  Deep learning has been shown to achieve impressive results in several domains
like computer vision and natural language processing. A key element of this
success has been the development of new loss functions, like the popular
cross-entropy loss, which has been shown to provide faster convergence and to
reduce the vanishing gradient problem in very deep structures. While the
cross-entropy loss is usually justified from a probabilistic perspective, this
paper shows an alternative and more direct interpretation of this loss in terms
of t-norms and their associated generator functions, and derives a general
relation between loss functions and t-norms. In particular, the presented work
shows intriguing results leading to the development of a novel class of loss
functions. These losses can be exploited in any supervised learning task and
which could lead to faster convergence rates that the commonly employed
cross-entropy loss.
