LODESTAR: Trustworthy Entropy Is Navigated, Not Merely Measured -- Reinforced Polarizer Keeps a Frozen LLM from Being Confidently Misled by the Wrong Evidence
Predictive-distribution entropy makes a strong selection rule in retrieval-augmented question answering: across five QA benchmarks, keeping the candidate answer that a frozen respondent LLM produces with the lowest answer-token entropy lifts mean answer F1 from 0.4769 to 0.5148 over the retriever's top-ranked passage, with no gold answers. Yet this lowest-entropy rule, which prior entropy-based selectors adopt, fails in a specific and consequential way: a misleading passage makes the respondent confidently wrong, driving its entropy down precisely where the signal looks most trustworthy. We show that the failure comes from the passage the respondent reads -- and the context that passage 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 across one question's candidates. LODESTAR uses reinforcement learning to train, once and offline, a polarizer -- a short fixed natural-language string inserted into the respondent's prompt and never into its weights; its training labels are built offline from gold answers and two LLM judges, and inference reads neither. Evaluating every competing selector under the same frozen respondent and the same candidate pools on 5,008 questions, LODESTAR attains the highest mean F1 of any inference-ready selector (0.5148 to 0.5339), the highest 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 method-by-dataset F1 cells against fourteen published configurations while remaining paired-significant against every one. The gain holds both in-domain and out-of-domain, and ablating the polarizer shows it is what makes the respondent read a misleading passage less often (26.0% against 30.3%).
Retrieval-augmented generation improves knowledge-intensive question answering, but indiscriminate retrieval can introduce irrelevant evidence and unnecessary computation. We investigate whether verbalized confidence from black-box language models can serve as an actionable signal for retrieval routing. Our method, BeyondUncertainty, first elicits a structured provisional answer and confidence estimate, then applies a model-specific threshold selected on held-out validation data and frozen before test evaluation. Low-confidence questions receive top-5 TF-IDF retrieval followed by a second answer call, whereas high-confidence questions return the provisional answer directly. We evaluate 27,000 policy instances across six QA benchmarks, three model families, and three retrieval policies. BeyondUncertainty achieves 0.483 mean token-level F1, compared with 0.467 for always retrieval and 0.401 for no retrieval, while reducing retrieved passages by 20.4% relative to always retrieval. When matched on the number of questions routed to retrieval within each dataset-model cell, it outperforms a post-hoc random allocation in 17 of 18 settings, with an average gain of 0.024 F1. Although poorly calibrated as an absolute probability, probe uncertainty modestly predicts question-level retrieval benefit (AUROC = 0.628). However, the additional probe increases total token usage by 28.2%, revealing a trade-off between more selective evidence acquisition and end-to-end token efficiency.
A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.
Large Language Models (LLMs) can reason well, yet often miss decisive evidence when it is buried in long, noisy contexts. We introduce HiLight, an Evidence Emphasis framework that decouples evidence selection from reasoning for frozen LLM solvers. HiLight avoids compressing or rewriting the input, which can discard or distort evidence, by training a lightweight Emphasis Actor to insert minimal highlight tags around pivotal spans in the unaltered context. A frozen Solver then performs downstream reasoning on the emphasized input. We cast highlighting as a weakly supervised decision-making problem and optimize the Actor with reinforcement learning using only the Solver's task reward, requiring no evidence labels and no access to or modification of the Solver. Across sequential recommendation and long-context question answering, HiLight consistently improves performance over strong prompt-based and automated prompt-optimization baselines. The learned emphasis policy transfers zero-shot to both smaller and larger unseen Solver families, including an API-based Solver, suggesting that the Actor captures genuine, reusable evidence structure rather than overfitting to a single backbone.