# Unsupervised Conformal Inference: Bootstrapping and Alignment to Control LLM Uncertainty

arXiv: https://arxiv.org/abs/2509.23002 · HTML: https://mlsanity.com/paper/2509.23002/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Self-rewarding alignment and self-training, one of 13 directions in Synthetic data and self-improvement for LLMs.
- Builds on 19 of its 29 references that are in the map.
- First posted on arXiv 26 Sep 2025.

## Placed in

- Synthetic data and self-improvement for LLMs / [Self-rewarding alignment and self-training](https://mlsanity.com/synth/self-rewarding-alignment-and-self-training/)

## Builds on (most cited first, 19 of 19)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [BERTScore: Evaluating Text Generation with BERT](https://mlsanity.com/paper/1904.09675/) (2019)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [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)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [Distribution-Free Predictive Inference For Regression](https://mlsanity.com/paper/1604.04173/) (2016)
- [AmbigQA: Answering Ambiguous Open-domain Questions](https://mlsanity.com/paper/2004.10645/) (2020)
- [Adaptive Conformal Inference Under Distribution Shift](https://mlsanity.com/paper/2106.00170/) (2021)
- [Conformal prediction beyond exchangeability](https://mlsanity.com/paper/2202.13415/) (2022)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [ASQA: Factoid Questions Meet Long-Form Answers](https://mlsanity.com/paper/2204.06092/) (2022)
- [Risk-Sensitive and Robust Decision-Making: a CVaR Optimization Approach](https://mlsanity.com/paper/1506.02188/) (2015)
- [Language Models with Conformal Factuality Guarantees](https://mlsanity.com/paper/2402.10978/) (2024)
- [Large language model validity via enhanced conformal prediction methods](https://mlsanity.com/paper/2406.09714/) (2024)
- [Semantic Volume: Quantifying and Detecting both External and Internal Uncertainty in LLMs](https://mlsanity.com/paper/2502.21239/) (2025)
- [LLM Web Dynamics: Tracing Model Collapse in a Network of LLMs](https://mlsanity.com/paper/2506.15690/) (2025)

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

- [CARE: A Conformal Safety Layer for Medical Summarization](https://mlsanity.com/paper/2606.08969/) (2026)
- [SIGMA: Scalable Spectral Insights for LLM Model Collapse](https://mlsanity.com/paper/2601.03385/) (2026)

## Abstract (arXiv)

Deploying black-box LLMs requires managing uncertainty in the absence of token-level probability or true labels. We propose introducing an unsupervised conformal inference framework for generation, which integrates: generative models, incorporating: (i) an LLM-compatible atypical score derived from response-embedding Gram matrix, (ii) UCP combined with a bootstrapping variant (BB-UCP) that aggregates residuals to refine quantile precision while maintaining distribution-free, finite-sample coverage, and (iii) conformal alignment, which calibrates a single strictness parameter τ so a user predicate (e.g., factuality lift) holds on unseen batches with probability ≥ 1-α. Across different benchmark datasets, our gates achieve close-to-nominal coverage and provide tighter, more stable thresholds than split UCP, while consistently reducing the severity of hallucination, outperforming lightweight per-response detectors with similar computational demands. The result is a label-free, API-compatible gate for test-time filtering that turns geometric signals into calibrated, goal-aligned decisions.