# Monte Carlo Temperature: a robust sampling strategy for LLM's uncertainty quantification methods

arXiv: https://arxiv.org/abs/2502.18389 · HTML: https://mlsanity.com/paper/2502.18389/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 32 references that are in the map.
- First posted on arXiv 25 Feb 2025.

## Builds on (most cited first, 15 of 15)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [The Falcon Series of Open Language Models](https://mlsanity.com/paper/2311.16867/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [On Hallucination and Predictive Uncertainty in Conditional Language Generation](https://mlsanity.com/paper/2103.15025/) (2021)
- [Handling Ontology Gaps in Semantic Parsing](https://mlsanity.com/paper/2406.19537/) (2024)

## Built on by (most cited first, 12 of 12)

- [Learned Hallucination Detection in Black-Box LLMs using Token-level Entropy Production Rate](https://mlsanity.com/paper/2509.04492/) (2025)
- [Estimating LLM Consistency: A User Baseline vs Surrogate Metrics](https://mlsanity.com/paper/2505.23799/) (2025)
- [On Calibration of Large Language Models: From Response To Capability](https://mlsanity.com/paper/2602.13540/) (2026)
- [FLIPS: Instance-Fingerprinting for LLMs via Pseudo-random Sequences](https://mlsanity.com/paper/2606.03330/) (2026)
- [SCOPE: Stochastic and Counterbiased Option Placement for Evaluating Large Language Models](https://mlsanity.com/paper/2507.18182/) (2025)
- [Contemplative Artificial Intelligence](https://mlsanity.com/paper/2504.15125/) (2025)
- [FUSE: Quantifying Uncertainty in Vision-Language Models by Bayesian Fusing Epistemic and Aleatoric Uncertainty](https://mlsanity.com/paper/2606.14728/) (2026)
- [Stochastic Sampling is Epistemically Shallow: The Dimensionality Gap Between Temperature Variation and Model Diversity in LLMs](https://mlsanity.com/paper/2607.20464/) (2026)
- [Group Fairness Meets the Black Box: Enabling Fair Algorithms on Closed LLMs via Post-Processing](https://mlsanity.com/paper/2508.11258/) (2025)
- [Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering](https://mlsanity.com/paper/2605.19220/) (2026)
- [Estimating Uncertainty from Reasoning: A Large-Scale Study of Multi- and Crosslingual MCQA Performance in LLMs](https://mlsanity.com/paper/2607.06327/) (2026)
- [QUORUM: QUality-Optimized Routing Using Multiple annotators](https://mlsanity.com/paper/2608.27974/) (2026)

## Abstract (arXiv)

Uncertainty quantification (UQ) in Large Language Models (LLMs) is essential for their safe and reliable deployment, particularly in critical applications where incorrect outputs can have serious consequences. Current UQ methods typically rely on querying the model multiple times using non-zero temperature sampling to generate diverse outputs for uncertainty estimation. However, the impact of selecting a given temperature parameter is understudied, and our analysis reveals that temperature plays a fundamental role in the quality of uncertainty estimates. The conventional approach of identifying optimal temperature values requires expensive hyperparameter optimization (HPO) that must be repeated for each new model-dataset combination. We propose Monte Carlo Temperature (MCT), a robust sampling strategy that eliminates the need for temperature calibration. Our analysis reveals that: 1) MCT provides more robust uncertainty estimates across a wide range of temperatures, 2) MCT improves the performance of UQ methods by replacing fixed-temperature strategies that do not rely on HPO, and 3) MCT achieves statistical parity with oracle temperatures, which represent the ideal outcome of a well-tuned but computationally expensive HPO process. These findings demonstrate that effective UQ can be achieved without the computational burden of temperature parameter calibration.