Title: Ripple Attention for Visual Perception with Sub-quadratic Complexity. Abstract: Transformer architectures are now central to modeling in natural language processing tasks. At its heart is the attention mechanism, which enables effective modeling of long-term dependencies in a sequence. Recently, transformers have been successfully applied in the computer vision domain, where 2D images are first segmented into patches and then treated as 1D sequences. Such linearization, however, impairs the notion of spatial locality in images, which bears important visual clues. To bridge the gap, we propose ripple attention, a sub-quadratic attention mechanism for visual perception. In ripple attention, contributions of different tokens to a query are weighted with respect to their relative spatial distances in the 2D space. To favor correlations with vicinal tokens yet permit long-term dependencies, we derive the spatial weights through a stick-breaking transformation. We further design a dynamic programming algorithm that computes weighted contributions for all queries in linear observed time, taking advantage of the summed-area table and recent advances in linearized attention. Extensive experiments and analyses demonstrate the effectiveness of ripple attention on various visual tasks.