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Attention, specifically scaled dot-product attention, has proven effectivefor natural language, but it does not have a mechanism for handlinghierarchical patterns of arbitrary nesting depth, which limits its ability torecognize certain syntactic structures. To address this shortcoming, we proposestack attention: an attention operator that incorporates stacks, inspired bytheir theoretical connections to context-free languages (CFLs). We show thatstack attention is analogous to standard attention, but with a latent model ofsyntax that requires no syntactic supervision. We propose two variants: onerelated to deterministic pushdown automata (PDAs) and one based onnondeterministic PDAs, which allows transformers to recognize arbitrary CFLs.We show that transformers with stack attention are very effective at learningCFLs that standard transformers struggle on, achieving strong results on a CFLwith theoretically maximal parsing difficulty. We also show that stackattention is more effective at natural language modeling under a constrainedparameter budget, and we include results on machine translation.

Stack Attention: Improving the Ability of Transformers to Model Hierarchical Patterns