Per some offline discussion, I'll note that while this paper is about the structure of hyperparams, it also starts with the analogy between Mandelbrot & Julia sets, Julia as the hyperparam space for Mandelbrot, the param space

Well, they both also have similar fractal dimensions. Mandlebrot's Hausdorff dimension is 2, Julia is 1-2.

I won't argue it here but just suggest that this is an important complexity relationship and that the neural net being fit may also have similar fractal complexity, and that the distinction between param and hyper-param in this sense may be somewhat a red-herring