I have some idea how backpropagation would work for loss function like:
Where predicted and true are vector of same length and same operation throughout the elements.
Now in object localization problem my neural network's output vector's 0th element would denote probability of particular object being in image and rest 4 would tell about bounding box. Now my loss function would be roughly something like this:
This loss function worked fine in tensorflow and my NN localized the object as I expected.
My problem is that I am not able to understand how mathematically differentiation would work when different operations are applied on different elements.