I wonder if the model can fit a polyline x = a * y**3 + b * y ** 2 + c * y + d without fitting offset s and horizontal line h, since the problem seems to be poor-formed.
Intuitively, at point y = 100pix, the equation would be x = a * 1000000 + b * 10000 + c * 100 + d. A tiny perturbation on a would introduce a dramatic change in x, which makes it too hard to learn the other parameters b, c, d, especially the offset parameter d.
So what are the important points that make the model successfully fit a polyline?
I wonder if the model can fit a polyline
x = a * y**3 + b * y ** 2 + c * y + d
without fitting offsets
and horizontal lineh
, since the problem seems to be poor-formed.Intuitively, at point
y = 100pix
, the equation would bex = a * 1000000 + b * 10000 + c * 100 + d
. A tiny perturbation ona
would introduce a dramatic change inx
, which makes it too hard to learn the other parametersb, c, d
, especially the offset parameterd
.So what are the important points that make the model successfully fit a polyline?