Training-Free Spectral Fingerprints of Voice Processing in Transformers

Different transformer architectures implement identical linguistic computations via distinct connectivity patterns, yielding model imprinted ``computational fingerprints'' detectable through spectral analysis. Using graph signal processing on attention induced token graphs, we track changes in algebraic connectivity (Fiedler value, $\Delta\lambda_2$) under voice alternation across 20 languages and three model families, with a prespecified early window (layers 2--5). Our analysis uncovers clear architectural signatures: Phi-3-Mini shows a dramatic English specific early layer disruption ($\overline{\Delta\lambda_2}_{[2,5]}\!\approx\!-0.446$) while effects in 19 other languages are minimal, consistent with public documentation that positions the model primarily for English use. Qwen2.5-7B displays small, distributed shifts that are largest for morphologically rich languages, and LLaMA-3.2-1B exhibits systematic but muted responses. These spectral signatures correlate strongly with behavioral differences (Phi-3: $r=-0.976$) and are modulated by targeted attention head ablations, linking the effect to early attention structure and confirming functional relevance. Taken together, the findings are consistent with the view that training emphasis can leave detectable computational imprints: specialized processing strategies that manifest as measurable connectivity patterns during syntactic transformations. Beyond voice alternation, the framework differentiates reasoning modes, indicating utility as a simple, training free diagnostic for revealing architectural biases and supporting model reliability analysis.

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

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.