Should estimated probabilities from multi class classification sum to 1
Summing up to one or not both can have their special meaning that I'll try to explain them. If you have classes that are not mutually exclusive, say you have dog and cat classes and they both can exist in an image. In such cases, you should use sigmoid nonlinearity as the output of each class and interpret each one separately. Each one that has a value greater than half can explain the existence of the corresponding label. On the contrary, your inputs may be mutually exclusive which means in each input you may just have a cat or a dog. In this case, you should employ softmax nonlinearity and yes, it sums up to one. The winner would be the one with the highest value.