Measurement Validity and Representation Dynamics of Confidence Signals in Large Language Models

Abstract

Whether a language model "knows what it knows" matters for trustworthy deployment and for deciding when it should abstain. Prior work usually measures this through one channel: verbalized confidence, a linear probe on hidden states, or agreement among sampled answers (semantic entropy), and often treats these as interchangeable. We compare all three in a pre-registered audit of five Qwen2.5 models (0.5B-7B, including a base/instruct pair at 7B) on factual retrieval (PopQA, SimpleQA) and multi-step reasoning (GSM8K, MATH). First, probes trained on prefill states to predict whether sampled answers will disagree become informative earlier for retrieval (about 7% of layer depth on average) than for reasoning (about 28%). The pre-registered five-layer test supported this only marginally; a finer 21-layer follow-up, designed after those results, supports it more clearly. In most retrieval cells, however, a prompt-only TF-IDF classifier matches the probe, so the early signal may reflect surface features of the question. Second, verbalized confidence is unstable: slightly different prompt templates yield scores that barely correlate. Third, Expected Calibration Error is misleading: verbal confidence looks well calibrated because it clusters near the base rate while discriminating poorly, whereas sampling agreement has worse ECE but about twice the resolution. Of five pre-registered hypotheses, two were falsified, one was partly supported, one was not supported, and one could not be tested because the base model's verbal confidence was degenerate.