Large Language Models (LLMs) increasingly rely on long-form, multi-step reasoning to solve complex tasks such as mathematical problem solving and scientific question answering. Despite strong performance, existing confidence estimation methods typically reduce an entire reasoning process to a single scalar score, ignoring how confidence evolves throughout the generation. As a result, these methods are often sensitive to superficial factors such as response length or verbosity, and struggle to distinguish correct reasoning from confidently stated errors. We propose to characterize the stepwise confidence signal using Signal Temporal Logic (STL). Using a discriminative STL mining procedure, we discover temporal formulas that distinguish confidence signals of correct and incorrect responses. Our analysis found that the STL patterns generalize across tasks, and numeric parameters exhibit sensitivity to individual questions. Based on these insights, we develop a confidence estimation approach that informs STL blocks with parameter hypernetworks. Experiments on multiple reasoning tasks show our confidence scores are more calibrated than the baselines.

翻译：大语言模型（LLMs）日益依赖长文本、多步骤的推理来解决复杂任务，如数学问题求解和科学问答。尽管性能优异，现有的置信度估计方法通常将整个推理过程简化为单一标量分数，忽略了置信度在生成过程中的动态演变。因此，这些方法往往对回答长度或表述冗余等表面因素敏感，难以区分正确推理与自信陈述的错误。我们提出使用时序信号逻辑（STL）来刻画逐步置信度信号。通过一种判别式STL挖掘流程，我们发现了能够区分正确与错误回答置信度信号的时序逻辑公式。分析表明，STL模式在不同任务间具有泛化性，而数值参数则对具体问题表现出敏感性。基于这些发现，我们开发了一种置信度估计方法，通过参数超网络为STL模块提供信息。在多个推理任务上的实验表明，我们的置信度评分比基线方法具有更好的校准性。