Unraveling Attention via Convex Duality: Analysis and Interpretations of Vision Transformers. (arXiv:2205.08078v2 [cs.LG] UPDATED)

Vision transformers using self-attention or its proposed alternatives have
demonstrated promising results in many image related tasks. However, the
underpinning inductive bias of attention is not well understood. To address
this issue, this paper analyzes attention through the lens of convex duality.
For the non-linear dot-product self-attention, and alternative mechanisms such
as MLP-mixer and Fourier Neural Operator (FNO), we derive equivalent
finite-dimensional convex problems that are interpretable and solvable to
global optimality. The convex programs lead to {\it block nuclear-norm …

analysis arxiv attention transformers vision