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

TL;DR

This paper introduces a spectral graph analysis framework for detecting hallucinations in large language models, revealing distinct spectral patterns associated with different error types and achieving high detection accuracy.

Contribution

It proposes a novel graph signal processing approach to model transformer layers and identify hallucinations, providing theoretical insights and practical detection methods.

Findings

Factual statements show low-frequency spectral convergence.

Hallucination types have distinct spectral signatures.

Spectral analysis achieves 88.75% detection accuracy.

Abstract

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.