The task of completing knowledge triplets has broad downstream applications. Both structural and semantic information plays an important role in knowledge graph completion. Unlike previous approaches that rely on either the structures or semantics of the knowledge graphs, we propose to jointly embed the semantics in the natural language description of the knowledge triplets with their structure information. Our method embeds knowledge graphs for the completion task via fine-tuning pre-trained language models with respect to a probabilistic structured loss, where the forward pass of the language models captures semantics and the loss reconstructs structures. Our extensive experiments on a variety of knowledge graph benchmarks have demonstrated the state-of-the-art performance of our method. We also show that our method can significantly improve the performance in a low-resource regime, thanks to the better use of semantics. The code and datasets are available at https://github.com/pkusjh/LASS.

Math word problem (MWP) is a challenging and critical task in natural language processing. Many recent studies formalize MWP as a generation task and have adopted sequence-to-sequence models to transform problem descriptions to mathematical expressions. However, mathematical expressions are prone to minor mistakes while the generation objective does not explicitly handle such mistakes. To address this limitation, we devise a new ranking task for MWP and propose Generate & Rank, a multi-task framework based on a generative pre-trained language model. By joint training with generation and ranking, the model learns from its own mistakes and is able to distinguish between correct and incorrect expressions. Meanwhile, we perform tree-based disturbance specially designed for MWP and an online update to boost the ranker. We demonstrate the effectiveness of our proposed method on the benchmark and the results show that our method consistently outperforms baselines in all datasets. Particularly, in the classical Math23k, our method is 7% (78.4% to 85.4%) higher than the state-of-the-art. Code could be found at https://github.com/huawei-noah/noah-research.