Preserving the structural properties of trees or graphs when embedding them into a metric space allows for a high degree of interpretability, and has been shown beneficial for downstream tasks (e.g., hypernym detection, natural language inference, multimodal retrieval). However, whereas the majority of prior work looks at using structure-preserving embeddings when encoding a structure given as input, e.g., WordNet (Fellbaum, 1998), there is little exploration on how to use such embeddings when predicting one. We address this gap for two structure generation tasks, namely dependency and semantic parsing. We test the applicability of disk embeddings (Suzuki et al., 2019) that has been proposed for embedding Directed Acyclic Graphs (DAGs) but has not been tested on tasks that generate such structures. Our experimental results show that for both tasks the original disk embedding formulation leads to much worse performance when compared to non-structure-preserving baselines. We propose enhancements to this formulation and show that they almost close the performance gap for dependency parsing. However, the gap still remains notable for semantic parsing due to the complexity of meaning representation graphs, suggesting a challenge for generating interpretable semantic parse representations.

Modern neural approaches to dependency parsing are trained to predict a tree structure by jointly learning a contextual representation for tokens in a sentence, as well as a head–dependent scoring function. Whereas this strategy results in high performance, it is difficult to interpret these representations in relation to the geometry of the underlying tree structure. Our work seeks instead to learn interpretable representations by training a parser to explicitly preserve structural properties of a tree. We do so by casting dependency parsing as a tree embedding problem where we incorporate geometric properties of dependency trees in the form of training losses within a graph-based parser. We provide a thorough evaluation of these geometric losses, showing that a majority of them yield strong tree distance preservation as well as parsing performance on par with a competitive graph-based parser (Qi et al., 2018). Finally, we show where parsing errors lie in terms of tree relationship in order to guide future work.