Large language model (LLM) agents that invoke external tools must make sequences of interdependent decisions, yet existing uncertainty quantification (UQ) methods treat each step in isolation, ignoring how confidence evolves and compounds across a full task trajectory.We propose a framework for trajectory-level confidence analysis in the tool-use agent setting. The thesis pursues three aims: (1) estimating action-level confidence by adapting step-wise UQ to the heterogeneous think-act-observe cycles of tool-using agents; (2) aggregating the diverse action space into semantically coherent action types to enable meaningful trajectory-level analysis; and (3) discovering temporal patterns in the resulting confidence trajectories that reliably predict task success or failure.We ground the work in standard tool-use benchmarks and expect the framework to expose early warning signals for agent failure and offer interpretable diagnostic tools for understanding when and why LLM agents lose confidence, with improved calibration of multi-step agentic pipelines as a secondary benefit.

Large Language Models (LLMs) have shown impressive performance in mathematical reasoning tasks when guided by Chain-of-Thought (CoT) prompting. However, they tend to produce highly confident yet incorrect outputs, which poses significant risks in domains like education, where users may lack the expertise to assess reasoning steps. To address this, we propose a structured framework that models stepwise confidence as a temporal signal and evaluates it using Signal Temporal Logic (STL). In particular, we define formal STL-based constraints to capture desirable temporal properties and compute robustness scores that serve as structured, interpretable confidence estimates. Our approach also introduces a set of uncertainty reshaping strategies to enforce smoothness, monotonicity, and causal consistency across the reasoning trajectory. Experiments show that our approach consistently improves calibration metrics and provides more reliable uncertainty estimates than conventional confidence aggregation and post-hoc calibration.