Visualization of the universal approximation theorem

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  • Опубліковано 7 вер 2024
  • Illustration of how a neural net with one hidden layer can approximate a function.
    Wikipedia: en.wikipedia.o...

КОМЕНТАРІ • 22

  • @beraulgd3662
    @beraulgd3662 2 роки тому +12

    So good, so clear, so concise.

  • @thepeelshorti2881
    @thepeelshorti2881 Рік тому +16

    I can see the ReLU function *_*

    • @hugomougard
      @hugomougard  Рік тому +5

      Indeed, good job :)

    • @4franz4
      @4franz4 3 місяці тому

      How do you see that?

  • @marvinlanger1155
    @marvinlanger1155 Рік тому +4

    Great visualization !

  • @user-fr2jr6hd4i
    @user-fr2jr6hd4i Рік тому +4

    very good, easy to understand 👍

  • @ikartikthakur
    @ikartikthakur Місяць тому +1

    hmm..makes sense ...so it finds the best possible linear function then the activation..n then finally add them up together to join them all

  • @jingli9995
    @jingli9995 7 місяців тому +3

    Thanks for the clear visualization! In this case, the activation function is ReLU right? Sigmoid will looks different

    • @hugomougard
      @hugomougard  7 місяців тому +3

      Well spotted! Indeed the activation in this case is ReLU, and SIgmoid would have looked smoother :)

    • @jingli9995
      @jingli9995 6 місяців тому

      @@hugomougard Thanks ;) This is the best video I have seen to explain universal approximation theorem, it's better than 1k words. Thanks for making it.

    • @hugomougard
      @hugomougard  6 місяців тому

      @@jingli9995 Thank you for your kind words.

  • @y.8901
    @y.8901 Рік тому +4

    Hello, thank you for your video, it helps to understand, but I have a question : How does the NN choose the "steps" of cut ? Because from what I understood, for next layer (i.e here f hat), we simply do the sum, as you did in blue below. Because if we do the real sum of the functions, we'll get simply a non linear function but that looks like a ReLU right ?

    • @hugomougard
      @hugomougard  Рік тому +2

      Hi Y.,
      For each hidden nueron, the cut is picked by tweaking the parameters (each neuron has 2 parameters, one that multiplies the input, and one that is just added to the multiplied input).
      The way those parameters are tweaked is usually by gradient descent.
      Sorry I'm aware that my response looks very generic, but going into more details is basically doing a full course on neural networks. I can recommend the videos by 3blue1brown on the subject if you want more details!

  • @Sammy15015
    @Sammy15015 2 місяці тому

    Can you do this with more layers? I want to know how adding more of them can increase the complexity of the function

  • @cffex3858
    @cffex3858 6 місяців тому

    Could you visualize the same thing but with multiple hidden layers?

    • @hugomougard
      @hugomougard  6 місяців тому

      I do not plan to make a visualization about that soon but I'll keep your suggestion in mind :)

  • @tuskiomisham
    @tuskiomisham 5 місяців тому

    now approximate sin(x^2)

  • @UCPlay334
    @UCPlay334 4 місяці тому

    how you do these visualizations please help.

    • @hugomougard
      @hugomougard  4 місяці тому

      I use github.com/ManimCommunity/manim :)

  • @mnky9800n
    @mnky9800n 3 місяці тому

    i wish there was gif version haha

  • @knowledgeclub4441
    @knowledgeclub4441 8 місяців тому +2

    How to implement in matlab ???