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Existing large language models (LLMs) are known for generating "hallucinated"content, namely a fabricated text of plausibly looking, yet unfounded, facts.To identify when these hallucination scenarios occur, we examine the propertiesof the generated text in the embedding space. Specifically, we draw inspirationfrom the dynamic mode decomposition (DMD) tool in analyzing the patternevolution of text embeddings across sentences. We empirically demonstrate howthe spectrum of sentence embeddings over paragraphs is constantly low-rank forthe generated text, unlike that of the ground-truth text. Importantly, we findthat evaluation cases having LLM hallucinations correspond to ground-truthembedding patterns with a higher number of modes being poorly approximated bythe few modes associated with LLM embedding patterns. In analogy to near-fieldelectromagnetic evanescent waves, the embedding DMD eigenmodes of the generatedtext with hallucinations vanishes quickly across sentences as opposed to thoseof the ground-truth text. This suggests that the hallucinations result fromboth the generation techniques and the underlying representation.

Representations Matter: Embedding Modes of Large Language Models using Dynamic Mode Decomposition