string: They initialize their orthogonal mapping using an adversarial training phase, much like Conneau et al. [2018], and solve the optimization problem with alternating minimization. Our approach differs from theirs: by bootstrapping on the solution of a smaller problem to initialize the mapping, we avoid the need for a neural network initialization that is used in their approach. In addition, our annealing scheme on the entropic regularization leads to smooth convergence, with very little sensitivity to initialization. Concurrently with our work,1 Grave et al. [2018] tackle the problem of unsupervised word embedding alignment with a similar optimization framework as the one proposed by Zhang et al.