Calibration of Structured Ignorance Certificates for Diagnosing Unknown Unknowns in Reasoning Models

• URL: http://arxiv.org/abs/2606.08571v1
• Date: Sun, 07 Jun 2026 11:01:13 GMT
• Title: Calibration of Structured Ignorance Certificates for Diagnosing Unknown Unknowns in Reasoning Models
• Abstract summary: Large language models frequently fail in a characteristic way: rather than acknowledging ignorance, they produce fluent but incorrect answers to questions that lie beyond their knowledge boundaries.<n>We introduce textbfStructured Ignorance Certificates (SICs), a paraphrase-formatted output schema that demands a model explicitly name the missing domain, enumerate concepts, and propose a productive retrieval query rather than hallucinating an answer.<n> Evaluation on 735 held-out UU questions achieves a 99.46% validity rate, a mean Certificate Specificity Score of 0.967, and a 3.6% ROUGE-L improvement over the base
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Large language models frequently fail in a characteristic way: rather than acknowledging ignorance, they produce fluent but incorrect answers to questions that lie beyond their knowledge boundaries. We introduce \textbf{Structured Ignorance Certificates} (SICs), a JSON-formatted output schema that demands a model explicitly name the missing domain intersection, enumerate required concepts, and propose a productive retrieval query rather than hallucinating an answer. To train models to produce high-quality SICs we construct a 7,347-sample \emph{Unknown-Unknown} (UU) dataset by prompting Qwen3-14B to stitch together questions from seven domains (physics, biology, engineering, CS, economics, medical, legal) into novel cross-domain queries that no single-domain expert could answer. We fine-tune a 14B-parameter model with Group Relative Policy Optimization (GRPO) using a composite reward that combines retrieval utility, concept specificity, and output-format validity. A paraphrase-divergence probe trained on model responses confirms that SIC-tuned outputs systematically exhibit higher unknown-unknown probability scores. Evaluation on 735 held-out UU questions achieves a 99.46\% JSON validity rate, a mean Certificate Specificity Score of 0.967, and a 3.6\% ROUGE-L improvement over the base model on retrieval-grounded generation -- demonstrating that explicit epistemic structuring is a learnable and measurable capability.

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