# Code-MUE: Measuring Code LLMs' Uncertainty through Execution-based Semantic Interaction Graphs

arXiv: https://arxiv.org/abs/2607.12273 · HTML: https://mlsanity.com/paper/2607.12273/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 47 of its 71 references that are in the map.
- First posted on arXiv 14 Jul 2026.

## Builds on (most cited first, 30 of 47)

- [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)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [Learning to Reason without External Rewards](https://mlsanity.com/paper/2505.19590/) (2025)
- [CodeNet: A Large-Scale AI for Code Dataset for Learning a Diversity of Coding Tasks](https://mlsanity.com/paper/2105.12655/) (2021)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [An Empirical Study of the Non-determinism of ChatGPT in Code Generation](https://mlsanity.com/paper/2308.02828/) (2023)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [LLM Hallucinations in Practical Code Generation: Phenomena, Mechanism, and Mitigation](https://mlsanity.com/paper/2409.20550/) (2024)
- [A Survey on Uncertainty Quantification Methods for Deep Learning](https://mlsanity.com/paper/2302.13425/) (2023)
- [Uncertainty Estimation and Quantification for LLMs: A Simple Supervised Approach](https://mlsanity.com/paper/2404.15993/) (2024)
- [Learning to Route LLMs with Confidence Tokens](https://mlsanity.com/paper/2410.13284/) (2024)
- [Overconfidence is Key: Verbalized Uncertainty Evaluation in Large Language and Vision-Language Models](https://mlsanity.com/paper/2405.02917/) (2024)
- [Calibration and Correctness of Language Models for Code](https://mlsanity.com/paper/2402.02047/) (2024)
- [No Need to Lift a Finger Anymore? Assessing the Quality of Code Generation by ChatGPT](https://mlsanity.com/paper/2308.04838/) (2023)
- [CodeJudge: Evaluating Code Generation with Large Language Models](https://mlsanity.com/paper/2410.02184/) (2024)
- [Look Before You Leap: An Exploratory Study of Uncertainty Measurement for Large Language Models](https://mlsanity.com/paper/2307.10236/) (2023)
- [What Can We Learn From The Selective Prediction And Uncertainty Estimation Performance Of 523 Imagenet Classifiers](https://mlsanity.com/paper/2302.11874/) (2023)
- [Uncertainty-Guided Chain-of-Thought for Code Generation with LLMs](https://mlsanity.com/paper/2503.15341/) (2025)
- [InternalInspector I2: Robust Confidence Estimation in LLMs through Internal States](https://mlsanity.com/paper/2406.12053/) (2024)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [EffiBench-X: A Multi-Language Benchmark for Measuring Efficiency of LLM-Generated Code](https://mlsanity.com/paper/2505.13004/) (2025)
- [Towards Characterizing Adversarial Defects of Deep Learning Software from the Lens of Uncertainty](https://mlsanity.com/paper/2004.11573/) (2020)
- [Hallucination Detection in Large Language Models with Metamorphic Relations](https://mlsanity.com/paper/2502.15844/) (2025)

## Abstract (arXiv)

As Code Large Language Models (LLMs) become central to modern software engineering, their inherent stochasticity poses significant real-world risks, where even minor errors can lead to severe functional, security, or safety consequences. Reliable automation, therefore, demands the ability to distinguish between confident, well-supported predictions and stochastic guessing. However, existing uncertainty estimation methods face a critical gap: white and grey-box techniques are often inapplicable to closed-source models, while standard "black-box" text metrics fail to capture the unique fragility of code, where syntactic variation does not always imply semantic divergence. To bridge this syntax-semantics gap, we introduce Code-MUE, a purely black-box framework that measures uncertainty through execution-based Semantic Interaction Graphs. Different from prior approaches that rely on superficial textual similarity, Code-MUE grounds uncertainty in observable runtime behavior, calculating the Von Neumann entropy of the solution space to quantify global semantic diversity. A large-scale empirical study across eight state-of-the-art LLMs demonstrates that Code-MUE achieves a strong negative correlation with functional correctness (Spearman's correlation up to -0.98), significantly outperforming lexical and embedding-based baselines while enabling robust risk detection and selective prediction in practical workflows.