# Functional Entropy: Predicting Functional Correctness in LLM-Generated Code with Uncertainty Quantification

arXiv: https://arxiv.org/abs/2605.28500 · HTML: https://mlsanity.com/paper/2605.28500/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 44 references that are in the map.
- First posted on arXiv 27 May 2026.

## Builds on (most cited first, 24 of 24)

- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [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)
- [CodeBLEU: a Method for Automatic Evaluation of Code Synthesis](https://mlsanity.com/paper/2009.10297/) (2020)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [MultiPL-E: A Scalable and Extensible Approach to Benchmarking Neural Code Generation](https://mlsanity.com/paper/2208.08227/) (2022)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Beyond Functional Correctness: Exploring Hallucinations in LLM-Generated Code](https://mlsanity.com/paper/2404.00971/) (2024)
- [Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraph](https://mlsanity.com/paper/2406.15627/) (2024)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [Calibration and Correctness of Language Models for Code](https://mlsanity.com/paper/2402.02047/) (2024)
- [CodeHalu: Investigating Code Hallucinations in LLMs via Execution-based Verification](https://mlsanity.com/paper/2405.00253/) (2024)
- [Uncertainty-Guided Chain-of-Thought for Code Generation with LLMs](https://mlsanity.com/paper/2503.15341/) (2025)
- [Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistency](https://mlsanity.com/paper/2502.04964/) (2025)
- [Atomic Calibration of LLMs in Long-Form Generations](https://mlsanity.com/paper/2410.13246/) (2024)
- [Generation Probabilities Are Not Enough: Uncertainty Highlighting in AI Code Completions](https://mlsanity.com/paper/2302.07248/) (2023)
- [Internal Representations as Indicators of Hallucinations in Agent Tool Selection](https://mlsanity.com/paper/2601.05214/) (2026)
- [Uncertainty Quantification for Language Models: A Suite of Black-Box, White-Box, LLM Judge, and Ensemble Scorers](https://mlsanity.com/paper/2504.19254/) (2025)
- [Collu-Bench: A Benchmark for Predicting Language Model Hallucinations in Code](https://mlsanity.com/paper/2410.09997/) (2024)
- [EAGer: Entropy-Aware GEneRation for Adaptive Inference-Time Scaling](https://mlsanity.com/paper/2510.11170/) (2025)
- [Hallucination Detection for LLM-based Text-to-SQL Generation via Two-Stage Metamorphic Testing](https://mlsanity.com/paper/2512.22250/) (2025)
- [A Systematic Literature Review of Code Hallucinations in LLMs: Characterization, Mitigation Methods, Challenges, and Future Directions for Reliable AI](https://mlsanity.com/paper/2511.00776/) (2025)
- [HalluJudge: A Reference-Free Hallucination Detection for Context Misalignment in Code Review Automation](https://mlsanity.com/paper/2601.19072/) (2026)
- [Fine-Grained Uncertainty Quantification for Long-Form Language Model Outputs: A Comparative Study](https://mlsanity.com/paper/2602.17431/) (2026)

## Built on by (most cited first, 3 of 3)

- [When Do Supervised UQ Ensembles Improve LLM Hallucination Detection? A Robustness Study](https://mlsanity.com/paper/2608.24492/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Certified Against Which Oracle? Execution Labels Set the Reported Risk of Conformal Abstention for Text-to-SQL](https://mlsanity.com/paper/2609.25938/) (2026)

## Abstract (arXiv)

Large language models have shown impressive capabilities in code generation, yet they often produce functionally incorrect code. Uncertainty quantification (UQ) methods have emerged as a promising approach for detecting hallucinations in natural language generation, but their effectiveness for code generation tasks remains underexplored. We systematically evaluate how UQ techniques transfer to code generation across three programming languages, five LLMs, and over 1,700 problems. We find that some token-probability-based methods generalize effectively without modification, while sampling-based methods relying on natural language inference (NLI) fail because NLI models cannot distinguish functionally different code, causing most responses to collapse into a single semantic cluster. To address this, we introduce functional equivalence methods, a family of code-specific methods that replace NLI-based semantic equivalence with an LLM-based functional equivalence assessment, including functional entropy, a code-specific analog of semantic entropy. Functional equivalence methods achieve top AUROC in 11 out of 15 model-benchmark combinations and the best calibration across most settings, consistently outperforming both NLI-based counterparts and all other methods evaluated.