> ...we show that the fundamental principle attributing to the success is the manifold structure in data... > Then we show for any deep neural network with fix

> ...we show that the fundamental principle attributing to the success is the manifold structure in data... > Then we show for any deep neural network with fixed architecture, there exists a manifold that cannot be learned by the network. I'd venture a guess that you can extend this result to show that, for any deep neural network with fixed architecture, there exists an adversarial manifold it must be vulnerable to. In other words not only is there a manifold the neural network cannot learn, but there is also a manifold it will learn, but incorrectly.