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

arXiv: https://arxiv.org/abs/2606.08571 · HTML: https://mlsanity.com/paper/2606.08571/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 20 references that are in the map.
- First posted on arXiv 7 Jun 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [REALM: Retrieval-Augmented Language Model Pre-Training](https://mlsanity.com/paper/2002.08909/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [The Geometry of Truth: Emergent Linear Structure in Large Language Model Representations of True/False Datasets](https://mlsanity.com/paper/2310.06824/) (2023)
- [Reliable Visual Question Answering: Abstain Rather Than Answer Incorrectly](https://mlsanity.com/paper/2204.13631/) (2022)
- [Linear Probes Detect Task Format, Not Reasoning Mode in Language Model Hidden States](https://mlsanity.com/paper/2606.02907/) (2026)
- [I Can't Believe It's Not Robust: Catastrophic Collapse of Safety Classifiers under Embedding Drift](https://mlsanity.com/paper/2603.01297/) (2026)
- [Calibration Collapse Under Sycophancy Fine-Tuning: How Reward Hacking Breaks Uncertainty Quantification in LLMs](https://mlsanity.com/paper/2604.10585/) (2026)

## Abstract (arXiv)

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 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 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.