# Self-Calibrating Language Models via Test-Time Discriminative Distillation

arXiv: https://arxiv.org/abs/2604.09624 · HTML: https://mlsanity.com/paper/2604.09624/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 40 references that are in the map.
- First posted on arXiv 18 Mar 2026.

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

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [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)
- [Think you have Solved Question Answering? Try ARC, the AI2 Reasoning Challenge](https://mlsanity.com/paper/1803.05457/) (2018)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Phi-3 Technical Report: A Highly Capable Language Model Locally on Your Phone](https://mlsanity.com/paper/2404.14219/) (2024)
- [Towards Understanding Sycophancy in Language Models](https://mlsanity.com/paper/2310.13548/) (2023)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (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)
- [Continual Test-Time Domain Adaptation](https://mlsanity.com/paper/2203.13591/) (2022)
- [How Can We Know When Language Models Know? On the Calibration of Language Models for Question Answering](https://mlsanity.com/paper/2012.00955/) (2020)
- [Learning to (Learn at Test Time): RNNs with Expressive Hidden States](https://mlsanity.com/paper/2407.04620/) (2024)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [Self-Adapting Language Models](https://mlsanity.com/paper/2506.10943/) (2025)
- [Efficient Test-Time Scaling via Self-Calibration](https://mlsanity.com/paper/2503.00031/) (2025)
- [Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models](https://mlsanity.com/paper/2503.02623/) (2025)
- [LitCab: Lightweight Language Model Calibration over Short- and Long-form Responses](https://mlsanity.com/paper/2310.19208/) (2023)
- [Do LLMs estimate uncertainty well in instruction-following?](https://mlsanity.com/paper/2410.14582/) (2024)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)

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

- [Unsupervised Post-Training of Foundation Models: A Survey](https://mlsanity.com/paper/2608.24982/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are systematically overconfident: they routinely express high certainty on questions they often answer incorrectly. Existing calibration methods either require labeled validation data, degrade under distribution shifts, or incur substantial inference costs. Recent work has shown that LLMs already contain a better-calibrated signal than the one they verbalize: the token probability of "True" when the model is asked "Is this answer correct?" (P(True)) consistently outperforms their stated confidence, a gap that is theoretically grounded as generative error is lower-bounded by roughly twice the corresponding discriminative error. We introduce SECL (SElf-Calibrating Language Models), a test-time training (TTT) pipeline that exploits this gap as label-free self-supervision, requiring no labeled data or human supervision. SECL adapts only when the input distribution shifts, training on just 6--26% of the question stream at lower cost than the baseline it distills from. Across four small language models from three model families and four diverse domains, SECL reduces Expected Calibration Error (ECE) by 56--78%, outperforming its own supervision signal and matching or outperforming recent inference-time methods. SECL is the first method to apply TTT to calibration; seven ablations covering signal quality, gating strategy, weight accumulation, loss design, domain ordering, hyperparameter sensitivity, and layer selection confirm that each component is crucial and robust across configurations. Code: https://anonymous.4open.science/r/secl-emnlp26-submission-C890