About multiple objectives in Inception networks

Inception networks, in contrast to most of the networks, can have multiple outputs, from which the gradient can propagate in order to update the weights.

These outputs can have different size and solve different tasks.

Do I correctly understand, that the main point in doing so, that the common for both output heads part of the CNN learns useful information from both inputs simultaneously?

To get something sensible, these two tasks most likely need to correlate in a certain way, share a lot of in common. Otherwise, It looks like, the gradient updates from both heads may interfere with each other, and one does not achieve a good solution for either of the tasks.

The distance from the input to one of the heads can differ a lot from the distance to another head. How to choose the learning rates to be adjusted, and the proportion of the net loss for each of the objectives?