Multi Object Detection Might sound like a very basic question, but in a detection problem with multiple objects (solved by regression) how does the weight update work such that regression equations of all classes are satisfied all at once. How is it that boxes of other objects do not interfere with the training of box weights of our object?
Help appreciated a lot. Thanking in advance! :)
Because a NN doesn't see a box. The only job it does is to minimize the loss using Feedforward and Backpropagation.

Let's say the image has 1 object - 
=> 4 o/p values => 4 o/p neurons => 4 y_train values => 4 losses into the NN
=>To have the loss minimum it will adjust itself to have all the 4 o/p neurons as close to the truth as posible.

Let's say the image has 2 object -
=> 8 o/p values => 8 o/p neurons => 8 y_train values => 8 losses into the NN
=>To have the loss minimum it will adjust itself to have all the 8 o/p neurons as close to the truth as posible.

The difference - Obviously, later will be a bigger network and need more epochs to get the golden values of weights

If you have just started Deep Learning - 
Michael Nielsen