Deep learning is not boosting at all. Deep learning is about composing trainable modules. Adding a layer f(x) to a layer g(x) to get h(x) = f(g(x)). Boosting creates a final classifier that is a weighted sum of the base classifiers, or something like h(x) = a * f(x) + b * g(x). Composition is what Professor Hinton means when he says "re-represent the input" and other similar phrases.