Luna: Linear Unified Nested Attention

Abstract

The quadratic computational and memory complexities of the Transformer’s at-tention mechanism have limited its scalability for modeling long sequences. Inthis paper, we propose Luna, a linear unified nested attention mechanism thatapproximates softmax attention withtwo nested linear attention functions, yieldingonly linear (as opposed to quadratic) time and space complexity. As compared toa more traditional attention mechanism, Luna introduces an additional sequencewith a fixed length as input and an additional corresponding output, which allowsLuna to perform attention operation linearly, while also storing adequate contextualinformation. We perform extensive evaluations on three benchmarks of sequencemodeling tasks: long-context sequence modeling, neural machine translation andmasked language modeling for large-scale pretraining. Competitive or even betterexperimental results demonstrate both the effectiveness and efficiency of Lunacompared to a variety of strong baseline methods including the full-rank attentionand other efficient sparse and dense attention methods. The implementation of ourmodel is available at https://github.com/XuezheMax/fairseq-apollo