Vision-Transformers are widely used in various vision tasks. Meanwhile, there is another line of works starting with the MLP-mixer trying to achieve similar performance using mlp-based architectures. Interestingly, until now those mlp-based architectures have not been adapted for NLP tasks. Additionally, until now, mlp-based architectures have failed to achieve state-of-the-art performance in vision tasks. In this paper, we analyze the expressive power of mlp-based architectures in modeling dependencies between multiple different inputs simultaneously, and show an exponential gap between the attention and the mlp-based mechanisms. Our results suggest a theoretical explanation for the mlp inability to compete with attention-based mechanisms in NLP problems, they also suggest that the performance gap in vision tasks may be due to the mlp relative weakness in modeling dependencies between multiple different locations, and that combining smart input permutations with mlp architectures may not be enough to close the performance gap alone.
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