# Uncertainty Quantification for LLM-based Code Generation

arXiv: https://arxiv.org/abs/2605.12201 · HTML: https://mlsanity.com/paper/2605.12201/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 41 references that are in the map.
- First posted on arXiv 12 May 2026.

## Builds on (most cited first, 25 of 25)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Qwen2.5-Coder Technical Report](https://mlsanity.com/paper/2409.12186/) (2024)
- [DeepSeek-Coder: When the Large Language Model Meets Programming -- The Rise of Code Intelligence](https://mlsanity.com/paper/2401.14196/) (2024)
- [Measuring Coding Challenge Competence With APPS](https://mlsanity.com/paper/2105.09938/) (2021)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [CodeT: Code Generation with Generated Tests](https://mlsanity.com/paper/2207.10397/) (2022)
- [Conformal Risk Control](https://mlsanity.com/paper/2208.02814/) (2022)
- [Distribution-Free, Risk-Controlling Prediction Sets](https://mlsanity.com/paper/2101.02703/) (2021)
- [Least Ambiguous Set-Valued Classifiers with Bounded Error Levels](https://mlsanity.com/paper/1609.00451/) (2016)
- [Learn then Test: Calibrating Predictive Algorithms to Achieve Risk Control](https://mlsanity.com/paper/2110.01052/) (2021)
- [Large Legal Fictions: Profiling Legal Hallucinations in Large Language Models](https://mlsanity.com/paper/2401.01301/) (2024)
- [Conformal Prediction with Large Language Models for Multi-Choice Question Answering](https://mlsanity.com/paper/2305.18404/) (2023)
- [Benchmarking LLMs via Uncertainty Quantification](https://mlsanity.com/paper/2401.12794/) (2024)
- [PAC Confidence Sets for Deep Neural Networks via Calibrated Prediction](https://mlsanity.com/paper/2001.00106/) (2019)
- [Predictive Inference with Feature Conformal Prediction](https://mlsanity.com/paper/2210.00173/) (2022)
- [Learning to Complete Code with Sketches](https://mlsanity.com/paper/2106.10158/) (2021)
- [A Theoretical Study on Bridging Internal Probability and Self-Consistency for LLM Reasoning](https://mlsanity.com/paper/2510.15444/) (2025)
- [Studying the Difference Between Natural and Programming Language Corpora](https://mlsanity.com/paper/1806.02437/) (2018)
- [Benchmarking Llama2, Mistral, Gemma and GPT for Factuality, Toxicity, Bias and Propensity for Hallucinations](https://mlsanity.com/paper/2404.09785/) (2024)
- [Probably Approximately Correct Labels](https://mlsanity.com/paper/2506.10908/) (2025)
- [PAC Prediction Sets for Large Language Models of Code](https://mlsanity.com/paper/2302.08703/) (2023)

## Abstract (arXiv)

Prediction sets provide a theoretically grounded framework for quantifying uncertainty in machine learning models. Adapting them to structured generation tasks, in particular, large language model (LLM) based code generation, remains a challenging problem. An existing attempt proposes PAC prediction sets but is limited by its strong monotonicity assumption on risk and single-label classification framework, which severely limits the space of candidate programs and cannot accommodate the multiple valid outputs inherent to code generation. To address these limitations, we propose an approach RisCoSet that leverages multiple hypothesis testing to construct risk-controlling predictions for LLM-based code generation. Given a trained code generation model, we produce a prediction set represented by a partial program, which is guaranteed to contain a correct solution with high confidence. Extensive experiments on three LLMs demonstrate the effectiveness of the proposed method. For instance, compared with the state-of-the-art, our method can significantly reduce the code removal by up to 24.5%, at the same level of risk.