# SAGE: Answer-Conditioned Uncertainty Targets for Verbal Uncertainty Alignment

arXiv: https://arxiv.org/abs/2606.11512 · HTML: https://mlsanity.com/paper/2606.11512/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in LLM preference optimization methods, one of 10 directions in LLM alignment / RLHF / preference optimisation.
- Builds on 28 of its 42 references that are in the map.
- First posted on arXiv 9 Jun 2026.

## Placed in

- LLM alignment / RLHF / preference optimisation / [LLM preference optimization methods](https://mlsanity.com/alignment/llm-preference-optimization-methods/)

## Builds on (most cited first, 28 of 28)

- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [MMLU-Pro: A More Robust and Challenging Multi-Task Language Understanding Benchmark](https://mlsanity.com/paper/2406.01574/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [LM-Polygraph: Uncertainty Estimation for Language Models](https://mlsanity.com/paper/2311.07383/) (2023)
- [Language Model Cascades: Token-level uncertainty and beyond](https://mlsanity.com/paper/2404.10136/) (2024)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [The Obvious Invisible Threat: LLM-Powered GUI Agents' Vulnerability to Fine-Print Injections](https://mlsanity.com/paper/2504.11281/) (2025)
- [CLEAR: Towards Contextual LLM-Empowered Privacy Policy Analysis and Risk Generation for Large Language Model Applications](https://mlsanity.com/paper/2410.13387/) (2024)
- [AgentRouter: A Knowledge-Graph-Guided LLM Router for Collaborative Multi-Agent Question Answering](https://mlsanity.com/paper/2510.05445/) (2025)
- [Adaptive Testing for LLM Evaluation: A Psychometric Alternative to Static Benchmarks](https://mlsanity.com/paper/2511.04689/) (2025)
- [Finetuning Language Models to Emit Linguistic Expressions of Uncertainty](https://mlsanity.com/paper/2409.12180/) (2024)
- [AutoData: A Multi-Agent System for Open Web Data Collection](https://mlsanity.com/paper/2505.15859/) (2025)
- [Deliberate Reasoning in Language Models as Structure-Aware Planning with an Accurate World Model](https://mlsanity.com/paper/2410.03136/) (2024)
- [LoVeC: Reinforcement Learning for Better Verbalized Confidence in Long-Form Generations](https://mlsanity.com/paper/2505.23912/) (2025)
- [MAPRO: Recasting Multi-Agent Prompt Optimization as Maximum a Posteriori Inference](https://mlsanity.com/paper/2510.07475/) (2025)
- [EvolveRouter: Co-Evolving Routing and Prompt for Multi-Agent Question Answering](https://mlsanity.com/paper/2604.05149/) (2026)
- [ChefFusion: Multimodal Foundation Model Integrating Recipe and Food Image Generation](https://mlsanity.com/paper/2409.12010/) (2024)
- [Graph-based Uncertainty Metrics for Long-form Language Model Outputs](https://mlsanity.com/paper/2410.20783/) (2024)
- [NG-Router: Graph-Supervised Multi-Agent Collaboration for Nutrition Question Answering](https://mlsanity.com/paper/2510.09854/) (2025)
- [Verbalized Confidence Triggers Self-Verification: Emergent Behavior Without Explicit Reasoning Supervision](https://mlsanity.com/paper/2506.03723/) (2025)
- [Drift-Bench: Diagnosing Cooperative Breakdowns in LLM Agents under Input Faults via Multi-Turn Interaction](https://mlsanity.com/paper/2602.02455/) (2026)
- [GLEN-Bench: A Graph-Language based Benchmark for Nutritional Health](https://mlsanity.com/paper/2601.18106/) (2026)
- [Why Semantic Entropy Fails: Geometry-Aware and Calibrated Uncertainty for Policy Optimization](https://mlsanity.com/paper/2605.21801/) (2026)

## Built on by (most cited first, 3 of 3)

- [Optimizing What Policies Learn From: Recoverability-aware Rollout Intervention Learning](https://mlsanity.com/paper/2608.05080/) (2026)
- [On the Pitfalls of Verbalized Confidence Priors for Calibrating Large Reasoning Models](https://mlsanity.com/paper/2609.32470/) (2026)
- [CLEAT: Learning Value-Guided Clarification for Interactive Agents](https://mlsanity.com/paper/2610.12655/) (2026)

## Abstract (arXiv)

Large language models increasingly express uncertainty through natural-language statements, yet these expressions often fail to reflect the model's sampled behavior. We study verbal uncertainty alignment as a distributional calibration problem: the appropriate uncertainty target for a prompt should be estimated from repeated model outputs rather than from an isolated response. However, group rollouts alone are insufficient, since the resulting target must provide a useful training signal. Existing targets only partially satisfy this requirement. We propose SAGE, Semantic-Answer Guided Entropy, a group-level uncertainty target that constructs an answer-conditioned uncertainty geometry over sampled responses. SAGE preserves categorical, numeric, and symbolic answer distinctions while maintaining a smooth and scale-preserving calibration signal. We further apply this target through Group-Uncertainty Preference Optimization, or GUPO, an uncertainty-channel training framework that supervises verbal uncertainty expressions rather than the full response. Experiments across factual, mathematical, and multiple-choice reasoning tasks show improved uncertainty ranking, lower calibration error, and reduced overconfidence.