  Since its introduction in 2017, Transformer has emerged as the leading neural
network architecture, catalyzing revolutionary advancements in many AI
disciplines. The key innovation in Transformer is a Self-Attention (SA)
mechanism designed to capture contextual information. However, extending the
original Transformer design to models of greater depth has proven exceedingly
challenging, if not impossible. Even though various modifications have been
proposed in order to stack more layers of SA mechanism into deeper models, a
full understanding of this depth problem remains lacking. In this paper, we
conduct a comprehensive investigation, both theoretically and empirically, to
substantiate the claim that the depth problem is caused by \emph{token
similarity escalation}; that is, tokens grow increasingly alike after repeated
applications of the SA mechanism. Our analysis reveals that, driven by the
invariant leading eigenspace and large spectral gaps of attention matrices,
token similarity provably escalates at a linear rate. Based on the gained
insight, we propose a new strategy of surgically removing excessive similarity
in contrast to the existing approach of diminishing the SA mechanism explicitly
or implicitly (such as in pre-norm transformers). Preliminary experimental
results confirm the effectiveness of the proposed strategy in small-scale
post-norm Transformer models.
