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A common misconception about deep learning is that gradient descent is meant to reach the "global minimum" of the loss, while avoiding "local minima". In practice, a deep neural network that's anywhere close to the global minimum would be utterly useless (extremely overfit)
The only setup where a global minimum has any chance to generalize is for underparameterized models, such as logistic regression, or a 1-layer network with few units. Otherwise, the points in parameter space that you are looking for during training are pretty far from the minima
An important research direction would be to use the information bottleneck principle to come up with models that have exactly the right amount of memorization capacity for a given task, as well as optimization methods to get to the global optimum
Most “loss functions” are pretty primitive. I mean the way the “loss” is made to depend on the “parameters” that you put into your model. Not all parameters are created equal!
Why is gradient descent still effective for DL? After all, it is a method to find critical points. But seems like the place that generalize well is more or less a random point of the loss function?
If driving down empirical risk does not mean anything in terms of generalization, why is gradient descent superior than random search?
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