# A Graph Signal Processing Framework for Hallucination Detection in Large Language Models

arXiv: https://arxiv.org/abs/2510.19117 · HTML: https://mlsanity.com/paper/2510.19117/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 30 references that are in the map.
- First posted on arXiv 21 Oct 2025.

## Builds on (most cited first, 18 of 18)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Qwen Technical Report](https://mlsanity.com/paper/2309.16609/) (2023)
- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [A Survey on Hallucination in Large Language Models: Principles, Taxonomy, Challenges, and Open Questions](https://mlsanity.com/paper/2311.05232/) (2023)
- [Attention is not Explanation](https://mlsanity.com/paper/1902.10186/) (2019)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Siren's Song in the AI Ocean: A Survey on Hallucination in Large Language Models](https://mlsanity.com/paper/2309.01219/) (2023)
- [Transformer Interpretability Beyond Attention Visualization](https://mlsanity.com/paper/2012.09838/) (2020)
- [Knowledge Neurons in Pretrained Transformers](https://mlsanity.com/paper/2104.08696/) (2021)
- [Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth](https://mlsanity.com/paper/2103.03404/) (2021)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [Analysis Methods in Neural Language Processing: A Survey](https://mlsanity.com/paper/1812.08951/) (2018)
- [Factuality Enhanced Language Models for Open-Ended Text Generation](https://mlsanity.com/paper/2206.04624/) (2022)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [A Primer on Neural Network Models for Natural Language Processing](https://mlsanity.com/paper/1510.00726/) (2015)
- [Discrete Signal Processing on Graphs: Frequency Analysis](https://mlsanity.com/paper/1307.0468/) (2013)
- [Transformers are Graph Neural Networks](https://mlsanity.com/paper/2506.22084/) (2025)

## Built on by (most cited first, 3 of 3)

- [HalluSAE: Detecting Hallucinations in Large Language Models via Sparse Auto-Encoders](https://mlsanity.com/paper/2604.16430/) (2026)
- [Spectral Guardrails for Agents in the Wild: Detecting Tool Use Hallucinations via Attention Topology](https://mlsanity.com/paper/2602.08082/) (2026)
- [Spectral Geometry of Attention: From Information Routing to Uncertainty](https://mlsanity.com/paper/2610.06012/) (2026)

## Abstract (arXiv)

Large language models achieve impressive results but distinguishing factual reasoning from hallucinations remains challenging. We propose a spectral analysis framework that models transformer layers as dynamic graphs induced by attention, with token embeddings as signals on these graphs. Through graph signal processing, we define diagnostics including Dirichlet energy, spectral entropy, and high-frequency energy ratios, with theoretical connections to computational stability. Experiments across GPT architectures suggest universal spectral patterns: factual statements exhibit consistent "energy mountain" behavior with low-frequency convergence, while different hallucination types show distinct signatures. Logical contradictions destabilize spectra with large effect sizes (g>1.0), semantic errors remain stable but show connectivity drift, and substitution hallucinations display intermediate perturbations. A simple detector using spectral signatures achieves 88.75% accuracy versus 75% for perplexity-based baselines, demonstrating practical utility. These findings indicate that spectral geometry may capture reasoning patterns and error behaviors, potentially offering a framework for hallucination detection in large language models.