Superformula(en.wikipedia.org)

27 pointsby EndXAvor 2 Jahren3 comments

en.wikipedia.org

https://en.wikipedia.org/wiki/Superformula

3 comments

llmzerovor 2 Jahren

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.

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

bigbillheckvor 2 Jahren

> The superformula depends of four parameters

Looks like six to me:

m, n1, n2, n3, a, b.

TrainedMonkeyvor 2 Jahren

All the examples on the linked wiki are given without a and b parameters... so these might be meta-parameters... maybe scale?