# Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models

arXiv: https://arxiv.org/abs/2601.13368 · HTML: https://mlsanity.com/paper/2601.13368/

## Key facts

- Cited by 5 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 20 of its 22 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, 20 of 20)

- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [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)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [Chain of Thought Monitorability: A New and Fragile Opportunity for AI Safety](https://mlsanity.com/paper/2507.11473/) (2025)
- [Evaluating the Performance of Large Language Models on GAOKAO Benchmark](https://mlsanity.com/paper/2305.12474/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [CLadder: Assessing Causal Reasoning in Language Models](https://mlsanity.com/paper/2312.04350/) (2023)
- [LUQ: Long-text Uncertainty Quantification for LLMs](https://mlsanity.com/paper/2403.20279/) (2024)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [UProp: Investigating the Uncertainty Propagation of LLMs in Multi-Step Agentic Decision-Making](https://mlsanity.com/paper/2506.17419/) (2025)
- [Understanding the Uncertainty of LLM Explanations: A Perspective Based on Reasoning Topology](https://mlsanity.com/paper/2502.17026/) (2025)
- [AdaptiveStep: Automatically Dividing Reasoning Step through Model Confidence](https://mlsanity.com/paper/2502.13943/) (2025)
- [On the Efficacy of Sampling Adapters](https://mlsanity.com/paper/2307.03749/) (2023)
- [Language Model Uncertainty Quantification with Attention Chain](https://mlsanity.com/paper/2503.19168/) (2025)
- [MMBoundary: Advancing MLLM Knowledge Boundary Awareness through Reasoning Step Confidence Calibration](https://mlsanity.com/paper/2505.23224/) (2025)
- [Temporalizing Confidence: Evaluation of Chain-of-Thought Reasoning with Signal Temporal Logic](https://mlsanity.com/paper/2506.08243/) (2025)
- [Zero-shot Safety Prediction for Autonomous Robots with Foundation World Models](https://mlsanity.com/paper/2404.00462/) (2024)
- [Language-Enhanced Latent Representations for Out-of-Distribution Detection in Autonomous Driving](https://mlsanity.com/paper/2405.01691/) (2024)

## Built on by (most cited first, 5 of 5)

- [Entropy trajectory shape predicts LLM reasoning reliability: A diagnostic study of uncertainty dynamics in chain-of-thought](https://mlsanity.com/paper/2603.18940/) (2026)
- [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)
- [From Sequence to Structure: Relational Uncertainty Propagation for LLM Agents](https://mlsanity.com/paper/2608.16002/) (2026)
- [Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains](https://mlsanity.com/paper/2610.20328/) (2026)

## Abstract (arXiv)

As reasoning modules, such as the chain-of-thought mechanism, are applied to large language models, they achieve strong performance on various tasks such as answering common-sense questions and solving math problems. The main challenge now is to assess the uncertainty of answers, which can help prevent misleading or serious hallucinations for users. Although current methods analyze long reasoning sequences by filtering unrelated tokens and examining potential connections between nearby tokens or sentences, the temporal spread of confidence is often overlooked. This oversight can lead to inflated overall confidence, even when earlier steps exhibit very low confidence. To address this issue, we propose a novel method that incorporates inter-step attention to analyze semantic correlations across steps. For handling long-horizon responses, we introduce a hidden confidence mechanism to retain historical confidence information, which is then combined with stepwise confidence to produce a more accurate overall estimate. We evaluate our method on the GAOKAO math benchmark and the CLadder causal reasoning dataset using mainstream open-source large language models. Our approach is shown to outperform state-of-the-art methods by achieving a superior balance between predictive quality and calibration, demonstrated by strong performance on both Negative Log-Likelihood and Expected Calibration Error.