[llamaz]

When I was implementing a neural network for a university assignment (2 years ago so my memory might fail me), we had to run our algorithm multiple time with different starting positions, then take the minimum of those local minima.

I'm not sure what momentum and dropout are, but I agree with Eleizer, without these things (which I didn't use) local minima are a problem.

[eat_veggies]

Dropout is where you randomly remove neurons from your network during training, which prevents them from depending too much on specific neurons (making the output more generalizable). It was developed in 2014 so it would have been brand new tech back when you were in your class.