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?

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.