Grounding the Ungrounded: A Spectral-Graph Framework for Quantifying Hallucinations in Multimodal LLMs

We present a rigorous information-geometric framework, grounded in diffusion dynamics, to quantify hallucinations in MLLMs where model outputs are embedded via spectral decompositions of multimodal graph Laplacians, and their gaps to a truth manifold define a semantic distortion metric. We derive Courant-Fischer bounds on a temperature-dependent hallucination profile and use RKHS eigen-modes to obtain modality-aware, interpretable measures that track evolution over prompts and time.