# LODESTAR: Robust Entropy-Based Answer Selection in Retrieval-Augmented Generation for Question Answering -- Directing Frozen-LLM Entropy with a Reinforcement-Learned Prompt Polarizer under Misleading Passages

arXiv: https://arxiv.org/abs/2608.11922 · HTML: https://mlsanity.com/paper/2608.11922/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in RAG robustness and adaptive retrieval, one of 15 directions in Retrieval-augmented generation.
- Builds on 38 of its 49 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Placed in

- Retrieval-augmented generation / [RAG robustness and adaptive retrieval](https://mlsanity.com/rag/rag-robustness-and-adaptive-retrieval/)

## Builds on (most cited first, 30 of 38)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
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- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [SQuAD: 100,000+ Questions for Machine Comprehension of Text](https://mlsanity.com/paper/1606.05250/) (2016)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Qwen3 Embedding: Advancing Text Embedding and Reranking Through Foundation Models](https://mlsanity.com/paper/2506.05176/) (2025)
- [Unsupervised Dense Information Retrieval with Contrastive Learning](https://mlsanity.com/paper/2112.09118/) (2021)
- [M3-Embedding: Multi-Linguality, Multi-Functionality, Multi-Granularity Text Embeddings Through Self-Knowledge Distillation](https://mlsanity.com/paper/2402.03216/) (2024)
- [GEPA: Reflective Prompt Evolution Can Outperform Reinforcement Learning](https://mlsanity.com/paper/2507.19457/) (2025)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Replacing Judges with Juries: Evaluating LLM Generations with a Panel of Diverse Models](https://mlsanity.com/paper/2404.18796/) (2024)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [Optimizing Instructions and Demonstrations for Multi-Stage Language Model Programs](https://mlsanity.com/paper/2406.11695/) (2024)
- [Simple Entity-Centric Questions Challenge Dense Retrievers](https://mlsanity.com/paper/2109.08535/) (2021)
- [Large language models can accurately predict searcher preferences](https://mlsanity.com/paper/2309.10621/) (2023)
- [Min-K%++: Improved Baseline for Detecting Pre-Training Data from Large Language Models](https://mlsanity.com/paper/2404.02936/) (2024)
- [FIRST: Faster Improved Listwise Reranking with Single Token Decoding](https://mlsanity.com/paper/2406.15657/) (2024)
- [SeaKR: Self-aware Knowledge Retrieval for Adaptive Retrieval Augmented Generation](https://mlsanity.com/paper/2406.19215/) (2024)
- [Adaptive Retrieval Without Self-Knowledge? Bringing Uncertainty Back Home](https://mlsanity.com/paper/2501.12835/) (2025)
- [MBA-RAG: a Bandit Approach for Adaptive Retrieval-Augmented Generation through Question Complexity](https://mlsanity.com/paper/2412.01572/) (2024)
- [Entropy-Based Decoding for Retrieval-Augmented Large Language Models](https://mlsanity.com/paper/2406.17519/) (2024)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Why Uncertainty Estimation Methods Fall Short in RAG: An Axiomatic Analysis](https://mlsanity.com/paper/2505.07459/) (2025)

## Abstract (arXiv)

Predictive-distribution entropy is a strong answer-selection rule in retrieval-augmented generation (RAG) for question answering: across five QA benchmarks, selecting the answer a frozen respondent LLM produces with the lowest answer-token entropy lifts mean F1 from 0.4769 to 0.5148 over the retriever's top-ranked passage, without gold answers. Yet this rule, which prior entropy-based selectors adopt, fails: a misleading passage makes the respondent confidently wrong, driving entropy down where the uncertainty signal looks most trustworthy. The failure comes from the passage the respondent reads, and the context it is read in is an input we can intervene on. We introduce LODESTAR: to our knowledge the first method to score a text intervention by the uncertainty it induces in a third-party frozen respondent, compared within one question. LODESTAR uses reinforcement learning (GRPO) to train, once and offline, a polarizer -- a short fixed natural-language string inserted into the respondent's prompt and never into its weights, directing entropy so that entropy-based answer selection stays robust to misleading passages; training labels are built from gold answers and two LLM judges, and inference reads neither. With every competing selector under the same frozen respondent and candidate pools on 5,008 questions, LODESTAR attains the highest mean F1 of any inference-ready selector (0.5339), the highest macro exact match (0.4136), and the highest GPT-4o judge score of the frozen-respondent configurations judged (0.6435); its three-seed mean wins all 70 F1 cells against fourteen published configurations and is paired-significant on F1 against every one. The gain holds in-domain on NQ-Open and out-of-domain over SQuAD, TriviaQA, EntityQuestions and WebQuestions. Ablating the polarizer shows it is what makes the respondent read a misleading passage less often (26.0% vs 30.3%).