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Questions tagged [universal-approximation-theorems]

For questions related to the (different) universal approximation theorems (UATs), for example, in the context of neural networks.

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31 votes
3 answers
16k views

Where can I find the proof of the universal approximation theorem?

The Wikipedia article for the universal approximation theorem cites a version of the universal approximation theorem for Lebesgue-measurable functions from this conference paper. However, the paper ...
Leroy Od's user avatar
  • 475
10 votes
2 answers
783 views

What are the learning limitations of neural networks trained with backpropagation?

In 1969, Seymour Papert and Marvin Minsky showed that Perceptrons could not learn the XOR function. This was solved by the backpropagation network with at least one hidden layer. This type of network ...
S.L. Barth is on codidact.com's user avatar
20 votes
1 answer
1k views

What is the number of neurons required to approximate a polynomial of degree n?

I learned about the universal approximation theorem from this guide. It states that a network even with a single hidden layer can approximate any function within some bound, given a sufficient number ...
mark mark's user avatar
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8 votes
1 answer
2k views

Which machine learning models are universal function approximators?

The universal approximation theorem states that a feed-forward neural network with a single hidden layer containing a finite number of neurons can approximate any continuous function (provided some ...
nbro's user avatar
  • 40.8k
3 votes
3 answers
733 views

Is there a way to calculate the closed-form expression of the function that a neural network computes?

As stated in the universal approximation theorem, a neural network can approximate almost any function. Is there a way to calculate the closed-form (or analytical) expression of the function that a ...
holistic's user avatar
  • 133
1 vote
0 answers
76 views

Is the capability of RNN more than the capability of MLP?

Consider the following excerpt paragraph taken from the section titled "Recurrent Neural Networks" of the chapter 10: Sequence Modeling: Recurrent and Recursive Nets of the textbook named ...
hanugm's user avatar
  • 3,890
1 vote
1 answer
204 views

Are the capabilities of connectionist AI and symbolic AI the same?

The universal approximation theorem says that MLP with a single hidden layer and enough number of neurons can able to approximate any bounded continuous function. You can validate it from the ...
hanugm's user avatar
  • 3,890