We study the loss landscape of training problems for deep artificial neural networks with a one-dimensional real output whose activation functions contain an affine segment and whose hidden layers have width at least two. It is shown that such problems possess a continuum of spurious (i.e., not globally optimal) local minima for all target functions that are not affine. In contrast to previous works, our analysis covers all sampling and parameterization regimes, general differentiable loss functions, arbitrary continuous nonpolynomial activation functions, and both the finite- and infinite-dimensional setting. It is further shown that the appearance of the spurious local minima in the considered training problems is a direct consequence of the universal approximation theorem and that the underlying mechanisms also cause, e.g., $L^p$-best approximation problems to be ill-posed in the sense of Hadamard for all networks that do not have a dense image. The latter result also holds without the assumption of local affine linearity and without any conditions on the hidden layers.

An impressive level of technological progress and wealth characterize modern economies nowadays. While in the early period of human history, the pace of technological progress was relatively slow, the success of today's companies is strongly defined by time-to-market and state-of-the-artness. Key factors for competitiveness are therefore the capability of reacting quickly and predicting successfully the development of new and old technologies. A look into the landscape of technological trends 2018 reveals that innovativeness seems to be driven by data, cloud, intelligence and algorithm. Artificial Intelligence (AI) is thereby rapidly moving from theory to reality. The simulation of human intelligence processes, as can be defined AI, has become an omnipresent buzzword and is undoubtfully shaping the direction of technological progress.

This brings up another facet of these communications, namely how many of them can your self-driving car handle at once? Suppose that there are a hundred other self-driving cars around you, and all of them are bombarding your AI with what's going on. Meanwhile, let's suppose that the roadway infrastructure has dozens of broadcasting sites near your self-driving car as it is traveling along on the highway. How does your self-driving car decide which of these sources to give attention to? Trying to decipher all of them at once might be daunting and consume a tremendous amount of on-board processing and memory. Right now, we have so few V2X's in place that it is an easy task for an experimental self-driving car to cope with, but once we have lots of V2V, V2I, and V2P, it will be a deluge of data, some of which is useful and some not, some of which is timely and some not, etc.