0.3 kan

[ndem0]

Description

The PR fixes the KAN model and block to be compatible with the latest Spline model. Moreover, a vectorized spline model is also implemented for efficiency.
I also added a test on the KAN training, and it is working. Despite that, the current model still needs (too) many iterations to converge. Further validation before merging 0.3 in master are needed.

This PR fixes #612

Checklist

• Code follows the project’s Code Style Guidelines
• Tests have been added or updated
• Documentation has been updated if necessary
• Pull request is linked to an open issue

[adendek]

Hello all,

Just out of curiosity, did you consider the efficient KAN implementation?

Honestly speaking, I did not managed to compare those two implementations, but if you see a performance-related issue, may be worth to do so. I can take a look, later.

[ndem0]

Hi, I've fixed almost all the KAN-related issues. There are still several failing tests, but they are inherited from 0.3 at the moment.

The KanBlock class actually needs a minimal restyling, but I'm afraid to keep this PR open for too long. I put a TODO list on top of the file. I would merge now, since the method is working, and postpone the cosmetic part before merging the 0.3.

[GiovanniCanali]

Hi, a quick update on this PR:

• VectorizedSpline now supports independent knot vectors for each univariate spline.
• Fixed an issue with einsum indices in the forward method of VectorizedSpline.
• Refactored both KolmogorovArnoldNetwork and the corresponding block for improved structure and clarity.
• The KolmogorovArnoldNetwork has been validated on benchmark problems and is behaving as expected.
• Temporarily removed all grid_extension-related logic from KolmogorovArnoldNetwork; this will be reintroduced shortly.

Pending tasks before merge:

• Implement grid_extension logic for KolmogorovArnoldNetwork
• Add analytical derivatives for VectorizedSpline
• Implement or update tests for
  • VectorizedSpline
  • KolmogorovArnoldNetwork
  • KANBlock
• Write docstrings for KANBlock and KolmogorovArnoldNetwork
• Add .rst documentation for the new classes

I plan to complete these items and finalize the PR by the end of next week.