# CORDIAL: Calibrating Ordinal LLM Outputs from Few Labels

arXiv: https://arxiv.org/abs/2609.29807 · HTML: https://mlsanity.com/paper/2609.29807/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 15 of its 23 references that are in the map.
- First posted on arXiv 24 Sep 2026.

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

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [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)
- [Beyond temperature scaling: Obtaining well-calibrated multiclass probabilities with Dirichlet calibration](https://mlsanity.com/paper/1910.12656/) (2019)
- [Sentiment Analysis in the Era of Large Language Models: A Reality Check](https://mlsanity.com/paper/2305.15005/) (2023)
- [Batch Calibration: Rethinking Calibration for In-Context Learning and Prompt Engineering](https://mlsanity.com/paper/2309.17249/) (2023)
- [Combining Human Predictions with Model Probabilities via Confusion Matrices and Calibration](https://mlsanity.com/paper/2109.14591/) (2021)
- [Ordinal-Aware Calibration for Ordinal Classification](https://mlsanity.com/paper/2410.15658/) (2024)
- [Auditing Multimodal LLM Raters: Central Tendency Bias in Clinical Ordinal Scoring](https://mlsanity.com/paper/2605.16386/) (2026)
- [Are LLMs Positionally Consistent Ordinal Classifiers? A Systematic Evaluation](https://mlsanity.com/paper/2608.08869/) (2026)

## Abstract (arXiv)

A large language model (LLM) can turn a text into a distribution over an ordered scale, but that distribution is a noisy measurement: saturated, compressed or exaggerated, and biased in a consistent direction. We propose CORDIAL, which treats the model's output as a noisy reading of the true label and corrects it with a channel of five interpretable parameters. The channel is small enough for its posterior to be averaged from a handful of labels, and we prove that the resulting calibration preserves first-order stochastic order. On Amazon reviews and CMU-MOSEI transcripts with four LLMs, CORDIAL has the lowest log loss among nine calibrators in 76 of 80 settings with 5 to 100 labels; with 20 labels and the main 7B reader, it matches the strongest baseline using 28-54 labels. The same posterior lets us learn priors from other tasks and fuse several LLMs. Unrestricted calibrators such as Dirichlet calibration overtake it only as the calibration set grows into the hundreds or thousands.