One of the main difficulties in analyzing neural networks is the non-convexity of the loss function which may have many bad local minima. In this paper, we study the landscape of neural networks for binary classification tasks. Under mild assumptions, we prove that after adding one special neuron with a skip connection to the output, or one special neuron per layer, every local minimum is a global minimum.

This phenomenon is a bit curious and perhaps deserves more elaboration. This, I am afraid, is likely what is going on here (if you drop the separable assumption). The main contribution of this work is to prove that by adding a single exponential function (directly) from input to output and adding a mild l_2 regularizer, the slightly modified, highly nonconvex loss function does not have any non-global local minima. Moreover, all of these local minima actually correspond to the global minima of the original, unmodified nonconvex loss. This surprising result, to the best of my knowledge, is new and of genuine interest.

If you've ever tried to operate an office printer or some other piece of unreliable technology, you may have some doubt about whether machines could ever destroy humanity. But experts fear it's only a matter of time before artificial intelligence becomes so advanced that it begins to wipe us off the face of the planet. Now Subhash Kak, regents professor of electrical and computer engineering at Oklahoma State University, has sketched out a'frightening scenario' in which murderous machines'eliminate us altogether'. He said there was currently some debate about whether computers will ever achieve consciousness, putting their intellect on a par with humanity's own powers of reasoning. If this happens, it could be curtains for our species.

If you've ever tried to operate an office printer or some other piece of unreliable technology, you may have some doubt about whether machines could ever destroy humanity. But experts fear it's only a matter of time before artificial intelligence becomes so advanced that it begins to wipe us off the face of …