# Language Model Uncertainty Quantification with Attention Chain

arXiv: https://arxiv.org/abs/2503.19168 · HTML: https://mlsanity.com/paper/2503.19168/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 37 of its 45 references that are in the map.
- First posted on arXiv 24 Mar 2025.

## Builds on (most cited first, 30 of 37)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Measuring Mathematical Problem Solving With the MATH Dataset](https://mlsanity.com/paper/2103.03874/) (2021)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Neural Machine Translation by Jointly Learning to Align and Translate](https://mlsanity.com/paper/1409.0473/) (2014)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Deep contextualized word representations](https://mlsanity.com/paper/1802.05365/) (2018)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [Effective Approaches to Attention-based Neural Machine Translation](https://mlsanity.com/paper/1508.04025/) (2015)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Generating with Confidence: Uncertainty Quantification for Black-box Large Language Models](https://mlsanity.com/paper/2305.19187/) (2023)
- [Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Models](https://mlsanity.com/paper/2307.01379/) (2023)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Decomposing Uncertainty for Large Language Models through Input Clarification Ensembling](https://mlsanity.com/paper/2311.08718/) (2023)
- [Rejection Improves Reliability: Training LLMs to Refuse Unknown Questions Using RL from Knowledge Feedback](https://mlsanity.com/paper/2403.18349/) (2024)

## Built on by (most cited first, 14 of 14)

- [Detection and Mitigation of Hallucination in Large Reasoning Models: A Mechanistic Perspective](https://mlsanity.com/paper/2505.12886/) (2025)
- [From Calibration to Collaboration: LLM Uncertainty Quantification Should Be More Human-Centered](https://mlsanity.com/paper/2506.07461/) (2025)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [United Minds or Isolated Agents? Exploring Coordination of LLMs under Cognitive Load Theory](https://mlsanity.com/paper/2506.06843/) (2025)
- [Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2601.13368/) (2026)
- [HalluSAE: Detecting Hallucinations in Large Language Models via Sparse Auto-Encoders](https://mlsanity.com/paper/2604.16430/) (2026)
- [Entropy-Guided Loop: Achieving Reasoning through Uncertainty-Aware Generation](https://mlsanity.com/paper/2509.00079/) (2025)
- [The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2606.22792/) (2026)
- [Uncertainty Quantification for Computer-Use Agents: A Benchmark across Vision-Language Models and GUI Grounding Datasets](https://mlsanity.com/paper/2606.25760/) (2026)
- [GRADE: Probing Knowledge Gaps in LLMs through Gradient Subspace Dynamics](https://mlsanity.com/paper/2604.02830/) (2026)
- [Monitoring Web Agents Without Internal Signals: Observable Trajectories and Key-Step Supervision](https://mlsanity.com/paper/2609.02057/) (2026)
- [Detecting Hallucinations in Large Language Models via Internal Attention Divergence Signals](https://mlsanity.com/paper/2605.05025/) (2026)
- [Reverse Probing: Supervised Token-level Uncertainty Quantification for Large Language Models in Clinical Text](https://mlsanity.com/paper/2605.28740/) (2026)

## Abstract (arXiv)

Accurately quantifying a large language model's (LLM) predictive uncertainty is crucial for judging the reliability of its answers. While most existing research focuses on short, directly answerable questions with closed-form outputs (e.g., multiple-choice), involving intermediate reasoning steps in LLM responses is increasingly important. This added complexity complicates uncertainty quantification (UQ) because the probabilities assigned to answer tokens are conditioned on a vast space of preceding reasoning tokens. Direct marginalization is infeasible, and the dependency inflates probability estimates, causing overconfidence in UQ. To address this, we propose UQAC, an efficient method that narrows the reasoning space to a tractable size for marginalization. UQAC iteratively constructs an "attention chain" of tokens deemed "semantically crucial" to the final answer via a backtracking procedure. Starting from the answer tokens, it uses attention weights to identify the most influential predecessors, then iterates this process until reaching the input tokens. The resulting chain is further refined with similarity filtering and probability thresholding, which reduce the reasoning space, facilitating the approximation of the marginal answer token probabilities. We validate UQAC on multiple reasoning benchmarks with advanced open-source LLMs, demonstrating that it consistently delivers reliable UQ estimates with high computational efficiency.