Verbalized Confidence Triggers Self-Verification: Emergent Behavior Without Explicit Reasoning Supervision

TL;DR

This paper demonstrates that fine-tuning large language models with scalar confidence labels alone can induce self-verification behavior, improving calibration, accuracy, and interpretability without explicit reasoning supervision.

Contribution

It reveals that scalar confidence supervision alone can elicit self-verification in LLMs, a behavior previously thought to require explicit training signals.

Findings

Confidence-aware fine-tuning improves calibration and accuracy.

Models generate longer, self-checking responses for low-confidence queries.

Test-time scaling based on calibrated uncertainty boosts performance.

Abstract

Uncertainty calibration is essential for the safe deployment of large language models (LLMs), particularly when users rely on verbalized confidence estimates. While prior work has focused on classifiers or short-form generation, confidence calibration for chain-of-thought (CoT) reasoning remains largely unexplored. Surprisingly, we find that supervised fine-tuning with scalar confidence labels alone suffices to elicit self-verification behavior of language models, without any explicit reasoning supervision or reinforcement learning-based rewards. Despite being trained only to produce a verbalized confidence score without any self-verifying examples, the model learns to generate longer and self-checking responses for low-confidence queries while providing more concise answers for high-confidence ones. We further propose a simple rethinking method that boosts performance via test-time scaling based on calibrated uncertainty. Experiments on GSM8K and held-out reasoning tasks such as MATH-500 and ARC-Challenge show that our confidence-aware fine-tuning improves both calibration and accuracy, while also enhancing interpretability by aligning the model's reasoning path with its confidence.