One common way of interpreting Deep Neural Netowrks (DNNs) is that the first layers work as feature extractors and the middle layers map extracted features to a new low dimensional manifold such that a Generalized Linear Model can make the discremenation. Thus for a classification task, we want to map the instances to a manifold that the classes are linearly seperated. From a probabilistic point of view, minimization of negative log-likelihood leads to the loss functions that are being used in Deep Learning. In order to see this connection more detailly, I invite you to take a look at my medium article on Generalized Linear Models.