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

TL;DR

This paper demonstrates that token-level confidence trajectories in large language models encode meaningful signals about reasoning correctness, enabling improved evaluation and aggregation without external tools.

Contribution

It introduces a geometric analysis of confidence trajectories and NeuralConf, a new method for correctness estimation based solely on confidence data.

Findings

Confidence trajectories separate correct from incorrect reasoning traces.

Stronger clustering of correct and incorrect traces correlates with higher correctness.

Tail confidence signals carry key information for correctness evaluation.

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.