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DUCH714 / SincKAN

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Setting for ChebyKAN #1

Open yihang-gao opened 4 days ago

yihang-gao commented 4 days ago

Hello. It is a very interesting paper. I just have a question regarding the experimental setting (Table 6). For the vanilla KAN, your setting is 8 8 (wide degree), I think the total parameters also depend on the number of turning points. For ChebyKAN, the width is 40 and the degree of freedom is also 40. Is the setting appropriate? Why both the width and degree of ChebyKAN is significantly greater than KAN and SincKAN? Based on your results, I guess ChebyKAN is the most efficient one, right? According to Table 7, the vanilla KAN is very slow, and the proposed SincKAN is also slow. If ChebyKAN is also reduced to 8 \times 8, should it be significantly faster than KAN and SincKAN? Thank you very much.

DUCH714 commented 3 days ago

Hi, yes, if ChebyKAN is also reduced to 8 \times 8, it will be faster than 40 \times 40. However, the price is the accuracy. We want to explore ChebyKAN's capability so we increase the size of ChebyKAN to have a balance of accuracy and training time.Herein, the setting is appropriate enough to compare the performance under a simliar training rate.

Indeed, we agree with paper that ChebyKAN is a pretty efficient network, despite it has instability.

yihang-gao commented 2 days ago

Hi, thanks so much for your reply. You enlarge the model size of ChebyKAN to compare them in similar computational time.

yihang-gao commented 2 days ago

Sorry, can I ask another question? In Section 2.3 Coordinate transformation", I cannot follow this part. I checked your codes, for the given input x, you first apply tanh to normalize it? And then scale and shift it with different step size h and position k. Then input them into sinc function. The scaling and shifting refer to Equation (13) for mixture of step size. But what doesCoordinate transformation" refer to in the codes?

I am interested in your paper. Thank you so much for your time and help.