Construction Grammar (CxG) has recently been used as the basis for probing studies that have investigated the performance of large pretrained language models (PLMs) with respect to the structure and meaning of constructions. In this position paper, we make suggestions for the continuation and augmentation of this line of research. We look at probing methodology that was not designed with CxG in mind, as well as probing methodology that was designed for specific constructions. We analyse selected previous work in detail, and provide our view of the most important challenges and research questions that this promising new field faces.

Cross-lingual language tasks typically require a substantial amount of annotated data or parallel translation data. We explore whether language representations that capture relationships among languages can be learned and subsequently leveraged in cross-lingual tasks without the use of parallel data. We generate dense embeddings for 29 languages using a denoising autoencoder, and evaluate the embeddings using the World Atlas of Language Structures (WALS) and two extrinsic tasks in a zero-shot setting: cross-lingual dependency parsing and cross-lingual natural language inference.