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

• URL: http://arxiv.org/abs/2103.03404v2
• Date: Tue, 1 Aug 2023 14:27:08 GMT
• Title: Attention is Not All You Need: Pure Attention Loses Rank Doubly Exponentially with Depth
• Authors: Yihe Dong, Jean-Baptiste Cordonnier, Andreas Loukas
• Abstract summary: 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. We prove that self-attention possesses a strong inductive bias towards "token"
• Score: 48.16156149749371
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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