Is KAN particularly not good at fitting the multiplication operations?

[SimingShan]

Hi, what an interesting work! However, during my experiments, i found that KAN is particularly not very good at the multiplications, or maybe it is just the way i implement it is not quite right. For example, the most simple problem of x * y, and i set my experiment to be
model = KAN(width=[2,2,1], grid=5, k=3) (which I assume is the same as the paper)
f = lambda x:x[:,[0]] * x[:,[1]]
dataset = create_dataset(f, n_var=2)
then train the model by
# model.train(dataset, opt="LBFGS", steps=200, lamb=0.00);
and the result turns out to be like this

which is quite different with the paper. I have also tried other hyper-parameters, but still didn't work out, which part of my code is wrong?

[KindXiaoming]

I would count this as a success. (0,0,0) -> linear, (0,0,1) -> quadratic, (0,1,0) -> linear, (0,1,1) -> quadratic. (1,0,0) -> quadratic, (1,1,0) -> linear. Although the quadratic functions are not symmetric, but this is a random gauge degree of freedom. You may try varying random seeds; if you are lucky, you can get symmetry parabola. What do I mean by gauge degree of freedom is that the following equation holds for any $a$:

$2xy = (x+y+a)^2-(x+a)^2-(y+a)^2+a^2$

so the quadratic functions do not have to be symmetric (in the paper, it's just lucky that it's close to $a=0$).