The superformula depends of four parameters and is able to model many different curves. I wonder if that superformula would be useful to learn to generalize the form of a curve given few points. It could be that, in same way, the four parameters of that curve are a orthogonal bases in the hypothesis space, in the sense that each parameters add a lot the information. If this intuition has any meaning, it could be the start of a new theory for constructing bases of the hypothesis space, that is models with few parameters but great expressive power.
So my question is whether the superformula constitute an example of great expressivity and powerful generalization for curve fitting by using machine learning models.
Edited: (2) In the following link they use the superformula,
Automatic Generation of Smooth Curves from Interpretable
Low-Dimensional Parameters.
Edited: (1) The following link explains expressivity and generalization power in machine learning: https://blog.evjang.com/2017/11/exp-train-gen.html
So my question is whether the superformula constitute an example of great expressivity and powerful generalization for curve fitting by using machine learning models.
Edited: (2) In the following link they use the superformula, Automatic Generation of Smooth Curves from Interpretable Low-Dimensional Parameters.
So the intuition seems fruitful. https://arxiv.org/pdf/1808.08871.pdf