Distilling Self-Consistency into Verbal Confidence: A Pre-Registered Negative Result and Post-Hoc Rescue on Gemma 3 4B

Verbal confidence elicitation is widely used to extract uncertainty estimates from LLMs. We tested whether seven instruction-tuned open-weight models (3-9B parameters, four families) produce verbalised confidence that meets minimal validity criteria for item-level Type-2 discrimination under minimal numeric elicitation with greedy decoding. In a pre-registered study (OSF: osf.io/azbvx), 524 TriviaQA items were administered under numeric (0-100) and categorical (10-class) elicitation to eight models at Q5_K_M quantisation on consumer hardware, yielding 8,384 deterministic trials. A psychometric validity screen was applied to each model-format cell. All seven instruct models were classified Invalid on numeric confidence (H2 confirmed, 7/7 vs. predicted >=4/7), with a mean ceiling rate of 91.7% (H1 confirmed). Categorical elicitation did not rescue validity. Instead, it disrupted task performance in six of seven models, producing accuracy below 5% (H4 not confirmed). Token-level logprobability did not usefully predict verbalised confidence under the observed variance regime (H5 confirmed, mean cross-validated R^2 < 0.01). Within the reasoning-distilled model, reasoning-trace length showed a strong negative partial correlation with confidence (rho = -0.36, p < .001), consistent with the Reasoning Contamination Effect. These results do not imply that internal uncertainty representations are absent. They show that minimal verbal elicitation fails to preserve internal signals at the output interface in this model-size regime. Psychometric screening should precede any downstream use of such signals.

Large language models often express high confidence in answers that are wrong. Standard calibration remedies typically act globally or at the score level, reducing unwarranted confidence but also risking erosion of warranted confidence on correct answers. We introduce Probe-Conditioned Head Intervention (PCHI), an inference-time method that uses a frozen probe to detect likely wrong-but-confident responses and conditionally rescales downstream attention-head outputs during confidence generation. On Qwen3-4B-Instruct solving OpenMathInstruct problems with a structured binary confidence field, readout-token PCHI converts 82.2% of originally wrong-yes confidence readouts to $\texttt{no}$, while a joint intervention across upstream confidence-template tokens reduces ECE from 21.9% to 9.2% and damages only 5.1% of originally correct-yes readouts. The readout-token effect also appears on Gemma3-4B, though upstream interventions are weaker and more mask-dependent. These results show that verbalized overconfidence can be selectively reduced through conditionally applied internal intervention, partially decoupling the suppression of unwarranted confidence from the loss of warranted confidence.

Large language models (LLMs) often produce answers with high certainty even when they are incorrect, making reliable confidence estimation essential for deployment in real-world scenarios. Verbalized confidence, where models explicitly state their confidence in natural language, provides a flexible and user-facing uncertainty signal that can be applied even when token logits are unavailable. However, existing verbalized-confidence methods often optimize answer generation and confidence generation jointly, which can cause confidence-alignment objectives to interfere with answer accuracy. In this work, we propose a decoupled and order-aware framework for verbalized confidence calibration. Our method first generates an answer and then estimates confidence conditioned on the fixed question--answer pair, allowing confidence optimization without directly perturbing the answer-generation process. To align confidence with correctness likelihood, we construct a sampling-based surrogate from multiple model completions and optimize rank-based reinforcement learning objectives that encourage responses with higher estimated correctness likelihood to receive higher verbalized confidence. Experiments on reasoning and knowledge-intensive benchmarks show that our method improves calibration and failure prediction performance while largely preserving answer accuracy. These results demonstrate that verbalized confidence can be more reliably aligned by decoupling confidence estimation from answer generation and optimizing the relative ordering of confidence across responses.