One often hears about "local" shape of non-Gaussianity in bispectrum estimators, and how introduction of higher derivative operators in effective field theory of inflation alters this shape. Yet this is probably not the end of the story. A non-linear point-wise transformation applied to a Gaussian random field can generate apparent correlations between various Fourier modes even in a single field model, if the non-linearity is strong enough. The leading order cubic interaction term in models like DBI inflation does not actually depend on wave momentum, just local time derivative operators, and so perhaps can be viewed as a point process with extended time correlations. Is there a sense in trying to disentangle non-linearity from the choice of mode decomposition, or is the usual Fourier basis good enough? To make my questions more concrete, I solve fully non-linear equations of motion in separate universe approximation (i.e. k=0 limit) for DBI and (\nabla\phi)^4 actions, show how expansion history depends on the field and why it is different from the usual slow roll chaotic inflation, and discuss what that implies for three-point correlators of primordial curvature fluctuations and the notion of "locality".