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Transformers provide a class of expressive architectures that are extremelyeffective for sequence modeling. However, the key limitation of transformers istheir quadratic memory and time complexity $\mathcal{O}(L^2)$ with respect tothe sequence length in attention layers, which restricts application inextremely long sequences. Most existing approaches leverage sparsity orlow-rank assumptions in the attention matrix to reduce cost, but sacrificeexpressiveness. Instead, we propose Combiner, which provides full attentioncapability in each attention head while maintaining low computation and memorycomplexity. The key idea is to treat the self-attention mechanism as aconditional expectation over embeddings at each location, and approximate theconditional distribution with a structured factorization. Each location canattend to all other locations, either via direct attention, or through indirectattention to abstractions, which are again conditional expectations ofembeddings from corresponding local regions. We show that most sparse attentionpatterns used in existing sparse transformers are able to inspire the design ofsuch factorization for full attention, resulting in the same sub-quadratic cost($\mathcal{O}(L\log(L))$ or $\mathcal{O}(L\sqrt{L})$). Combiner is a drop-inreplacement for attention layers in existing transformers and can be easilyimplemented in common frameworks. An experimental evaluation on bothautoregressive and bidirectional sequence tasks demonstrates the effectivenessof this approach, yielding state-of-the-art results on several image and textmodeling tasks.

Combiner: Full Attention Transformer with Sparse Computation Cost