Can Pi be predicted by a neural network?

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Discussion Overview

The discussion centers around the feasibility of predicting the digits of Pi using a neural network. Participants explore the implications of such a prediction on the nature of Pi, debating whether it can be considered random or not. The conversation touches on theoretical aspects of neural networks, mathematical functions, and existing formulas for calculating Pi.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant proposes training a neural network to predict the digits of Pi, suggesting that success would imply Pi is not random.
  • Another participant outright disagrees with the feasibility of this approach, asserting that it would not work.
  • Some participants argue that while neural networks can approximate complex functions, existing series expansions can already calculate Pi accurately.
  • A participant suggests that a sufficiently large and recursive neural network might be able to represent formulas like the Bailey–Borwein–Plouffe formula, which could potentially yield the Nth hexadecimal digit of Pi.
  • There is a discussion about the existence of a formula that could provide the Nth decimal digit of Pi, with one participant expressing uncertainty about its existence.
  • Another participant expresses interest in the project but indicates they currently lack the time to pursue it.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether a neural network could successfully predict the digits of Pi. There are competing views, with some asserting it would not work while others believe it might be possible under certain conditions.

Contextual Notes

Participants mention the need for large amounts of data to train neural networks and the complexity of the models involved. There is also uncertainty regarding the existence of a formula for the Nth decimal digit of Pi.

arnesinnema
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Hi all,

Would it be possible to try to predict Pi by a neural net. So basically when you input 1 into the neural net you will train it to output 3. Next input 2 and train it to ouput 1. Etc... Next after training the net such that it will predict the first 1000 positions correctly would it predict the 1001th, 1002th, etc... position correctly.

If so Pi is not random. Otherwise Pi is random.

Would this be possible?
 
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No.
 
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Why not?
 
arnesinnema said:
If so Pi is not random. Otherwise Pi is random.

Pi is not random.
 
You don't understand what a neural net does. They are complex models which have many parameters and can approximate arbitrary mathematical functions. You need to train them on large amounts of data to tune the parameters and fit the model to your training data.

There are simple series expansions which can already calculate Pi accurately.
 
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Hmm okay, so it probably would work but it would only prove what we already know.
 
arnesinnema said:
Hmm okay, so it probably would work

I'm not sure how you got that out of the replies so far. It would not work.
 
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Okay thanks for the explanation.
 
arnesinnema said:
Hmm okay, so it probably would work but it would only prove what we already know.
No it wouldn't. Neural networks detect patterns. The digits of pi have no pattern.
 
  • #10
I disagree with everyone saying it wouldn't work outright. I think it might be possible, given a large enough network that has some recursion.

Basically with a large number of nodes a NN can represent any differentiable function. The Bailey–Borwein–Plouffe formula rapidly converges to pi, and is a summation. It also be used to give you the Nth hexadecimal digit of pi. So if you can accurately represent the formula by your network, it should be able to give you the Nth hexadecimal digit of pi. Bellard's formula does the same in binary digits.

Now, ASSUMING there exists a formula similar to BPP that will give you the Nth DECIMAL digit, (is there one?) If the neural network can simulate the other two accurately, I see no reason why it could not do the same for decimal digits.

I would believe that you couldn't just use some basic feed-forward NN, but would have to have something much deeper that at minimum loops backward.

This is an interesting project. If you want to work on it and write a paper it would be interesting.EDIT: I should add that I'm currently using neural networks in my research.
 
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  • #11
Oke thanks for the positive feedback that's what this world needs more.

At the moment however I have no interest and opportunity to work on this. I put this in the open so I guess it's open-source now.
 
  • #12
No problem, its actually quite an interesting problem and perhaps I'll look into it further, though I need to finish up these 3 other projects first.
 

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