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arXiv · 2508.19366

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

Supratik Sarkar·Swagatam Das
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Abstract

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.

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Supratik Sarkar, Swagatam Das. 2025-08-26. Grounding the Ungrounded: A Spectral-Graph Framework for Quantifying Hallucinations in Multimodal LLMs. https://arxiv.org/abs/2508.19366

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