Certainty Is Not Just Correctness: Rethinking Token-Level Certainty in LLM Reasoning

Large language models (LLMs) generate not only reasoning text, but also token-level confidence trajectories that record how uncertainty evolves during inference. Whether these trajectories are relevant to reasoning correctness remains unclear. Here we show that confidence trajectories encode a content-agnostic confidence geometry associated with trace-level final-answer correctness. Using only token-level confidence values, without access to the input question, reasoning text, hidden states, or external verifiers, we find that low-dimensional representations of confidence trajectories separate correct from incorrect reasoning traces. Across GSM8K, MATH, and MMLU, this geometric separation is quantitatively linked to downstream predictability: stronger clustering of correct and incorrect traces, measured by the Davies--Bouldin index, consistently corresponds to higher correctness-discrimination AUC. We further show that correctness-related information is enriched in the tail of reasoning, suggesting that late-stage confidence dynamics carry key correctness signals. We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation. Under a fixed trace budget, NeuralConf-derived scores improve confidence-weighted answer aggregation over majority voting, tail confidence, and other static baselines. These results reveal that LLMs expose trace-intrinsic statistical signals of correctness through their own confidence dynamics, offering a route to improve inference using information already present within generation.

Confidence is an estimate of the probability that a chosen answer is correct. Verbal confidence reports are widely used as uncertainty measures in large language models, but whether they are best understood as estimates of correctness is unclear. We test this with a two-stage abstention paradigm from the neuroscience of perceptual decision making: a model first answers and reports its confidence, then decides whether to commit it to a user or abstain. Across four non-reasoning models, prompt framings, and confidence formats, verbal confidence predicted the commit/abstain decision substantially better than whether the answer was correct. Calibrated token log-probabilities showed the opposite profile, with abstention-prediction coupled to correctness discrimination, the signature of an answer-evidence signal. After removing the variance verbal confidence shared with log-probabilities, the residual stayed aligned with commitment while its link to correctness fell to near chance. The dissociation generalised to four reasoning models across four benchmarks of varying difficulty, from hard multiple-choice to frontier-level freeform questions. Mechanistic analyses in Gemma 3 and 4 were convergent: a post-answer state known to causally support verbal-confidence generation already encoded the future abstention decision before the abstention prompt, organised mainly by that decision rather than by correctness, the two lying in approximately orthogonal directions in activation space. Steering along a verbal-confidence-specific direction causally shifted abstention. Verbal and log-probability confidence are thus not interchangeable: log-probabilities track answer evidence and correctness, whereas verbal confidence is better understood as a behaviour-facing readout of an internal commit-readiness state, challenging the practice of treating verbal reports as proxies for reliability.

A model should refuse two different things: answers it would get wrong, and questions it should not answer at all, such as unanswerable ones or ones resting on a false premise. The usual recipe thresholds a single confidence score, which cannot tell these apart. Across five instruction-tuned models from three families (2B to 14B), we find they are separate axes. Ordinary answer-confidence tracks whether an answer is right but is nearly blind to whether the question is answerable; a linear probe on hidden states does the reverse. The blind spot does not shrink with scale. It is worst on naturally occurring false-premise questions (CREPE). There, answer-confidence, P(IK), P(True), and even asking the model outright whether a premise is false all stay near chance, while a hidden-state probe reaches 0.69 to 0.77 AUROC: the model represents a problem it will not report. This turns out to be fixable. Instructing a model to check premises backfires, because it then disputes sound and false premises alike (57% false challenges), unable to tell them apart; routing the same instruction with the probe roughly triples challenge precision. We turn the two axes into a calibrated policy that answers only when an answerability score and a correctness score each clear a separately certifies behave differently: the unanswerable-answer rate is controllable at every scale, while the wrong-answer rate is capped by model accuracy, so the guarantee tightens as threshold policy certifies both budgets at 0.75 coverage of correct answers, against 0.31 for a single threshold; at 14B it is the only policy that certifies at all.