Never the Number: Structural Abstention for AI Systems Whose Answers Are Consumed as Fact

For Large Language Models (LLMs) to be reliably deployed, models must effectively know when not to answer: abstain. Reasoning models, in particular, have gained attention for impressive performance on complex tasks. However, reasoning models have been shown to have worse abstention abilities. Taking the vulnerabilities of reasoning models into account, we propose our Query Misalignment Framework. Hallucinations resulting in failed abstention can be reinterpreted as LLMs answering the wrong question (rather than answering a question incorrectly). Based on this framework, we develop a new class of state-of-the-art abstention methods called Trace Inversion. First, we generate the reasoning trace of a model. Based on only the trace, we then reconstruct the most likely query that the model responded to. Finally, we compare the initial query with the reconstructed query. Low similarity score between the initial query and reconstructed query suggests that the model likely answered the question incorrectly and is flagged to abstain. Extensive experiments demonstrate that Trace Inversion effectively boosts abstention performance in four frontier LLMs across nine abstention QA datasets, beating competitive baselines in 33 out of 36 settings.

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.

LLM analytics agents are evaluated on SQL syntax accuracy, but production failures look different: questions with two valid business definitions, questions the warehouse cannot answer, deprecated columns after a schema change, and queries that execute successfully while returning the wrong business number. No execution-match metric can score them. This paper introduces WarehouseReliabilityBench, 400 frozen tasks over two synthetic warehouses in which roughly half the correct responses are a clarification, an abstention or a refusal, with pinned denominators and a pre-registered paired bootstrap fixing each claim verb before the numbers existed. QueryProof, a 7B agent, uses rules derived from a semantic layer and physical catalog to determine its behaviour, and gates every answer on deterministic post-execution checks. On an 80-task synthetic test split evaluated once, QueryProof outperforms a direct-prompted 32B baseline by +0.237 [+0.112, +0.375] Business Truth Rate at 71.0% lower cost per correct answer; against a cost-matched few-shot baseline the accuracy gain holds but the cost difference does not resolve. This compares systems rather than model sizes: the 32B baseline receives none of the scaffolding. False success falls from 0.754 to 0.351 of returned answers, and no wrong number was returned on an answerable task (0 of 24), though 13 answers went to questions requiring clarification or abstention. Removing the routing layer changes little (0.562 against 0.537), so the result does not depend on escalation. Routing tuned on validation over-abstains on test, and the fitted confidence model loses to the heuristic it replaced. Resampling template families rather than tasks widens both accuracy intervals to include zero, so the effect's direction is better supported than its magnitude. The gain tracks the deterministic layer, though no component ablation was run.