# The Well-Tempered Classifier: Some Elementary Properties of Temperature Scaling

arXiv: https://arxiv.org/abs/2602.14862 · HTML: https://mlsanity.com/paper/2602.14862/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 59 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Builds on (most cited first, 30 of 33)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Revisiting the Calibration of Modern Neural Networks](https://mlsanity.com/paper/2106.07998/) (2021)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Mix-n-Match: Ensemble and Compositional Methods for Uncertainty Calibration in Deep Learning](https://mlsanity.com/paper/2003.07329/) (2020)
- [Conformal Prediction With Conditional Guarantees](https://mlsanity.com/paper/2305.12616/) (2023)
- [Is Temperature the Creativity Parameter of Large Language Models?](https://mlsanity.com/paper/2405.00492/) (2024)
- [Classifier Calibration: A survey on how to assess and improve predicted class probabilities](https://mlsanity.com/paper/2112.10327/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Intra Order-preserving Functions for Calibration of Multi-Class Neural Networks](https://mlsanity.com/paper/2003.06820/) (2020)
- [Position: Bayesian Deep Learning is Needed in the Age of Large-Scale AI](https://mlsanity.com/paper/2402.00809/) (2024)
- [Calibrating Language Models with Adaptive Temperature Scaling](https://mlsanity.com/paper/2409.19817/) (2024)
- [Parameterized Temperature Scaling for Boosting the Expressive Power in Post-Hoc Uncertainty Calibration](https://mlsanity.com/paper/2102.12182/) (2021)
- [Sample-dependent Adaptive Temperature Scaling for Improved Calibration](https://mlsanity.com/paper/2207.06211/) (2022)
- [Don't Just Blame Over-parametrization for Over-confidence: Theoretical Analysis of Calibration in Binary Classification](https://mlsanity.com/paper/2102.07856/) (2021)
- [Thermometer: Towards Universal Calibration for Large Language Models](https://mlsanity.com/paper/2403.08819/) (2024)
- [When Does Optimizing a Proper Loss Yield Calibration?](https://mlsanity.com/paper/2305.18764/) (2023)
- [Attended Temperature Scaling: A Practical Approach for Calibrating Deep Neural Networks](https://mlsanity.com/paper/1810.11586/) (2018)
- [Trained on Tokens, Calibrated on Concepts: The Emergence of Semantic Calibration in LLMs](https://mlsanity.com/paper/2511.04869/) (2025)
- [Theoretical characterization of uncertainty in high-dimensional linear classification](https://mlsanity.com/paper/2202.03295/) (2022)
- [Long Horizon Temperature Scaling](https://mlsanity.com/paper/2302.03686/) (2023)
- [UNO: Uncertainty-aware Noisy-Or Multimodal Fusion for Unanticipated Input Degradation](https://mlsanity.com/paper/1911.05611/) (2019)
- [Rethinking Early Stopping: Refine, Then Calibrate](https://mlsanity.com/paper/2501.19195/) (2025)
- [On double-descent in uncertainty quantification in overparametrized models](https://mlsanity.com/paper/2210.12760/) (2022)
- [On Temperature Scaling and Conformal Prediction of Deep Classifiers](https://mlsanity.com/paper/2402.05806/) (2024)
- [Expectation consistency for calibration of neural networks](https://mlsanity.com/paper/2303.02644/) (2023)
- [Structured Matrix Scaling for Multi-Class Calibration](https://mlsanity.com/paper/2511.03685/) (2025)
- [Combining probability distributions: Extending the logarithmic pooling approach](https://mlsanity.com/paper/1502.04206/) (2015)

## Built on by (most cited first, 1 of 1)

- [Failed Reasoning Traces Tell You What Is Fixable (But Not by Reading Them)](https://mlsanity.com/paper/2606.05145/) (2026)

## Abstract (arXiv)

Temperature scaling is a simple method that allows to control the uncertainty of probabilistic models. It is mostly used in two contexts: improving the calibration of classifiers and tuning the stochasticity of large language models (LLMs). In both cases, temperature scaling is the most popular method for the job. Despite its popularity, a rigorous theoretical analysis of the properties of temperature scaling has remained elusive. We investigate here some of these properties. For classification, we show that increasing the temperature increases the uncertainty in the model in a very general sense (and in particular increases its entropy). However, for LLMs, we challenge the common claim that increasing temperature increases diversity. Furthermore, we introduce two new characterisations of temperature scaling. The first one is geometric: the tempered model is shown to be the information projection of the original model onto the set of models with a given entropy. The second characterisation clarifies the role of temperature scaling as a submodel of more general linear scalers such as matrix scaling and Dirichlet calibration: we show that temperature scaling is the only linear scaler that does not change the hard predictions of the model.