  Softmax function is widely used in artificial neural networks for multiclass
classification, multilabel classification, attention mechanisms, etc. However,
its efficacy is often questioned in literature. The log-softmax loss has been
shown to belong to a more generic class of loss functions, called spherical
family, and its member log-Taylor softmax loss is arguably the best alternative
in this class. In another approach which tries to enhance the discriminative
nature of the softmax function, soft-margin softmax (SM-softmax) has been
proposed to be the most suitable alternative. In this work, we investigate
Taylor softmax, SM-softmax and our proposed SM-Taylor softmax, an amalgamation
of the earlier two functions, as alternatives to softmax function. Furthermore,
we explore the effect of expanding Taylor softmax up to ten terms (original
work proposed expanding only to two terms) along with the ramifications of
considering Taylor softmax to be a finite or infinite series during
backpropagation. Our experiments for the image classification task on different
datasets reveal that there is always a configuration of the SM-Taylor softmax
function that outperforms the normal softmax function and its other
alternatives.

Machine Learning