I'm not programming a neural network but I'm looking at it from a non-hands-on, theoretical point of view and I'm currently wondering how to escape a local minimum and how to get to a global minimum.
When you compute the gradient of the error function and step in the direction of greatest descent, you'd end up in that immediate local minimum. AFAIK, you'd get stuck there. How do neural network trainers go about this? Do they start from a new random configuration of weights at each batch and see if the cost is smaller, or is there some way of immediately getting to the global minimum?
I've heard of a method resetting the learning rate to 'pop' out of local minimums but I'm not sure how that works when the gradient is 0. I've also heard that stochastic gradient descent is more reliable than gradient descent at finding global minimums, but I don't know how using the training data in batches rather than all at once allows it to steer around local minimum in the example, which is clearly steeper than the path to the global minimum behind it.