Papers › Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth

Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth

5 Mar 2021arXiv:2103.03404archive 2025-07-28

Yihe Dong, Jean-Baptiste Cordonnier, Andreas Loukas

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.

PaperPDFCode

In Syntology View this paper on Syntology: its repositories, every harvested function with whether it ran, its licence and the call to fetch it.

Open this paper in Syntology's Atlas, the map of the papers in Syntology's graph and their citations.

Code

twistedcubic/attention-rank-collapse officialmentioned in papermentioned on GitHubpytorch report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Tasks

AllInductive Bias

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Methods

Absolute Position EncodingsAdamAttentionBPEDense ConnectionsDropoutLabel SmoothingLayer NormalizationLinear LayerMulti-Head AttentionPosition-Wise Feed-Forward LayerResidual ConnectionSoftmaxTransformer

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections