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My other comment addresses some of this but you're overstating things a bit. Throwing more data at the model is one solution. Its just not the only, or even best, approach. Properly measured performance on good holdouts and the application of regularization avoids the worst of overfitting. This is standard practice is most of machine learning, not just deep learning.

Deep learning gets a lot of hype because for many applications they perform better and scale better without a lot of tricks and extensions which are now possible with SVMs. You can even use a large margin loss with deep models to get some of the benefits of SVMs.

Adversarial examples are way overblown. First, SVMs are not immune to them either. Second, very few applications are threatened by things like adversarial examples.

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