# Calibrating LLMs with Semantic-level Reward

arXiv: https://arxiv.org/abs/2605.15588 · HTML: https://mlsanity.com/paper/2605.15588/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 27 references that are in the map.
- First posted on arXiv 15 May 2026.

## Builds on (most cited first, 20 of 20)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [MS MARCO: A Human Generated MAchine Reading COmprehension Dataset](https://mlsanity.com/paper/1611.09268/) (2016)
- [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)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [Beyond Binary Rewards: Training LMs to Reason About Their Uncertainty](https://mlsanity.com/paper/2507.16806/) (2025)
- [SaySelf: Teaching LLMs to Express Confidence with Self-Reflective Rationales](https://mlsanity.com/paper/2405.20974/) (2024)
- [On Verbalized Confidence Scores for LLMs](https://mlsanity.com/paper/2412.14737/) (2024)
- [Overconfidence is Key: Verbalized Uncertainty Evaluation in Large Language and Vision-Language Models](https://mlsanity.com/paper/2405.02917/) (2024)
- [Rewarding Doubt: A Reinforcement Learning Approach to Calibrated Confidence Expression of Large Language Models](https://mlsanity.com/paper/2503.02623/) (2025)
- [ConfTuner: Training Large Language Models to Express Their Confidence Verbally](https://mlsanity.com/paper/2508.18847/) (2025)

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

- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)

## Abstract (arXiv)

As large language models (LLMs) are deployed in consequential settings such as medical question answering and legal reasoning, the ability to estimate when their outputs are likely to be correct is essential for safe and reliable use, requiring well-calibrated uncertainty. Standard reinforcement learning with verifiable rewards (RLVR) trains models with a binary correctness reward that is indifferent to confidence, providing no penalty for confident but wrong predictions and thereby degrading calibration. Recent work addresses this by training models to produce verbalized confidence scores alongside answers and rewarding agreement with correctness. However, verbalized confidence is calibrated at the token level and thus exhibits inconsistency across textual variations with same semantic meaning. We propose Calibration with Semantic Reward (CSR), a framework that calibrates language models directly in semantic space without a verbalized confidence interface. CSR combines the correctness reward with a novel semantic calibration reward that encourages exploitation among correct rollouts by promoting semantic agreement, and exploration among incorrect ones by discouraging spurious consistency. Experiments across three model families on HotpotQA (in-distribution) and TriviaQA, MSMARCO, and NQ-Open (out-of-distribution) show that CSR consistently achieves lower ECE and higher AUROC than verbalized-confidence baselines across nearly all settings, reducing ECE by up to 40% and improving AUROC by up to 31% over verbalized-confidence baselines, with calibration behavior generalizing robustly across all four evaluation settings.