There are so much Polynomial KANs, is this meaningful?

[Da1sypetals]

There are sooo much polynomial KANs, beside this there are Chebyshev, Legendre, etc... After implementing several of these KANs, I wonder

• is this really meaningful?
• are these types of polynomial KANs inherently the same?

[Muyuzhierchengse]

Sorry for getting back to you only after the end of the term. You have raised a very good question!

• Yes, it is certainly worth noting that such work is meaningful, provided that we are not just trying out various polynomial methods randomly, but rather extending the polynomial approach itself to deeper layers of the network.
• In our view, we believe polynomial methods are equivalent, with each method having its own unique characteristics.

[Muyuzhierchengse]

Meanwhile, we would like to introduce our understanding of polynomial networks.

• First, polynomial expansion is a method to increase the width of neural networks. In fact, any expansion method might be viewed as a single-layer infinite-width neural network, and our goal is to reduce its width while extending its finite depth. The reason for choosing Taylor expansion is that it provides sufficient nonlinear combinations, and polynomial methods can follow the idea of KAN as learnable activation functions.
• Second, polynomial networks can offer good interpretability because the contribution of each term can be explicitly measured, allowing us to reconstruct the function itself to some extent through the expanded terms.

[Da1sypetals]

Thanks a lot for your explanation!