Per your interest on predicting probabilities, you can compute the probabilities for classification, by using the "net3" and the "trainedNet3" which use the SoftmaxLayer and the output as a string (e.g., "1", not 1.0.

{finalNet3[{9987, 13}, "Probabilities"] 
 finalNet3[{5062, 4938}, "Probabilities"] 
 finalNet3[{0, 10000}, "Probabilities"] }

Note that the following three samples are classified correctly. For example, using the 1st, 25th, and 50th samples, the 3 samples are correctly classified with the highest probabilities.

• {9987,13} -> "1": {9987,13} show the highest probability to be classified as "1"
• {5062,4938}->"25": {5062,4938} show the highest probability to be classified as "25"
• {0,10000}-> "50": {0,10000} show the highest probability to be classified as "50"

I am not sure what you mean by: "the output in training has inverted commas " ", that is {{9988, 12} -> "1"} instead of {{9988, 12} -> 1}." I think you mean string not a number.

You can compute the probabilities for each class by using the SoftmaxLayer but the SoftmaxLayer requires the output to be a string, not a number, which I called classification.

By the way, you can check and plot the sensitivities of each input by changing the 1st input while holding the 2nd input constant and vice versa.

Table[{x1, finalNet3[{x1, 5000}]}, {x1, 4000, 6000, 100}]

Hope this helps.

The followings are mere suggestions.

• The inputs are a 100 x 2 matrix (i.e., only 2 input parameters), but the outputs are a 100 x 100 matrix (a vector of 100 values due to one-hot vectors) which is huge compared to the 2 predictors. It might be helpful to change the one-hot coding as a number or string. e.g., {1,0,0,0,0.......} to 1, {0,1,0,0,0.......} to 2, etc.

  trainingData2 = Thread[trainingData[[All, 1]] -> Range[100]]
  net = NetChain[{LinearLayer[50], ElementwiseLayer["ReLU"], 
      LinearLayer[50], ElementwiseLayer["ReLU"], LinearLayer[1]}];  
  

• The "net" has only very few hidden layers and it might be helpful to increase the number of hidden layers. Adding more layers does not necessarily increase the accuracy thus apply other layers such as batch normalization layer (adding which layer may not be straightforward)

• The last 4 samples of the "trainingData" have the same input values but the output values are different, which does not make sense.