, the paper offers a pragmatic, theoretically backed recipe for developers who need hard guarantees against contextual hallucinations in fixed‑input LLM workflows.

Authors

• Nils Rautenberg
• Sven Schippkus

Paper Information

• arXiv ID: 2601.00641v1
• Categories: cs.CL
• Published: January 2, 2026
• PDF: Download PDF