Title: Empirical observations on the instability of aligning word vector spaces with GANs. Abstract: Unsupervised bilingual dictionary induction (UBDI) is useful for unsupervised machine translation and for cross-lingual transfer of models into low-resource languages. One approach to UBDI is to align word vector spaces in different languages using Generative adversarial networks (GANs) with linear generators, achieving state-of-the-art performance for several language pairs. For some pairs, however, GAN-based induction is unstable or completely fails to align the vector spaces. We focus on cases where linear transformations provably exist, but the performance of GAN-based UBDI depends heavily on the model initialization. We show that the instability depends on the shape and density of the vector sets, but not on noise; it is the result of local optima, but neither over-parameterization nor changing the batch size or the learning rate consistently reduces instability. Nevertheless, we can stabilize GAN-based UBDI through best-of-N model selection, based on an unsupervised stopping criterion. 