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force rational functions rather than polynomials #38

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guyko81 opened this issue Jun 16, 2017 · 2 comments
Closed

force rational functions rather than polynomials #38

guyko81 opened this issue Jun 16, 2017 · 2 comments
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@guyko81
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guyko81 commented Jun 16, 2017

Hi @trevorstephens ,

I still love your work and found a good paper:
Neural networks and rational functions
It describes that rational functions can approximate arbitrary functions better than polynomials. That made me think that the gplearn should generate 2 separate polynomials in parallel and use the ratio of them as the function approximate.
My argument is the following (without exactly knowing the proof of theorems):

  1. it is proven that a neural network with non-linear activations can approximate any function
  2. it is proven in this paper that a rational function (functions represented as the ratio of two polynomials) can approximate any RELU neural network (which is nonlinear)
    ==>
  3. so the rational functions can approximate any functions

I'm not sure that the performance or the size will be optimal, but I think it worth a try. What do you think?

guyko

@guyko81
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guyko81 commented Jun 16, 2017

I think the only modification (or option) would be to hold the first branch on the '/' value (DIVIDE)

@trevorstephens
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Hi @guyko81 , thanks for the suggestion... I think at 3 citations it will need more support for me to integrate this into gplearn though.

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