Universal Approximation Theorem

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Can a neural network approximate ANY function?
00:00 Theorem
04:38 Proof
15:55 Joke Break
16:53 Python Demo
20:35 Limits of the Theorem
  1. Jeff Orchard
  2. neural networks
  3. approximation theorem
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Комментарии
Автор

Very clear presentation, thank you. Just curious : is this proof of universal approximation the one given in Cybenko's original paper ? I never read it, but I remembered that the argument had something to do with Fourier transforms...

StratosFair
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Very clear and nice lecture! Thanks a lot!

t-gee
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Analysis nerd here. I think you should be muttering things about compact spaces having finite subcovers to show that you have a finite number of pieces.

tomwright
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Thank you for such a lucid explanation!!

ranjanmukherjee
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Accuracy can also be achieved by means of increasing the number of neurons in the single output-layer.

zofe
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Your proof is very easy to understand. How can I get your source code in this video? Thanks.

lehoangtuan
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Couldn't the error of your approximation from the true value be arbitrarily big?

nohofoos
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In higher dimensions, when we construct the piece-wise constant functions, do we need to multiply multiple heaviside step functions together, one per dimension?

ibrahim-work
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are alphas in the summation of G's expression diffenent for different x?
as if not how can i select the right peice function for that x?

sanketgandhi
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Assume N in Theorem 2 is a fixed number. Can functions G(x) still be dense in C(I_n)?

yonac.-kenv