# Measuring LLM Code Generation Stability via Structural Entropy

arXiv: https://arxiv.org/abs/2508.14288 · HTML: https://mlsanity.com/paper/2508.14288/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 19 references that are in the map.
- First posted on arXiv 19 Aug 2025.

## Builds on (most cited first, 13 of 13)

- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Spider: A Large-Scale Human-Labeled Dataset for Complex and Cross-Domain Semantic Parsing and Text-to-SQL Task](https://mlsanity.com/paper/1809.08887/) (2018)
- [A Survey on Large Language Models for Code Generation](https://mlsanity.com/paper/2406.00515/) (2024)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [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)
- [SPoC: Search-based Pseudocode to Code](https://mlsanity.com/paper/1906.04908/) (2019)
- [An Empirical Study of the Non-determinism of ChatGPT in Code Generation](https://mlsanity.com/paper/2308.02828/) (2023)
- [Out of the BLEU: how should we assess quality of the Code Generation models?](https://mlsanity.com/paper/2208.03133/) (2022)
- [Does BLEU Score Work for Code Migration?](https://mlsanity.com/paper/1906.04903/) (2019)
- [Revisiting Code Similarity Evaluation with Abstract Syntax Tree Edit Distance](https://mlsanity.com/paper/2404.08817/) (2024)
- [Benchmarks and Metrics for Evaluations of Code Generation: A Critical Review](https://mlsanity.com/paper/2406.12655/) (2024)
- [Applying Information Theory to Software Evolution](https://mlsanity.com/paper/2303.13729/) (2023)

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

- [SQLStructEval: Structural Evaluation of LLM Text-to-SQL Generation](https://mlsanity.com/paper/2604.06736/) (2026)
- [FASE: Fast Adaptive Semantic Entropy for Code Quality](https://mlsanity.com/paper/2606.09800/) (2026)

## Abstract (arXiv)

Assessing the stability of code generation from large language models (LLMs) is essential for judging their reliability in real-world development. We extend prior "structural-entropy concepts" to the program domain by pairing entropy with abstract syntax tree (AST) analysis. For any fixed prompt, we collect the multiset of depth-bounded subtrees of AST in each generated program and treat their relative frequencies as a probability distribution. We then measure stability in two complementary ways: (i) Jensen-Shannon divergence, a symmetric, bounded indicator of structural overlap, and (ii) a Structural Cross-Entropy ratio that highlights missing high-probability patterns. Both metrics admit structural-only and token-aware variants, enabling separate views on control-flow shape and identifier-level variability. Unlike pass@k, BLEU, or CodeBLEU, our metrics are reference-free, language-agnostic, and execution-independent. We benchmark several leading LLMs on standard code generation tasks, demonstrating that AST-driven structural entropy reveals nuances in model consistency and robustness. The method runs in O(n,d) time with no external tests, providing a lightweight addition to the code-generation evaluation toolkit.