  Autoregressive decoding limits the efficiency of transformers for Machine
Translation (MT). The community proposed specific network architectures and
learning-based methods to solve this issue, which are expensive and require
changes to the MT model, trading inference speed at the cost of the translation
quality. In this paper, we propose to address the problem from the point of
view of decoding algorithms, as a less explored but rather compelling
direction. We propose to reframe the standard greedy autoregressive decoding of
MT with a parallel formulation leveraging Jacobi and Gauss-Seidel fixed-point
iteration methods for fast inference. This formulation allows to speed up
existing models without training or modifications while retaining translation
quality. We present three parallel decoding algorithms and test them on
different languages and models showing how the parallelization introduces a
speedup up to 38% w.r.t. the standard autoregressive decoding and nearly 2x
when scaling the method on parallel resources. Finally, we introduce a decoding
dependency graph visualizer (DDGviz) that let us see how the model has learned
the conditional dependence between tokens and inspect the decoding procedure.
