Unraveling Attention via Convex Duality: Analysis and Interpretations of Vision Transformers
This provides interpretability for vision transformers, addressing a foundational problem in machine learning for researchers and practitioners, though it is incremental as it builds on existing attention mechanisms.
The paper tackled the lack of understanding of the inductive bias in attention mechanisms for vision transformers by analyzing them through convex duality, deriving equivalent convex problems that reveal block nuclear-norm regularization and implicit token clustering, and showed that fine-tuning convex attention heads on CIFAR-100 classification outperforms existing MLP or linear heads.
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 regularization} that promotes low rank in the latent feature and token dimensions. In particular, we show how self-attention networks implicitly clusters the tokens, based on their latent similarity. We conduct experiments for transferring a pre-trained transformer backbone for CIFAR-100 classification by fine-tuning a variety of convex attention heads. The results indicate the merits of the bias induced by attention compared with the existing MLP or linear heads.