@SangdonLee Thanks, all the discussions are very helpful. The physics problem that I am considering, for learning purposes at this stage, is the problem of a rotating qubit. I consider that a qubit rotates about it's y-axis by an angle of \theta in [0, pi]. For training we consider the z measurements of spin-up and spin-down for discretized angles of [0, pi]. Hence the training result {9989, 11} -> "1" indicates that I obtain 9989 spin up results and 11 spin down when measuring the qubit during the first discretized rotation angle. Since I discretize the range [0, pi] in 50 intervals, I obtain 50 such training data results. Have a look at my final code, let me know what you think of my attempt to model this example (not sure how familiar you are with quantum mechanics?). You can advise if anything is unclear in the code or example.

Attachments:

Nolan_Paper_Exam...nb

@SangdonLee Many thanks for your response, just one query, when I try to evaluate NetMeasurements using the following code:

validationData = trainingData2b;
accuracy = NetMeasurements[trainedNet, validationData, "Accuracy"]
precision = NetMeasurements[trainedNet, validationData, "Precision"]

I obtain the following strange results: 
1.
<|1 -> 1., 2 -> 1., 3 -> 1., 4 -> 1., 5 -> 1., 6 -> 1., 7 -> 1., 
 8 -> 1., 9 -> 1., 10 -> 1., 11 -> 1., 12 -> 1., 13 -> 1., 14 -> 1., 
 15 -> 1., 16 -> 1., 17 -> 1., 18 -> 1., 19 -> 1., 20 -> 1., 21 -> 1.,
  22 -> 1., 23 -> 1., 24 -> 1., 25 -> 1., 26 -> 1., 27 -> 1., 
 28 -> 1., 29 -> 1., 30 -> 1., 31 -> 1., 32 -> 1., 33 -> 1., 34 -> 1.,
  35 -> 1., 36 -> 1., 37 -> 1., 38 -> 1., 39 -> 1., 40 -> 1., 
 41 -> 1., 42 -> 1., 43 -> 1., 44 -> 1., 45 -> 1., 46 -> 1., 47 -> 1.,
  48 -> 1., 49 -> 1., 50 -> 1.|>

Firstly, I don't think the accuracy could be 1. Secondly, I would have expected some real number between 0 and 1 for the precision (instead I get this strange output). Do you have any idea what is going on here?

@SangdonLee Thanks for your response. Having implemented your suggestions I do note an improvement. One query, do you maybe know how to incorporate the ValidationSet[] built-in function into the type of neural network to increase the accuracy and prevent overfitting? I left highlighted in purple my attempt at including the ValidationSet[]. It does run but I don't think it is set in an optimal way. I attach the revised Notebook.