通过分析模型自动生成的置信度轨迹,可精准判断推理过程对错。
Confidence Geometry Reveals Trace-Level Correctness in Large Language Model Reasoning

- 利用置信度轨迹构建低维几何结构,区分正确与错误推理路径。
- 在GSM8K、MATH、MMLU上,几何分离度越高,预测准确率越强。
- 后期置信度变化蕴含关键正确性信号,适合用于轻量级评估系统。
大型语言模型(LLMs)不仅生成推理文本,还记录推理过程中每个标记的置信度轨迹。这些轨迹是否反映推理正确性尚不明确。本文发现,置信度轨迹编码了与内容无关的置信度几何结构,与推理痕迹的最终答案正确性相关。仅使用标记级置信度值,无需输入问题、推理文本、隐藏状态或外部验证器,我们发现置信度轨迹的低维表示能有效分离正确与错误推理痕迹。在GSM8K、MATH和MMLU数据集上,这种几何分离度(以Davies-Bouldin指数衡量)与下游预测能力(正确性区分的AUC)呈定量正相关。进一步表明,正确性信息集中于推理末期,晚期置信度动态承载关键信号。为此提出NeuralConf,一种从置信度轨迹中学习的轻量级正确性估计器。在固定推理痕迹预算下,其得分优于多数投票、尾部置信度等静态基线,在加权答案聚合中表现更优。结果表明,LLMs通过自身置信度动态暴露了内在的正确性统计信号,为利用生成过程中的已有信息提升推理性能提供了新路径。
原文摘要 · Abstract (English)
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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