I'd argue that deep networks, seen as recursive generative linear models, owe much of their success to increased computational power but also to the transformations (RKHS) and optimization developments. On the flip-side, GPU makers are rewiring their hardware to make deep nets go. Exciting times ahead!
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I would agree. Using Moores law, as the densities double and the price per chip decreases, the computational power on a given density of silicon increases at a stable price. Pair that with the computational ingenuity using/creating neural networks and the future has infinite potential.
Quantum computers will revolutionize this area and make neural network based algorithms ubiquitous.
We have to wait