Based on my understanding, after your forward pass (for the 1st iteration), the differentiable loss makes updated weights and bias on backward pass that will be used on in the 2nd iteration and the process follows till number of iterations that makes an epoch.
In this case - a single network for 2 predictions with different weighted loss functions, how will the network keep associating parameters during iterations for an epoch for each predictions that enables it master what has been learnt in previous iterations (or epochs)?