If deep learning is a black box, then why are companies still investing in it?
Easy answer: utility.
The strength and applicability of "black box" NNs has been regularly validated in the past few years, and business is concerned with results. (i.e. they don't care how the sausage is made, so long as it gets made.)
The human brain is a black box too (so far), but we keep investing in them too.
There is no back end to a network. There are inner layers, and one can analyze what they might represent conceptually sometimes, such as in the case of computer vision convolution layer sequences. That is also true of brain neural networks.
There are many proofs in AI literature, so it is not that there are baseless and arbitrary designs behind AI system design, but the need to explicitly understand what each neuron is doing is usually wasted investigation to find that the neuron does very little or it does so much that the characterization of its purpose is as large as the dataset that trains the entire network.
Deeplearning itself can be questioned if it's working. Most users are reporting, that they are not able to train a network under a certain error. That means, they are using the latest hardware and software and aren't able to figure out the right weights. Additional, the problem with the blackbox phenomena is there, which means that even after a network was trained successfully, nobody knows what the connections internally are doing, so the result of the learning process has to be questioning.
The reason, why the hype around deeplearning isn't over has to do with the process in which neural network datasets are created. Before a 12 layer convolutional neural network can be trained so called raw data are needed. This can be a collection of images, motion capture recordings of biped walking or annotated game-logs from Starcraft AI. The prestep before the training itself is the reason why the subjects remains interesting. Even if the dataset isn't used for training neural networks, it's an important step in engineering artificial intelligence. AI without datasets isn't working, and neural networks have a large demand for datasets.
Instead of simply calling it neural networks, the underlying technology should be stated as datadriven algorithms. The idea is to connect machine intelligence which is stored in computer programs with real life domains which are provided as images, trajectories and textual corpora.
I think that the universal approximation theorem plays a large role in why companies and governments are investing in deep learning, it states that theoretically an ann can approximate any continuous function with n-dimension input variables. Specifically it states that feed forward nets with a single hidden layer can do this lending credence to the implication that rnns and cnns are also capable of universal function approximation. So they are investing because they have continuous functions that need to be approximated and really the best tool for the job is neural networks.