  Cross-lingual semantic parsing transfers parsing capability from a
high-resource language (e.g., English) to low-resource languages with scarce
training data. Previous work has primarily considered silver-standard data
augmentation or zero-shot methods, however, exploiting few-shot gold data is
comparatively unexplored. We propose a new approach to cross-lingual semantic
parsing by explicitly minimizing cross-lingual divergence between probabilistic
latent variables using Optimal Transport. We demonstrate how this direct
guidance improves parsing from natural languages using fewer examples and less
training. We evaluate our method on two datasets, MTOP and MultiATIS++SQL,
establishing state-of-the-art results under a few-shot cross-lingual regime.
Ablation studies further reveal that our method improves performance even
without parallel input translations. In addition, we show that our model better
captures cross-lingual structure in the latent space to improve semantic
representation similarity.
