The answer is really very simple: because we use training and test sets, and generally use iterative training methods. As soon as test set error plateaus or sta

The answer is really very simple: because we use training and test sets, and generally use iterative training methods. As soon as test set error plateaus or starts to degrade, you stop training. This is called early stopping and can be considered a form of regularization. In theory it would seem a neural network (with early stopping "correctly" implemented) can never overfit, although I suppose in practice it can vary a little (because of test variance, too large step sizes, etc.). It's possible to train huge overparametrized networks this way. One big problem I can see with this approach (maybe compared to over forms of regularization) is that it might be very space/memory inefficient. But if you've got a big budget I think it's a surefire way to make sure your model performs as well as possible (without having to tune hyperparameters too much or deal with local minima that probably happens at near-capacity networks).