# SupportCal: Label-Free Calibration of Post-Trained LLMs via Reference Support and Corroboration

arXiv: https://arxiv.org/abs/2609.24303 · HTML: https://mlsanity.com/paper/2609.24303/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 27 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Builds on (most cited first, 23 of 23)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Gemma 3 Technical Report](https://mlsanity.com/paper/2503.19786/) (2025)
- [DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Model](https://mlsanity.com/paper/2405.04434/) (2024)
- [Qwen2.5-Math Technical Report: Toward Mathematical Expert Model via Self-Improvement](https://mlsanity.com/paper/2409.12122/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [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)
- [Yi: Open Foundation Models by 01.AI](https://mlsanity.com/paper/2403.04652/) (2024)
- [MathQA: Towards Interpretable Math Word Problem Solving with Operation-Based Formalisms](https://mlsanity.com/paper/1905.13319/) (2019)
- [MedMCQA : A Large-scale Multi-Subject Multi-Choice Dataset for Medical domain Question Answering](https://mlsanity.com/paper/2203.14371/) (2022)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [Calibration of Pre-trained Transformers](https://mlsanity.com/paper/2003.07892/) (2020)
- [A Survey of Confidence Estimation and Calibration in Large Language Models](https://mlsanity.com/paper/2311.08298/) (2023)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [Your Pre-trained LLM is Secretly an Unsupervised Confidence Calibrator](https://mlsanity.com/paper/2505.16690/) (2025)
- [BaseCal: Unsupervised Confidence Calibration via Base Model Signals](https://mlsanity.com/paper/2601.03042/) (2026)
- [CaliDist: Calibrating Large Language Models via Behavioral Robustness to Distraction](https://mlsanity.com/paper/2606.05799/) (2026)

## Abstract (arXiv)

Post-training often improves task performance but can degrade confidence calibration, leaving post-trained language models (PoLMs) more overconfident than their corresponding pretrained language models (PLMs). Because task-specific labeled calibration data can be costly or unavailable, the corresponding PLM provides a natural label-free reference for post-hoc calibration. Prior agreement-gated PLM-referenced calibration fits a scalar temperature using only examples on which the PoLM and its PLM reference agree, excluding disagreement examples because direct alignment can drive the fitted temperature excessively high and induce under-confidence. We revisit this binary treatment. A controlled reintroduction diagnostic reveals a non monotonic aggregate effect: admitting a moderate fraction of disagreement examples can improve calibration, whereas the benefit diminishes as unit weight inclusion approaches the full disagreement set. We introduce SupportCal, a label-free post-hoc method that retains agreement examples at unit weight and assigns disagreement examples continuous weights based on the own-base PLM's relative support and corroboration from pretrained references selected from a size-compatible candidate pool. We further characterize when the resulting weighted objective admits a finite optimal temperature. Across MedMCQA and MathQA, SupportCal yields lower mean ECE than the agreement-only baseline for nearly all evaluated target-model configurations; supplementary TweetEval Sentiment results show the same pattern on a fixed-label classification task.