Answers.Body: <p>Yes, RNN can work on the functions you have mentioned. In fact, neural networks can approximate anything (Universal Approximation Theorem). This question also reminds me of Neural Turing Machine.</p>
  <p>But, it would be a complete waste to use RNNs or NNs for such a task.</p>
  
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Answers.CreationDate: 2021-02-13T16:54:35.097Z
Answers.Text: Neural networks cannot approximate "anything". They can approximate continuous functions and provided that certain conditions are met. It may be a good idea to provide a link to some article that provides more details.
Answers.UserDisplayName: nbro
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Answers.CreationDate: 2021-02-13T23:37:36.413Z
Answers.Text: Thank you. It would not be a waste because i need the thing that this assumption is true to build my own algorithm.
Answers.UserDisplayName: passa kelly
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Answers.CreationDate: 2021-02-16T21:05:00.853Z
Answers.Text: I know UAT doesn't cover it all but it is the only mathematical thing I can point out. Otherwise, I can say it is magic, because nobody can explain the unreasonable effectiveness of neural networks. It is a black-box which we frankly no nothing about. Hence, the need to run helter-skelter building bigger things or hitting any arrow that hits in the dark..
Answers.UserDisplayName: Abhishek Verma
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Answers.CreationDate: 2021-02-22T13:19:40.013Z
Answers.Text: Recently, there has been some interesting research around topology which may explain this. But, then, that would be another Pandora's box. That is why, using UAT is a good idea since everybody knows that.
Answers.UserDisplayName: Abhishek Verma
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Answers.UserDisplayName: Abhishek Verma
Body: <p>There were some posts that using RNN can predict the next point of the sine wave function with data history.</p>
  <p>However, I wondered if it also works on all the functions of <span class="math-container">$x$</span>, such as <span class="math-container">$x^2$</span>, <span class="math-container">$x^3$</span>, <span class="math-container">$\log(x)$</span>, <span class="math-container">$\frac{1}{(x+1)}$</span> functions.</p>
  
Tags: <neural-networks><recurrent-neural-networks><long-short-term-memory><function-approximation><universal-approximation-theorems>
Title: Is it possible to predict $x^2$, $\log(x)$, or variable function of $x$ using RNN?
UserDisplayName: passa kelly
ThreadText: # Is it possible to predict $x^2$, $\log(x)$, or variable function of $x$ using RNN?
  
  (Asked by: username_0 on 2021-02-12)
  
  There were some posts that using RNN can predict the next point of the sine wave function with data history.
  
  However, I wondered if it also works on all the functions of $x$, such as $x^2$, $x^3$, $\log(x)$, $\frac{1}{(x+1)}$ functions.
  
  **Tags:** neural-networks, recurrent-neural-networks, long-short-term-memory, function-approximation, universal-approximation-theorems
  
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  ## 1 answers
  
  ### Answer by username_1 on 2021-02-13. Score: -2 | Accepted answer
  
  Yes, RNN can work on the functions you have mentioned. In fact, neural networks can approximate anything (Universal Approximation Theorem). This question also reminds me of Neural Turing Machine.
  
  But, it would be a complete waste to use RNNs or NNs for such a task.
  
  > **Comments:**
  > **username_2**: Neural networks cannot approximate "anything". They can approximate continuous functions and provided that certain conditions are met. It may be a good idea to provide a link to some article that provides more details.  
  > **username_0**: Thank you. It would not be a waste because i need the thing that this assumption is true to build my own algorithm.  
  > **username_1**: I know UAT doesn't cover it all but it is the only mathematical thing I can point out. Otherwise, I can say it is magic, because nobody can explain the unreasonable effectiveness of neural networks. It is a black-box which we frankly no nothing about. Hence, the need to run helter-skelter building bigger things or hitting any arrow that hits in the dark..  
  > **username_1**: Recently, there has been some interesting research around topology which may explain this. But, then, that would be another Pandora's box. That is why, using UAT is a good idea since everybody knows that.  
  
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