# Confidence over Time: Confidence Calibration with Temporal Logic for Large Language Model Reasoning

arXiv: https://arxiv.org/abs/2601.13387 · HTML: https://mlsanity.com/paper/2601.13387/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 10 of its 51 references that are in the map.
- First posted on arXiv 19 Jan 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 10 of 10)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [HyperNetworks](https://mlsanity.com/paper/1609.09106/) (2016)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Neural-Symbolic Computing: An Effective Methodology for Principled Integration of Machine Learning and Reasoning](https://mlsanity.com/paper/1905.06088/) (2019)
- [Enforcing Temporal Constraints for LLM Agents](https://mlsanity.com/paper/2512.23738/) (2025)
- [Confidence Modeling for Neural Semantic Parsing](https://mlsanity.com/paper/1805.04604/) (2018)
- [Principled Detection of Hallucinations in Large Language Models via Multiple Testing](https://mlsanity.com/paper/2508.18473/) (2025)

## Built on by (most cited first, 4 of 4)

- [Large Language Models Decide Early and Explain Later](https://mlsanity.com/paper/2604.22266/) (2026)
- [Quantifying Faithful Confidence Expression in Large Reasoning Models](https://mlsanity.com/paper/2606.03969/) (2026)
- [Chronofy: A Temporal-Logical Decay Architecture for Information Validity in Time-Aware Retrieval-Augmented Generation](https://mlsanity.com/paper/2607.20560/) (2026)
- [Learning More by Training Less: Uncertainty-Guided Progressive Contraction for Efficient Reasoning Post-Training](https://mlsanity.com/paper/2610.12933/) (2026)

## Abstract (arXiv)

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.