SAGE: Answer-Conditioned Uncertainty Targets for Verbal Uncertainty Alignment

• URL: http://arxiv.org/abs/2606.11512v1
• Date: Tue, 09 Jun 2026 23:17:16 GMT
• Title: SAGE: Answer-Conditioned Uncertainty Targets for Verbal Uncertainty Alignment
• Abstract summary: We propose a group-level uncertainty target that constructs an answer-conditioned uncertainty geometry over sampled responses.<n>Experiments show improved uncertainty ranking, lower calibration error, and reduced overconfidence.
• Score: 20.5795766462733
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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