Title: On Loss Functions for Deep Neural Networks in Classification,
Abstract: Deep neural networks are currently among the most commonly used classifiers.
Despite easily achieving very good performance, one of the best selling points
of these models is their modular design - one can conveniently adapt their
architecture to specific needs, change connectivity patterns, attach
specialised layers, experiment with a large amount of activation functions,
normalisation schemes and many others. While one can find impressively wide
spread of various configurations of almost every aspect of the deep nets, one
element is, in authors' opinion, underrepresented - while solving
classification problems, vast majority of papers and applications simply use
log loss. In this paper we try to investigate how particular choices of loss
functions affect deep models and their learning dynamics, as well as resulting
classifiers robustness to various effects. We perform experiments on classical
datasets, as well as provide some additional, theoretical insights into the
problem. In particular we show that L1 and L2 losses are, quite surprisingly,
justified classification objectives for deep nets, by providing probabilistic
interpretation in terms of expected misclassification. We also introduce two
losses which are not typically used as deep nets objectives and show that they
are viable alternatives to the existing ones.