“Attention Is Not All You Need: Pure Attention Loses Rank Doubly Exponentially With Depth”, 2021-03-05 ():
Attention-based architectures have become ubiquitous in machine learning, yet our understanding of the reasons for their effectiveness remains limited.
This work proposes a new way to understand self-attention networks: we show that their output can be decomposed into a sum of smaller terms, each involving the operation of a sequence of attention heads across layers. Using this decomposition, we prove that self-attention possesses a strong inductive bias towards “token uniformity”. Specifically, without skip connections or multi-layer perceptrons (MLPs), the output converges doubly exponentially to a rank-1 matrix.
On the other hand, skip connections and MLPs stop the output from degeneration.
Our experiments verify the identified convergence phenomena on different variants of standard transformer architectures.