# HalluZig: Hallucination Detection using Zigzag Persistence

arXiv: https://arxiv.org/abs/2601.01552 · HTML: https://mlsanity.com/paper/2601.01552/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 43 references that are in the map.
- First posted on arXiv 4 Jan 2026.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [TruthfulQA: Measuring How Models Mimic Human Falsehoods](https://mlsanity.com/paper/2109.07958/) (2021)
- [The Internal State of an LLM Knows When It's Lying](https://mlsanity.com/paper/2304.13734/) (2023)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)
- [RAGTruth: A Hallucination Corpus for Developing Trustworthy Retrieval-Augmented Language Models](https://mlsanity.com/paper/2401.00396/) (2023)
- [Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMs](https://mlsanity.com/paper/2406.15927/) (2024)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Fact-Checking the Output of Large Language Models via Token-Level Uncertainty Quantification](https://mlsanity.com/paper/2403.04696/) (2024)
- [Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similarities](https://mlsanity.com/paper/2405.20003/) (2024)
- [Fine-grained Hallucination Detection and Editing for Language Models](https://mlsanity.com/paper/2401.06855/) (2024)
- [Lookback Lens: Detecting and Mitigating Contextual Hallucinations in Large Language Models Using Only Attention Maps](https://mlsanity.com/paper/2407.07071/) (2024)
- [A Comprehensive Survey of Hallucination in Large Language, Image, Video and Audio Foundation Models](https://mlsanity.com/paper/2405.09589/) (2024)
- [Enhancing Uncertainty-Based Hallucination Detection with Stronger Focus](https://mlsanity.com/paper/2311.13230/) (2023)
- [HaloScope: Harnessing Unlabeled LLM Generations for Hallucination Detection](https://mlsanity.com/paper/2409.17504/) (2024)
- [Do Androids Know They're Only Dreaming of Electric Sheep?](https://mlsanity.com/paper/2312.17249/) (2023)
- [Hallucination Detection in LLMs Using Spectral Features of Attention Maps](https://mlsanity.com/paper/2502.17598/) (2025)
- [Hallucination Detection in LLMs with Topological Divergence on Attention Graphs](https://mlsanity.com/paper/2504.10063/) (2025)
- [Computing Zigzag Persistence on Graphs in Near-Linear Time](https://mlsanity.com/paper/2103.07353/) (2021)
- [Computing Zigzag Persistent Cohomology](https://mlsanity.com/paper/1608.06039/) (2016)

## Built on by (most cited first, 2 of 2)

- [CrossHallu: Do Hallucination Signals Generalize Across Languages and Domains in Large Language Model's Internals?](https://mlsanity.com/paper/2607.04029/) (2026)
- [Topological Signatures of Context-Level Reliability in TabPFN](https://mlsanity.com/paper/2607.17962/) (2026)

## Abstract (arXiv)

The factual reliability of Large Language Models (LLMs) remains a critical barrier to their adoption in high-stakes domains due to their propensity to hallucinate. Current detection methods often rely on surface-level signals from the model's output, overlooking the failures that occur within the model's internal reasoning process. In this paper, we introduce a new paradigm for hallucination detection by analyzing the dynamic topology of the evolution of model's layer-wise attention. We model the sequence of attention matrices as a zigzag graph filtration and use zigzag persistence, a tool from Topological Data Analysis, to extract a topological signature. Our core hypothesis is that factual and hallucinated generations exhibit distinct topological signatures. We validate our framework, HalluZig, on multiple benchmarks, demonstrating that it outperforms strong baselines. Furthermore, our analysis reveals that these topological signatures are generalizable across different models and hallucination detection is possible only using structural signatures from partial network depth.