# Semantic Uncertainty Quantification of Hallucinations in LLMs: A Quantum Tensor Network Based Method

arXiv: https://arxiv.org/abs/2601.20026 · HTML: https://mlsanity.com/paper/2601.20026/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 40 of its 66 references that are in the map.
- First posted on arXiv 27 Jan 2026.

## Builds on (most cited first, 30 of 40)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [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 of Large Language Models](https://mlsanity.com/paper/2303.18223/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [The RefinedWeb Dataset for Falcon LLM: Outperforming Curated Corpora with Web Data, and Web Data Only](https://mlsanity.com/paper/2306.01116/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Latent Retrieval for Weakly Supervised Open Domain Question Answering](https://mlsanity.com/paper/1906.00300/) (2019)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [HaluEval: A Large-Scale Hallucination Evaluation Benchmark for Large Language Models](https://mlsanity.com/paper/2305.11747/) (2023)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Challenges and Applications of Large Language Models](https://mlsanity.com/paper/2307.10169/) (2023)
- [Charformer: Fast Character Transformers via Gradient-based Subword Tokenization](https://mlsanity.com/paper/2106.12672/) (2021)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Truthful AI: Developing and governing AI that does not lie](https://mlsanity.com/paper/2110.06674/) (2021)
- [Unsupervised Real-Time Hallucination Detection based on the Internal States of Large Language Models](https://mlsanity.com/paper/2403.06448/) (2024)
- [RealFormer: Transformer Likes Residual Attention](https://mlsanity.com/paper/2012.11747/) (2020)
- [SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Models](https://mlsanity.com/paper/2403.02509/) (2024)
- [Identifying and Mitigating Vulnerabilities in LLM-Integrated Applications](https://mlsanity.com/paper/2311.16153/) (2023)
- [Detecting Hallucinations in Large Language Model Generation: A Token Probability Approach](https://mlsanity.com/paper/2405.19648/) (2024)
- [Chain of Natural Language Inference for Reducing Large Language Model Ungrounded Hallucinations](https://mlsanity.com/paper/2310.03951/) (2023)
- [Wat zei je? Detecting Out-of-Distribution Translations with Variational Transformers](https://mlsanity.com/paper/2006.08344/) (2020)
- [Beyond Semantic Entropy: Boosting LLM Uncertainty Quantification with Pairwise Semantic Similarity](https://mlsanity.com/paper/2506.00245/) (2025)

## Built on by (most cited first, 7 of 7)

- [HALT: Hallucination Assessment via Log-probs as Time series](https://mlsanity.com/paper/2602.02888/) (2026)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [Towards Generation-Efficient Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2605.06053/) (2026)
- [When Confidence Takes the Wrong Path: Diagnosing Retrieval-State Lock-In in RAG](https://mlsanity.com/paper/2606.22728/) (2026)
- [Do LLMs Understand Context? A Knowledge Graph-Based Evaluation Framework](https://mlsanity.com/paper/2609.30484/) (2026)
- [Spectral Geometry of Attention: From Information Routing to Uncertainty](https://mlsanity.com/paper/2610.06012/) (2026)
- [Embedding Graph Kernel Entropy (EGKE): Fine-grained Hallucination Detection for LLMs from Embeddings](https://mlsanity.com/paper/2610.14214/) (2026)

## Abstract (arXiv)

Large language models (LLMs) exhibit strong generative capabilities but remain vulnerable to confabulations, fluent yet unreliable outputs that vary arbitrarily even under identical prompts. Leveraging a quantum tensor network based pipeline, we propose a quantum physics inspired uncertainty quantification framework that accounts for aleatoric uncertainty in token sequence probability for semantic equivalence based clustering of LLM generations. This offers a principled and interpretable scheme for hallucination detection. We further introduce an entropy maximization strategy that prioritizes high certainty, semantically coherent outputs and highlights entropy regions where LLM decisions are likely to be unreliable, offering practical guidelines for when human oversight is warranted. We evaluate the robustness of our scheme under different generation lengths and quantization levels, dimensions overlooked in prior studies, demonstrating that our approach remains reliable even in resource constrained deployments. A total of 116 experiments on TriviaQA, NQ, SVAMP, and SQuAD across multiple architectures including Mistral-7B, Mistral-7B-instruct, Falcon-rw-1b, LLaMA-3.2-1b, LLaMA-2-13b-chat, LLaMA-2-7b-chat, LLaMA-2-13b, and LLaMA-2-7b show consistent improvements in AUROC and AURAC over state of the art baselines.