Self-attention and masked self-attention are at the heart of Transformers’ outstanding success. Still, our mathematical understanding of attention, in particular of its Lipschitz properties — which are key when it comes to analyzing robustness and expressive power — is incomplete. We provide a detailed study of the Lipschitz constant of self-attention in several practical scenarios, discussing the impact of the sequence length and layer normalization on the local Lipschitz constant of both unmasked and masked self-attention. In particular, we show that for inputs of length n in any compact…
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