# LLM Uncertainty Quantification through Directional Entailment Graph and Claim Level Response Augmentation

arXiv: https://arxiv.org/abs/2407.00994 · HTML: https://mlsanity.com/paper/2407.00994/

## Key facts

- Cited by 23 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 31 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [TriviaQA: A Large Scale Distantly Supervised Challenge Dataset for Reading Comprehension](https://mlsanity.com/paper/1705.03551/) (2017)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [A Survey on Large Language Model based Autonomous Agents](https://mlsanity.com/paper/2308.11432/) (2023)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [A large annotated corpus for learning natural language inference](https://mlsanity.com/paper/1508.05326/) (2015)
- [A Review of Uncertainty Quantification in Deep Learning: Techniques, Applications and Challenges](https://mlsanity.com/paper/2011.06225/) (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)
- [CoQA: A Conversational Question Answering Challenge](https://mlsanity.com/paper/1808.07042/) (2018)
- [Trustworthy LLMs: a Survey and Guideline for Evaluating Large Language Models' Alignment](https://mlsanity.com/paper/2308.05374/) (2023)
- [Leak, Cheat, Repeat: Data Contamination and Evaluation Malpractices in Closed-Source LLMs](https://mlsanity.com/paper/2402.03927/) (2024)
- [LLMs Can't Plan, But Can Help Planning in LLM-Modulo Frameworks](https://mlsanity.com/paper/2402.01817/) (2024)
- [Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthiness](https://mlsanity.com/paper/2308.16175/) (2023)
- [Enhancing Visual-Language Modality Alignment in Large Vision Language Models via Self-Improvement](https://mlsanity.com/paper/2405.15973/) (2024)
- [Open-TI: Open Traffic Intelligence with Augmented Language Model](https://mlsanity.com/paper/2401.00211/) (2023)
- [Prompt to Transfer: Sim-to-Real Transfer for Traffic Signal Control with Prompt Learning](https://mlsanity.com/paper/2308.14284/) (2023)
- [FACT-GPT: Fact-Checking Augmentation via Claim Matching with LLMs](https://mlsanity.com/paper/2402.05904/) (2024)

## Built on by (most cited first, 23 of 23)

- [A Survey on Uncertainty Quantification of Large Language Models: Taxonomy, Open Research Challenges, and Future Directions](https://mlsanity.com/paper/2412.05563/) (2024)
- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [A Survey of Sim-to-Real Methods in RL: Progress, Prospects and Challenges with Foundation Models](https://mlsanity.com/paper/2502.13187/) (2025)
- [Understanding the Uncertainty of LLM Explanations: A Perspective Based on Reasoning Topology](https://mlsanity.com/paper/2502.17026/) (2025)
- [Uncertainty Quantification of Large Language Models through Multi-Dimensional Responses](https://mlsanity.com/paper/2502.16820/) (2025)
- [Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directions](https://mlsanity.com/paper/2510.12040/) (2025)
- [Generative AI in Transportation Planning: A Survey](https://mlsanity.com/paper/2503.07158/) (2025)
- [Every Response Counts: Quantifying Uncertainty of LLM-based Multi-Agent Systems through Tensor Decomposition](https://mlsanity.com/paper/2604.08708/) (2026)
- [Are LLM Uncertainty and Correctness Encoded by the Same Features? A Functional Dissociation via Sparse Autoencoders](https://mlsanity.com/paper/2604.19974/) (2026)
- [MCQA-Eval: Efficient Confidence Evaluation in NLG with Gold-Standard Correctness Labels](https://mlsanity.com/paper/2502.14268/) (2025)
- [TruthTorchLM: A Comprehensive Library for Predicting Truthfulness in LLM Outputs](https://mlsanity.com/paper/2507.08203/) (2025)
- [Conformal Feedback Alignment: Quantifying Answer-Level Reliability for Robust LLM Alignment](https://mlsanity.com/paper/2601.17329/) (2026)
- [Fine-Grained Uncertainty Quantification for Long-Form Language Model Outputs: A Comparative Study](https://mlsanity.com/paper/2602.17431/) (2026)
- [ConfAgents: A Conformal-Guided Multi-Agent Framework for Cost-Efficient Medical Diagnosis](https://mlsanity.com/paper/2508.04915/) (2025)
- [SIMBA UQ: Similarity-Based Aggregation for Uncertainty Quantification in Large Language Models](https://mlsanity.com/paper/2510.13836/) (2025)
- [ALARM: Automated MLLM-Based Anomaly Detection in Complex-EnviRonment Monitoring with Uncertainty Quantification](https://mlsanity.com/paper/2512.03101/) (2025)
- [Diagnosing Multi-step Reasoning Failures in Black-box LLMs via Stepwise Confidence Attribution](https://mlsanity.com/paper/2605.19228/) (2026)
- [The Origins of Stochasticity: Comprehensive Investigations on Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2606.22792/) (2026)
- [GE-Chat: A Graph Enhanced RAG Framework for Evidential Response Generation of LLMs](https://mlsanity.com/paper/2505.10143/) (2025)
- [The Sim-to-Real Gap of Foundation Model Agents: A Unified MDP Perspective](https://mlsanity.com/paper/2606.07017/) (2026)
- [Fact-Checking with Large Language Models via Probabilistic Certainty and Consistency](https://mlsanity.com/paper/2601.02574/) (2026)
- [Position: Uncertainty Quantification in LLMs is Just Unsupervised Clustering](https://mlsanity.com/paper/2605.19220/) (2026)
- [SpanUQ: Span-Level Uncertainty Quantification for Large Language Model Generation](https://mlsanity.com/paper/2607.05721/) (2026)

## Abstract (arXiv)

The Large language models (LLMs) have showcased superior capabilities in sophisticated tasks across various domains, stemming from basic question-answer (QA), they are nowadays used as decision assistants or explainers for unfamiliar content. However, they are not always correct due to the data sparsity in specific domain corpus, or the model's hallucination problems. Given this, how much should we trust the responses from LLMs? This paper presents a novel way to evaluate the uncertainty that captures the directional instability, by constructing a directional graph from entailment probabilities, and we innovatively conduct Random Walk Laplacian given the asymmetric property of a constructed directed graph, then the uncertainty is aggregated by the derived eigenvalues from the Laplacian process. We also provide a way to incorporate the existing work's semantics uncertainty with our proposed layer. Besides, this paper identifies the vagueness issues in the raw response set and proposes an augmentation approach to mitigate such a problem, we conducted extensive empirical experiments and demonstrated the superiority of our proposed solutions.