Connect information-spreading and Fourier-mode-collapse perspectives

Determine how the effective-field-theory description of spatial mutual-information growth in diffusion models is connected to the perspective based on the collapse of Fourier modes across dynamical regimes.

Background

The paper compares its effective-field-theory analysis of spatial mutual-information growth with a separate perspective that describes transitions between diffusion-like pattern formation and snapping through the collapse of Fourier modes. The authors state that they believe the two perspectives are connected, but do not establish the connection. They identify exploring this relationship as future work.