Temporalizing Confidence: Evaluation of Chain-of-Thought Reasoning with Signal Temporal Logic

2025-06-09

AI Summary

Large language models (LLMs) rely on chain-of-thought (CoT) prompting for mathematical reasoning but frequently produce high-confidence incorrect answers—posing significant risks in safety-critical domains such as education. To address this, we introduce signal temporal logic (STL) for CoT confidence modeling for the first time, treating stepwise reasoning confidence as a temporal signal and formally encoding structural constraints—including smoothness, monotonicity, and causal consistency—to enable structured, interpretable uncertainty quantification. We propose an STL-based robustness scoring mechanism and an uncertainty recalibration strategy, substantially improving confidence calibration. Evaluated across multiple mathematical reasoning benchmarks, our approach outperforms conventional ensemble and post-hoc calibration methods, delivering more reliable and verifiable uncertainty estimates. This work establishes a novel paradigm for trustworthy AI reasoning through logically grounded, temporally aware confidence modeling.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Uncertainty Representations
• Natural Language Processing: Safety and Robustness

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

Abstract

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.

Problem

• Evaluating confidence in Chain-of-Thought reasoning steps
• Detecting incorrect but highly confident LLM outputs
• Improving reliability of uncertainty estimates in reasoning

Innovation

• Model stepwise confidence as temporal signal
• Evaluate confidence using Signal Temporal Logic
• Introduce uncertainty reshaping strategies