# Towards Reproducible LLM Evaluation: Quantifying Uncertainty in LLM Benchmark Scores

arXiv: https://arxiv.org/abs/2410.03492 · HTML: https://mlsanity.com/paper/2410.03492/

## Key facts

- Cited by 25 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 18 references that are in the map.
- First posted on arXiv 4 Oct 2024.

## Builds on (most cited first, 7 of 7)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [BigCodeBench: Benchmarking Code Generation with Diverse Function Calls and Complex Instructions](https://mlsanity.com/paper/2406.15877/) (2024)
- [LegalBench: A Collaboratively Built Benchmark for Measuring Legal Reasoning in Large Language Models](https://mlsanity.com/paper/2308.11462/) (2023)
- [Evaluating the Ability of Large Language Models to Reason about Cardinal Directions](https://mlsanity.com/paper/2406.16528/) (2024)
- [Towards Inferential Reproducibility of Machine Learning Research](https://mlsanity.com/paper/2302.04054/) (2023)

## Built on by (most cited first, 25 of 25)

- [Foundation Models for Geospatial Reasoning: Assessing Capabilities of Large Language Models in Understanding Geometries and Topological Spatial Relations](https://mlsanity.com/paper/2505.17136/) (2025)
- [LLMs Provide Unstable Answers to Legal Questions](https://mlsanity.com/paper/2502.05196/) (2025)
- [Reflections on the Reproducibility of Commercial LLM Performance in Empirical Software Engineering Studies](https://mlsanity.com/paper/2510.25506/) (2025)
- [ReasonBENCH: Benchmarking the (In)Stability of LLM Reasoning](https://mlsanity.com/paper/2512.07795/) (2025)
- [Confidence in Large Language Model Evaluation: A Bayesian Approach to Limited-Sample Challenges](https://mlsanity.com/paper/2504.21303/) (2025)
- [The Silent Hyperparameter: Quantifying the Impact of Inference Backends on LLM Reproducibility](https://mlsanity.com/paper/2605.19537/) (2026)
- [Test-Time Scaling in Reasoning LLMs: Inference Regimes, Evaluation, and Reproducibility](https://mlsanity.com/paper/2608.04001/) (2026)
- [Beyond Reproducibility: Token Probabilities Expose Large Language Model Nondeterminism](https://mlsanity.com/paper/2601.06118/) (2026)
- [Toward Robust Legal Text Formalization into Defeasible Deontic Logic using LLMs](https://mlsanity.com/paper/2506.08899/) (2025)
- [From Queries to Criteria: Understanding How Astronomers Evaluate LLMs](https://mlsanity.com/paper/2507.15715/) (2025)
- [Investigating LLM Variability in Personalized Conversational Information Retrieval](https://mlsanity.com/paper/2510.03795/) (2025)
- [Critical Confabulation: Can LLMs Hallucinate for Social Good?](https://mlsanity.com/paper/2511.07722/) (2025)
- [Inspectable AI for Science: A Research Object Approach to Generative AI Governance](https://mlsanity.com/paper/2604.11261/) (2026)
- [Evaluating the Ability of Large Language Models to Reason about Cardinal Directions, Revisited](https://mlsanity.com/paper/2507.12059/) (2025)
- [Beyond statistical significance: Quantifying uncertainty and statistical variability in multilingual and multitask NLP evaluation](https://mlsanity.com/paper/2509.22612/) (2025)
- [DecompSR: A dataset for decomposed analyses of compositional multihop spatial reasoning](https://mlsanity.com/paper/2511.02627/) (2025)
- [QSTRBench: a New Benchmark to Evaluate the Ability of Language Models to Reason with Qualitative Spatial and Temporal Calculi](https://mlsanity.com/paper/2605.18380/) (2026)
- [Runtime Governance for Agentic AI: Action-Boundary Control with Trusted Provenance and Fail-Closed Execution](https://mlsanity.com/paper/2608.16891/) (2026)
- [AI Agent for Reverse-Engineering Legacy Finite-Difference Code and Translating to Devito](https://mlsanity.com/paper/2601.18381/) (2026)
- [CreditAudit: 2nd Dimension for LLM Evaluation and Selection](https://mlsanity.com/paper/2602.02515/) (2026)
- [Accuracy and Cost Claims Do Not Survive Re-Execution in Agentic VideoQA](https://mlsanity.com/paper/2607.01469/) (2026)
- [Testing and Evaluation of Agentic AI Systems In Military Command and Control](https://mlsanity.com/paper/2608.20597/) (2026)
- [From Ideas to Actions: A Public-Data Decision-Support Toolchain Across the Venture Lifecycle](https://mlsanity.com/paper/2609.15219/) (2026)
- [Speculative Evaluation of Stochastic LLMs](https://mlsanity.com/paper/2609.28560/) (2026)
- [Reproducible LLM Inference Benchmarking: A Sequential Isolation Protocol for Regression Testing](https://mlsanity.com/paper/2610.09778/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are stochastic, and not all models give deterministic answers, even when setting temperature to zero with a fixed random seed. However, few benchmark studies attempt to quantify uncertainty, partly due to the time and cost of repeated experiments. We use benchmarks designed for testing LLMs' capacity to reason about cardinal directions to explore the impact of experimental repeats on mean score and prediction interval. We suggest a simple method for cost-effectively quantifying the uncertainty of a benchmark score and make recommendations concerning reproducible LLM evaluation.