  Softmax is widely used in neural networks for multiclass classification, gate
structure and attention mechanisms. The statistical assumption that the input
is normal distributed supports the gradient stability of Softmax. However, when
used in attention mechanisms such as transformers, since the correlation scores
between embeddings are often not normally distributed, the gradient vanishing
problem appears, and we prove this point through experimental confirmation. In
this work, we suggest that replacing the exponential function by periodic
functions, and we delve into some potential periodic alternatives of Softmax
from the view of value and gradient. Through experiments on a simply designed
demo referenced to LeViT, our method is proved to be able to alleviate the
gradient problem and yield substantial improvements compared to Softmax and its
variants. Further, we analyze the impact of pre-normalization for Softmax and
our methods through mathematics and experiments. Lastly, we increase the depth
of the demo and prove the applicability of our method in deep structures.
