We present a scalable neural method to solve the Gromov-Wasserstein (GW) Optimal Transport (OT) problem with the inner product cost. In this problem, given two distributions supported on (possibly different) spaces, one has to find the most isometric map between them. Our proposed approach uses neural networks and stochastic mini-batch optimization which allows to overcome the limitations of existing GW methods such as their poor scalability with the number of samples and the lack of out-of-sample estimation. To demonstrate the effectiveness of our proposed method, we conduct experiments on the synthetic data and explore the practical applicability of our method to the popular task of the unsupervised alignment of word embeddings.

翻译：我们提出了一种可扩展的神经方法，用于求解内积代价下的Gromov-Wasserstein (GW)最优输运(OT)问题。在该问题中，给定两个定义在（可能不同）空间上的分布，需要寻找它们之间最等距的映射。我们的方法利用神经网络和随机小批量优化，克服了现有GW方法的局限性，例如样本数量扩展性差以及缺乏样本外估计能力。为了证明所提方法的有效性，我们在合成数据上进行了实验，并探讨了该方法在无监督词嵌入对齐这一常见任务中的实际应用。