This paper aims to address the hallucination phenomenon in large-scale language models (LLMs), a fundamental challenge in the development of reliable AI, particularly in high-risk multimodal domains such as medicine, law, and finance. We propose a rigorous information-geometric framework to quantify the hallucination phenomenon in multimodal LLMs (MLLMs), overcoming the limitations of existing evaluation techniques that rely on qualitative benchmarking or ad hoc mitigations. This study represents the output of MLLMs as a spectral embedding based on the multimodal graph Laplacian and characterizes the manifold gap between truth and inconsistency as a semantic distortion. This establishes a narrow Rayleigh-Ritz bound on the multimodal hallucination energy as a function of time-dependent temperature profiles. Leveraging eigenmode decomposition in the replay kernel Hilbert space (RKHS) embedding, we provide a modality-aware and theoretically interpretable metric that captures the evolution of hallucinations over time and with input prompts.
