Transformers, parallel computation, and logarithmic depth

We show that a constant number of self-attention layers can efficiently simulate—and be simulated by—a constant number of communication rounds ofMassively 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.