# Conformal Sets in Multiple-Choice Question Answering under Black-Box Settings with Provable Coverage Guarantees

arXiv: https://arxiv.org/abs/2508.05544 · HTML: https://mlsanity.com/paper/2508.05544/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 22 references that are in the map.
- First posted on arXiv 7 Aug 2025.

## Builds on (most cited first, 20 of 20)

- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification](https://mlsanity.com/paper/2107.07511/) (2021)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [ConU: Conformal Uncertainty in Large Language Models with Correctness Coverage Guarantees](https://mlsanity.com/paper/2407.00499/) (2024)
- [PRISM: Self-Pruning Intrinsic Selection Method for Training-Free Multimodal Data Selection](https://mlsanity.com/paper/2502.12119/) (2025)
- [LLaVA Steering: Visual Instruction Tuning with 500x Fewer Parameters through Modality Linear Representation-Steering](https://mlsanity.com/paper/2412.12359/) (2024)
- [CoT-Kinetics: A Theoretical Modeling Assessing LRM Reasoning Process](https://mlsanity.com/paper/2505.13408/) (2025)
- [ASCD: Attention-Steerable Contrastive Decoding for Reducing Hallucination in MLLM](https://mlsanity.com/paper/2506.14766/) (2025)
- [Backdoor Cleaning without External Guidance in MLLM Fine-tuning](https://mlsanity.com/paper/2505.16916/) (2025)
- [Uncertainty-Aware Evaluation for Vision-Language Models](https://mlsanity.com/paper/2402.14418/) (2024)
- [SConU: Selective Conformal Uncertainty in Large Language Models](https://mlsanity.com/paper/2504.14154/) (2025)
- [COIN: Uncertainty-Guarding Selective Question Answering for Foundation Models with Provable Risk Guarantees](https://mlsanity.com/paper/2506.20178/) (2025)
- [SPOT! Revisiting Video-Language Models for Event Understanding](https://mlsanity.com/paper/2311.12919/) (2023)
- [Sample then Identify: A General Framework for Risk Control and Assessment in Multimodal Large Language Models](https://mlsanity.com/paper/2410.08174/) (2024)
- [Word-Sequence Entropy: Towards Uncertainty Estimation in Free-Form Medical Question Answering Applications and Beyond](https://mlsanity.com/paper/2402.14259/) (2024)
- [Hallucination Detection in Foundation Models for Decision-Making: A Flexible Definition and Review of the State of the Art](https://mlsanity.com/paper/2403.16527/) (2024)
- [FedBiP: Heterogeneous One-Shot Federated Learning with Personalized Latent Diffusion Models](https://mlsanity.com/paper/2410.04810/) (2024)
- [Does Machine Unlearning Truly Remove Knowledge?](https://mlsanity.com/paper/2505.23270/) (2025)

## Built on by (most cited first, 2 of 2)

- [Can VLMs Reliably Assess Sidewalk Accessibility Attributes from Pedestrian-Level Imagery?](https://mlsanity.com/paper/2609.17882/) (2026)
- [Conformal Prediction with Paraphrase-Aware Scoring for LLM Uncertainty Quantification](https://mlsanity.com/paper/2610.04239/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) have shown remarkable progress in multiple-choice question answering (MCQA), but their inherent unreliability, such as hallucination and overconfidence, limits their application in high-risk domains. To address this, we propose a frequency-based uncertainty quantification method under black-box settings, leveraging conformal prediction (CP) to ensure provable coverage guarantees. Our approach involves multiple independent samplings of the model's output distribution for each input, with the most frequent sample serving as a reference to calculate predictive entropy (PE). Experimental evaluations across six LLMs and four datasets (MedMCQA, MedQA, MMLU, MMLU-Pro) demonstrate that frequency-based PE outperforms logit-based PE in distinguishing between correct and incorrect predictions, as measured by AUROC. Furthermore, the method effectively controls the empirical miscoverage rate under user-specified risk levels, validating that sampling frequency can serve as a viable substitute for logit-based probabilities in black-box scenarios. This work provides a distribution-free model-agnostic framework for reliable uncertainty quantification in MCQA with guaranteed coverage, enhancing the trustworthiness of LLMs in practical applications.