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I would be less surprised if the paper claimed rational functions instead of polynomials. NN's are ~general non-linear functions which polynomials are very poor
by cozzyd 8y ago
I would be less surprised if the paper claimed rational functions instead of polynomials. NN's are ~general non-linear functions which polynomials are very poor at representing (e.g. you can't encode asymptotic behavior in polynomials).
edit: here's a paper about rational functions and NN's: https://arxiv.org/abs/1706.03301 https://arxiv.org/abs/1706.03301 . I'm not really in a position to evaluate the claims, but author just won an NSF CAREER award so that's something.
- jl2718 8y agoDo you know of any open source packages for doing multi-dimensional Chebyshev regression? I have seen coefficient determination only when the function is known, and one guide for how to do collocation in one dimension, but not really for a ‘best-fit’ in an overdetermined system.
- cozzyd 8y agoI don't, other than attempting to use a general minimization package, which I would expect not to work so well without hand tuning of initial guesses. I think gsl and chebfun (matlab, unfortunately) can do regression in one dimension but I don't think it can in 2 or 3d (much less general high dimensions).
- geezerjay 8y ago> NN's are ~general non-linear functions which polynomials are very poor at representing This is not true. Deep ReLU/leaky ReLU NN are piecewise polynomial functions generated in a contrived way (a chain of compositions). Even if we assume that piecewise polynomial functions aren't polynomial functions, they are still in the same class of linear functions.