Confidence Geometry Reveals Trace-Level Correctness in Large Language Model Reasoning

• URL: http://arxiv.org/abs/2605.16824v1
• Date: Sat, 16 May 2026 05:57:00 GMT
• Title: Confidence Geometry Reveals Trace-Level Correctness in Large Language Model Reasoning
• Abstract summary: We show that confidence trajectories separate correct from incorrect reasoning traces.<n> correctness-related information is enriched in the tail of reasoning.<n>We propose NeuralConf, a lightweight estimator that learns from confidence trajectories for correctness evaluation.
• Score: 5.094079537924077
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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