# How can an ANN efficiently predict multiple numbers with fixed sum (in other words, proportions)?

I need a neural network (or any other solution) to predict 3 values which sum equals a fixed number (100). This will help me calculate proportions. Which is the most efficient way to do this?

The learn data only contains extreme situations where each row contains one and only one output value set to 100. The data to predict is expected to contain more nuances in the output values. All my attempts lead to very low accuracy as the predicted output sum is almost never a 100. Even when I try to normalize the predicted output, the predictions show very poor accuracy.

Should I try to organize the data with 2 angles instead and deduct the 3rd angle as the remainder in a circle? How to normalize those 2 angles and how to make sure their sum will not exceed the maximum value making the 3rd angle negative?

Illustration of learn data extract (4 input columns and 3 output columns).

0    1    2    3    100  0    0
4    5    6    7    0    100  0
8    9    0    1    0    0    100


Illustration of desired output predictions where each line sums as 100:

7    83   10
39   12   49
68   24   8
28   72   0
86   6    8
32   49   19
0    0    100

• I think Normalization is the route— what approach did you try? Jul 21, 2019 at 15:05
• I tried several normalization approaches. One of them consisted in dividing each output value by the sum of the 3 and multiply by 100. Does this make sense? Jul 21, 2019 at 15:20
• Yes. That should be fine. What’s your loss? Jul 21, 2019 at 15:22
• Thanks for the confirmation. I didn't even try to calculate the loss, the numbers were completely off. Maybe my issue is not with the normalization then? Maybe I should rethink the whole learning process? Jul 21, 2019 at 15:24
• If you don’t have a loss— how did you train? Jul 23, 2019 at 1:48