A Graph Signal Processing Framework for Hallucination Detection in Large Language Models
This work addresses hallucination detection in large language models, which is a critical issue for improving reliability in AI applications, though it appears incremental as it builds on existing spectral methods.
The authors tackled the problem of distinguishing factual reasoning from hallucinations in large language models by proposing a spectral analysis framework based on graph signal processing, achieving 88.75% accuracy in detection compared to 75% for baselines.
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.