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

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. Unlike 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.

Code Is More Than Text: Uncertainty Estimation for Code Generation

Large language models (LLMs) are increasingly deployed as code generators, where silently wrong programs pose real safety and reliability risks. Reliable uncertainty estimation (UE) is essential for selective prediction, human-in-the-loop review, and downstream agentic decisions. Yet most existing code UE methods are inherited from natural language (NL) generation and ignore properties that make code distinct. We argue that code differs from NL in three ways: a single wrong token can break an entire program (token fragility); algorithmic intent and concrete implementation can disagree independently (intent-code gap); and programs can be executed (executability). We instantiate these properties as three orthogonal uncertainty axes: lexical (Top-K token entropy), algorithmic (pseudo-code consistency), and functional (behavioral consistency). Across five code LLMs, our three-axis ensemble improves average AUROC from 0.696 for the strongest NL-derived baseline to 0.776 (+8.1 points). Notably, on Qwen3-14B, our single-pass Top-K token entropy matches the strongest multi-pass baseline while being over 3x cheaper; across models, it remains a competitive low-cost signal. These results suggest that code UE deserves code-specific design rather than direct NL ports.