  Transformers have achieved remarkable success in several domains, ranging
from natural language processing to computer vision. Nevertheless, it has been
recently shown that stacking self-attention layers - the distinctive
architectural component of Transformers - can result in rank collapse of the
tokens' representations at initialization. The question of if and how rank
collapse affects training is still largely unanswered, and its investigation is
necessary for a more comprehensive understanding of this architecture. In this
work, we shed new light on the causes and the effects of this phenomenon.
First, we show that rank collapse of the tokens' representations hinders
training by causing the gradients of the queries and keys to vanish at
initialization. Furthermore, we provide a thorough description of the origin of
rank collapse and discuss how to prevent it via an appropriate depth-dependent
scaling of the residual branches. Finally, our analysis unveils that specific
architectural hyperparameters affect the gradients of queries and values
differently, leading to disproportionate gradient norms. This suggests an
explanation for the widespread use of adaptive methods for Transformers'
optimization.
