Hallucinations in LLMs--especially in multimodal settings--undermine reliability. 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 eigenmodes to obtain modality-aware, interpretable measures that track evolution over prompts and time. This reframes hallucination as quantifiable and bounded, providing a principled basis for evaluation and mitigation.
Cite
@article{arxiv.2508.19366,
title = {Grounding the Ungrounded: A Spectral-Graph Framework for Quantifying Hallucinations in Multimodal LLMs},
author = {Supratik Sarkar and Swagatam Das},
journal= {arXiv preprint arXiv:2508.19366},
year = {2025}
}