# COIN: Uncertainty-Guarding Selective Question Answering for Foundation Models with Provable Risk Guarantees

arXiv: https://arxiv.org/abs/2506.20178 · HTML: https://mlsanity.com/paper/2506.20178/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jun 2025.

## Built on by (most cited first, 21 of 21)

- [SCOPE: Selective Conformal Optimized Pairwise LLM Judging](https://mlsanity.com/paper/2602.13110/) (2026)
- [LEC: Linear Expectation Constraints for Selection-Conditioned Risk Control in Selective Prediction and Routing Systems](https://mlsanity.com/paper/2512.01556/) (2025)
- [TECP: Token-Entropy Conformal Prediction for LLMs](https://mlsanity.com/paper/2509.00461/) (2025)
- [SafeGround: Know When to Trust GUI Grounding Models via Uncertainty Calibration](https://mlsanity.com/paper/2602.02419/) (2026)
- [Conformal Lesion Segmentation for 3D Medical Images](https://mlsanity.com/paper/2510.17897/) (2025)
- [Set-Valued Prediction for Large Language Models with Feasibility-Aware Coverage Guarantees](https://mlsanity.com/paper/2603.22966/) (2026)
- [BalanceRAG: Joint Risk Calibration for Cascaded Retrieval-Augmented Generation](https://mlsanity.com/paper/2605.20084/) (2026)
- [EchoRL: Reinforcement Learning via Rollout Echoing](https://mlsanity.com/paper/2605.31228/) (2026)
- [Conformal Sets in Multiple-Choice Question Answering under Black-Box Settings with Provable Coverage Guarantees](https://mlsanity.com/paper/2508.05544/) (2025)
- [MM-Snowball: Evaluating and Mitigating Hallucination Snowballing in Multimodal Multi-Turn Dialogue](https://mlsanity.com/paper/2606.00622/) (2026)
- [Judge, Retrieve, or Abstain: Uncertainty-Guarded LLM Judging with Provable Risk Guarantees](https://mlsanity.com/paper/2608.17994/) (2026)
- [IUQ: Interrogative Uncertainty Quantification for Long-Form Large Language Model Generation](https://mlsanity.com/paper/2604.15109/) (2026)
- [Beyond Surface Statistics: Robust Conformal Prediction for LLMs via Internal Representations](https://mlsanity.com/paper/2604.16217/) (2026)
- [Uncertainty-Aware Abstention in Large Language Models with Provable Alignment Guarantees](https://mlsanity.com/paper/2607.04430/) (2026)
- [Calibrated Prediction Set in Fault Detection with Risk Guarantees via Significance Tests](https://mlsanity.com/paper/2508.01208/) (2025)
- [Conformal P-Value in Multiple-Choice Question Answering Tasks with Provable Risk Control](https://mlsanity.com/paper/2508.10022/) (2025)
- [Hierarchical Spatio-Temporal Attention Network with Adaptive Risk-Aware Decision for Forward Collision Warning in Complex Scenarios](https://mlsanity.com/paper/2511.19952/) (2025)
- [Asymptotic Risk Calibration for Selective Question Answering](https://mlsanity.com/paper/2608.12008/) (2026)
- [Occupancy-based Quantile Risk Control](https://mlsanity.com/paper/2609.03104/) (2026)
- [Target-Checked Reliability Score Refinement for Video Question Answering](https://mlsanity.com/paper/2609.13288/) (2026)
- [Conformal Prediction with Paraphrase-Aware Scoring for LLM Uncertainty Quantification](https://mlsanity.com/paper/2610.04239/) (2026)

## Abstract (arXiv)

Uncertainty quantification (UQ) for foundation models is essential to identify and mitigate potential hallucinations in automatically generated text. However, heuristic UQ approaches lack formal guarantees for key metrics such as the false discovery rate (FDR) in selective prediction. Previous work adopts the split conformal prediction (SCP) framework to ensure desired coverage of admissible answers by constructing prediction sets, but these sets often contain incorrect candidates, limiting their practical utility. To address this, we propose COIN, an uncertainty-guarding selection framework that calibrates statistically valid thresholds to filter a single generated answer per question under user-specified FDR constraints. COIN estimates the empirical error rate on a calibration set and applies confidence interval methods such as Clopper-Pearson to establish a high-probability upper bound on the true error rate (i.e., FDR). This enables the selection of the largest uncertainty threshold that ensures FDR control on test data while significantly increasing sample retention. We demonstrate COIN's robustness in risk control, strong test-time power in retaining admissible answers, and predictive efficiency under limited calibration data across both general and multimodal text generation tasks. Furthermore, we show that employing alternative upper bound constructions and UQ strategies can further boost COIN's power performance, which underscores its extensibility and adaptability to diverse application scenarios.