# Calibrating Language Models with Adaptive Temperature Scaling

arXiv: https://arxiv.org/abs/2409.19817 · HTML: https://mlsanity.com/paper/2409.19817/

## Key facts

- Cited by 58 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 27 of its 34 references that are in the map.
- First posted on arXiv 29 Sep 2024.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 27 of 27)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (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)
- [The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalization](https://mlsanity.com/paper/2006.16241/) (2020)
- [ImageNet-trained CNNs are biased towards texture; increasing shape bias improves accuracy and robustness](https://mlsanity.com/paper/1811.12231/) (2018)
- [When Does Label Smoothing Help?](https://mlsanity.com/paper/1906.02629/) (2019)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Deep Anomaly Detection with Outlier Exposure](https://mlsanity.com/paper/1812.04606/) (2018)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (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)
- [Instruction Tuning with GPT-4](https://mlsanity.com/paper/2304.03277/) (2023)
- [Measuring Robustness to Natural Distribution Shifts in Image Classification](https://mlsanity.com/paper/2007.00644/) (2020)
- [Verified Uncertainty Calibration](https://mlsanity.com/paper/1909.10155/) (2019)
- [On Mixup Training: Improved Calibration and Predictive Uncertainty for Deep Neural Networks](https://mlsanity.com/paper/1905.11001/) (2019)
- [Reducing conversational agents' overconfidence through linguistic calibration](https://mlsanity.com/paper/2012.14983/) (2020)
- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [Training OOD Detectors in their Natural Habitats](https://mlsanity.com/paper/2202.03299/) (2022)
- [Combining Ensembles and Data Augmentation can Harm your Calibration](https://mlsanity.com/paper/2010.09875/) (2020)
- [On the Calibration of Pre-trained Language Models using Mixup Guided by Area Under the Margin and Saliency](https://mlsanity.com/paper/2203.07559/) (2022)
- [A Study on the Calibration of In-context Learning](https://mlsanity.com/paper/2312.04021/) (2023)
- [Conservative Prediction via Data-Driven Confidence Minimization](https://mlsanity.com/paper/2306.04974/) (2023)

## Built on by (most cited first, 30 of 58)

- [Knowledge Boundary of Large Language Models: A Survey](https://mlsanity.com/paper/2412.12472/) (2024)
- [Optimizing Temperature for Language Models with Multi-Sample Inference](https://mlsanity.com/paper/2502.05234/) (2025)
- [Diverse Preference Learning for Capabilities and Alignment](https://mlsanity.com/paper/2511.08594/) (2025)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Know What You Don't Know: Uncertainty Calibration of Process Reward Models](https://mlsanity.com/paper/2506.09338/) (2025)
- [Your Pre-trained LLM is Secretly an Unsupervised Confidence Calibrator](https://mlsanity.com/paper/2505.16690/) (2025)
- [Beyond Log Likelihood: Probability-Based Objectives for Supervised Fine-Tuning across the Model Capability Continuum](https://mlsanity.com/paper/2510.00526/) (2025)
- [Do LLMs Really Forget? Evaluating Unlearning with Knowledge Correlation and Confidence Awareness](https://mlsanity.com/paper/2506.05735/) (2025)
- [Large Language Models Do Multi-Label Classification Differently](https://mlsanity.com/paper/2505.17510/) (2025)
- [The Confidence Paradox: Can LLM Know When It's Wrong](https://mlsanity.com/paper/2506.23464/) (2025)
- [Adaptive Decoding via Latent Preference Optimization](https://mlsanity.com/paper/2411.09661/) (2024)
- [Measuring Scalar Constructs in Social Science with LLMs](https://mlsanity.com/paper/2509.03116/) (2025)
- [Calibrating LLM Judges: Linear Probes for Fast and Reliable Uncertainty Estimation](https://mlsanity.com/paper/2512.22245/) (2025)
- [BaseCal: Unsupervised Confidence Calibration via Base Model Signals](https://mlsanity.com/paper/2601.03042/) (2026)
- [Vision-Language Introspection: Mitigating Overconfident Hallucinations in MLLMs via Interpretable Bi-Causal Steering](https://mlsanity.com/paper/2601.05159/) (2026)
- [Text-to-SQL Calibration: No Need to Ask -- Just Rescale Model Probabilities](https://mlsanity.com/paper/2411.16742/) (2024)
- [Beyond Accuracy: The Role of Calibration in Self-Improving Large Language Models](https://mlsanity.com/paper/2504.02902/) (2025)
- [NOVA: NOise-aware Verbal Confidence CAlibration for Robust Large Language Models in RAG Systems](https://mlsanity.com/paper/2601.11004/) (2026)
- [LLMs Should Express Uncertainty Explicitly](https://mlsanity.com/paper/2604.05306/) (2026)
- [Specialization after Generalization: Towards Understanding Test-Time Training in Foundation Models](https://mlsanity.com/paper/2509.24510/) (2025)
- [Gradient-Stable Attention Heads Signal LLM Correctness](https://mlsanity.com/paper/2602.13699/) (2026)
- [Instinct vs. Reflection: Unifying Token and Verbalized Confidence in Multimodal Large Models](https://mlsanity.com/paper/2604.17274/) (2026)
- [Decoding Uncertainty: The Impact of Decoding Strategies for Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2509.16696/) (2025)
- [SCOPE: Stochastic and Counterbiased Option Placement for Evaluating Large Language Models](https://mlsanity.com/paper/2507.18182/) (2025)
- [Less Diverse, Less Safe: The Indirect But Pervasive Risk of Test-Time Scaling in Large Language Models](https://mlsanity.com/paper/2510.08592/) (2025)
- [SDA: Steering-Driven Distribution Alignment for Open LLMs without Fine-Tuning](https://mlsanity.com/paper/2511.16324/) (2025)
- [Improving Semantic Uncertainty Quantification in Language Model Question-Answering via Token-Level Temperature Scaling](https://mlsanity.com/paper/2604.07172/) (2026)
- [LLM Benchmark Datasets Should Be Contamination-Resistant](https://mlsanity.com/paper/2605.19999/) (2026)
- [Hallucination as Commitment Failure: Larger LLMs Misfire Despite Knowing the Answer](https://mlsanity.com/paper/2605.22007/) (2026)
- [Focus on Likely Classes for Test-Time Prediction](https://mlsanity.com/paper/2505.03819/) (2025)

## Abstract (arXiv)

The effectiveness of large language models (LLMs) is not only measured by their ability to generate accurate outputs but also by their calibration-how well their confidence scores reflect the probability of their outputs being correct. While unsupervised pre-training has been shown to yield LLMs with well-calibrated conditional probabilities, recent studies have shown that after fine-tuning with reinforcement learning from human feedback (RLHF), the calibration of these models degrades significantly. In this work, we introduce Adaptive Temperature Scaling (ATS), a post-hoc calibration method that predicts a temperature scaling parameter for each token prediction. The predicted temperature values adapt based on token-level features and are fit over a standard supervised fine-tuning (SFT) dataset. The adaptive nature of ATS addresses the varying degrees of calibration shift that can occur after RLHF fine-tuning. ATS improves calibration by over 10-50% across three downstream natural language evaluation benchmarks compared to prior calibration methods and does not impede performance improvements from RLHF.