From Dispersion to Attraction: Spectral Dynamics of Hallucination Across Whisper Model Scales

Hallucinations in large ASR models present a critical safety risk. In this work, we propose the $\mathit{\text{Spectral}}\mathit{\text{Sensitivity}}\mathit{\text{Theorem}}$, which predicts a phase transition in deep networks from a dispersive regime (signal decay) to an attractor regime (rank-1 collapse) governed by layer-wise gain and alignment. We validate this theory by analyzing the eigenspectra of activation graphs in Whisper models (Tiny to Large-v3-Turbo) under adversarial stress. Our results confirm the theoretical prediction: intermediate models exhibit $\mathit{\text{Structural}}\mathit{\text{Disintegration}}$ (Regime I), characterized by a $13.4\mathrm{\%}$ collapse in Cross-Attention rank. Conversely, large models enter a $\mathit{\text{Compression-Seeking}}\mathit{\text{Attractor}}$ state (Regime II), where Self-Attention actively compresses rank ($-2.34\mathrm{\%}$) and hardens the spectral slope, decoupling the model from acoustic evidence.