Is there standard parameters that characterize how fast neural network learns to achieve specific error rate?
Sometimes you can estimate that by smoothing out your val_loss curve and hoping that your training is repeatable and stable, but seems that word "unpredictable" was invented specifically to describe loss curves. :) Especially if you're using some sort of dynamic data generation or custom cost function.

Take a look at few species at http://lossfunctions.tumblr.com/