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So the question is : Is it theoretically possible to feed a neural network with some random values to expect an output since randomness is a lack of knowledge in most case.

For this question, I've got some examples.


First case, not a real problem?

We just throw a coin and get the result and we do that a whole bunch of times. For each throw, we get the initial condition (air pressure, force, etc.). Now we put all this data into the neural network for it to process.

My guess : The result is not really random since it only depends on the initial conditions so it's possible and the neural network will do a great job. So I guess that example is not a real problem since the "randomness degree" is weak.

Second case, questioning

Now, we generate a random list of number and sentences that correspond to each other so we have something like :

'zefvkbdl' -> 1613841.009
'nfeovhlzm' -> 963478.29
'jhgcjbklnsczl' -> 1.535953
'ergz' -> 9138630.26
etc ...

In a way that everything was randomdly generated (still, the list of sentences and number were not generated seperatly but each number was generated after a sentence and correspond to that sentence). In that case, is it possible to give a neural network the half of the list (the list can be forever long) and expect it to predict the other half with a great precision ?

My guess : It depends on the generation algorithm but let's pretend that a letter is just a particular index in an array and that the index was randomly generated. Since most of the time, numbers are randomly generated thanks to the digits of time (the last decimals that are changing extremely fast) I'm not sure of that - I guess it might be possible with an extremly powerful neural network to theoretically do that job.

Third case

Let's now be even more theoretical and consider it is possible to store somehow the global state of the universe at each moment of time. The only thing that is truly random at my knowledge is quantum mechanics so let's try it out. At each point of time, we store the whole universe state and the outcome of measuring a quantum particle state (like the spin of an electron). Is it possible, after the biggest neural network training, to "predict" the outcome of measuring a quantum particle state knowing the state of the universe ?


Since I'm just a curious student, I don't have a lot of knowledge in neural network or quantum mechanics so I probably said a lot of wrong things and I'm sorry for that. I thank you for reading all of this and I hope someone is able to help me anwser or correct me.

Now, the real question I'm asking is : Do randomness truly exist ?

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    $\begingroup$ First case, I agree with you - not really random. Second case, again, if the numbers are a “hash function” of the string, then the neural net could “figure out” the hash function - but there may be some interesting NN/complexity results that say otherwise. Third case, as I understand modern interpretations of quantum theory, no, the state of the universe will not let you predict the outcome beyond probabilities and real randomness exists - but there are those who don’t accept that. $\endgroup$ – Daniel M Gessel Feb 22 at 21:44
  • $\begingroup$ What do you mean by "feed a neural network with some random values to expect an output"? That doesn't make any sense to me. I don't know what you mean by "to expect..." in this context. $\endgroup$ – D.W. Feb 23 at 3:29
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    $\begingroup$ @D.W. To feed a neural network means (I guess) to add changes in the time-state of the system. "To expect" in this contexts I think that means the same than in other context ... why not? $\endgroup$ – Ixer Feb 23 at 7:19
  • $\begingroup$ Of course what I'm saying at first makes nonsense and I explain my question after in the different cases. "Expect" means be able to predict randomness after feeding the neural network with the values I give the examples. Ixer answered rigth $\endgroup$ – Leo Bonn. Feb 23 at 10:21
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    $\begingroup$ “Feed a neural net ...”: train. “Expect an output”: expect the training to converge and be able to predict accurately when inferencing. $\endgroup$ – Daniel M Gessel Feb 23 at 11:13
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Purely randomness is not possible but in real-world the most randomness that a neural network can process is enough to discover an approximation pattern; the precision depends on the model of the context (exactitude of the Digital Twins) and processing power.

To extract the exact pattern from the pure randomness (I think) is impossible even with a quantum computer and even having all the time and resources of the universe. The reason is that nothing in the universe happens randomly, every effect has a cause. So regarding to the third case (theoretically) if you can reproduce every cause of a "twin universe" you can predict the future.

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This is maybe not the answer you are looking for but I hope it will clear some things up. Humans make models to better understand things and to predict behaviors. Do atoms (electrons, positrons, neutrons) actually exist ? Have we seen them ? Is it able to see them ? The answer is no. BUT, the atom theory explains perfectly all the experiments that have been made so far. Can we predict the outcome of a coin flip ? No. But, probabilistic models perfectly explain the expected outcome. Does randomness really exist ? I cannot answer this question because I am not god.

Now as far as your concern about if neural networks can be trained to predict randomness. This is a more general question and you may have a look here (one way functions) and here (random polynomial algorithms). These topics are both correlated with randomness on their very definition, and they are both open because both are very difficult to deal with. Randomness, entropy, time are concepts which we face at any given point and are truly amazing if you ask me.

Neural networks are trained to detect non linear patterns/rules between data. If the data are randomly generated then neural networks won’t succeed. But, on the other hand, if a neural network is able to achieve some sort of >50% prediction, then we should ask ourselves, is the generator actually random ? How can we check if a generator is actually random ? (The second link will be more helpful for these kind of questions).

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