Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth
This addresses a foundational issue for researchers in machine learning by revealing a critical limitation in transformer architectures, though it is incremental as it builds on existing theoretical analyses.
The paper tackled the problem of understanding why self-attention networks work by proving that pure attention layers, without skip connections or MLPs, cause the output to converge doubly exponentially to a rank-1 matrix, leading to token uniformity, while experiments confirmed this convergence in transformer variants.
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.