Transformers, parallel computation, and logarithmic depth

Abstract

We show that a constant number of self-attention layers can efficiently simulate, and be simulated by, a constant number of communication rounds of Massively Parallel Computation. As a consequence, we show that logarithmic depth is sufficient for transformers to solve basic computational tasks that cannot be efficiently solved by several other neural sequence models and sub-quadratic transformer approximations. We thus establish parallelism as a key distinguishing property of transformers.

58 pages, 19 figures, code available at https://github.com/chsanford/hop-induction-heads