Answering the Wrong Question: Reasoning Trace Inversion for Abstention in LLMs

Reinforcement fine-tuning improves the reasoning ability of large language models, but it can also encourage them to answer unanswerable queries by guessing or hallucinating missing information. Existing abstention methods either train models to produce generic refusals or encourage follow-up clarifications without verifying whether those clarifications identify the key missing information. We study queries that are clear in meaning but cannot be reliably resolved from the given information, and argue that a reliable model should not only abstain, but also explain what is missing. We propose a clarification-aware RLVR reward that, while rewarding correct answers on answerable queries, jointly optimizes explicit abstention and semantically aligned post-refusal clarification on unanswerable queries. Using this reward, we train Abstain-R1, a 3B model that improves abstention and clarification on unanswerable queries while preserving strong performance on answerable ones. Experiments on Abstain-Test, Abstain-QA, and SelfAware show that Abstain-R1 substantially improves over its base model and achieves unanswerable-query behavior competitive with larger systems including DeepSeek-R1, suggesting that calibrated abstention and clarification can be learned through verifiable rewards rather than emerging from scale alone.

Large language models (LLMs) can reduce hallucination by abstaining from questions they would likely get wrong. Abstention can be implemented outside the model (selective answering) using a confidence threshold that controls the answer rate (coverage), or learned inside it (abstention training), which can perform better but fixes coverage once trained. To compare the two, we match their coverage and decompose risk (error rate) into answering ability and distinguishing ability, i.e., how well the model answers and how accurately it abstains, respectively. The decomposition shows that abstention training performs better mainly by answering better: with strong confidence estimators, the two have nearly equal distinguishing ability. This motivates Train for Accuracy, then Post-hoc Select (TAPS), a modular approach that keeps coverage controllable, needs only standard post-training and an off-the-shelf confidence estimator, and benefits from advances in either component. Across three LLMs and three factual QA benchmarks, TAPS with a probing-based confidence estimator attains 1.5--9.4 percentage points lower mean risk than three representative abstention training methods at matched coverage. Within TAPS, accuracy training often weakens the model's own confidence signals, yet refitting the estimator largely preserves distinguishing ability. Together, these results establish TAPS as a strong yet controllable baseline and raise the bar for future abstention training: sacrificing control over coverage should yield gains beyond what can be achieved by optimizing answering and abstaining separately.

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.