Discarding correlation among inputs in a neural network I am working on a problem with 4 inputs and 1 continuous output variable. The sum of all values of the 4 input variables is always 1.


  a1+a2+a3+a4=1


So, they are correlated. 

My question is: should I use all 4 variables for neural network training? Or, should I use any 3 of them to get rid of correlation? Is there any problem if I use all 4?
You could try some feature selection techniques if you want to choose 3.

That said, have you tested the data for multicollinearity?  Maybe you have but I don't think that a1+a2+a3+a4=1 implies a high degree of correlation.

To answer your question though, it really doesn't hurt to try and train a neural net with the four variables.  If one of the inputs is unnecessary, the NN training may well set the weight on one to close to zero without you having to choose one.