Can neural network process randomness?

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 ?