State-of-the-art approaches to spelling error correction problem include Transformer-based Seq2Seq models, which require large training sets and suffer from slow inference time; and sequence labeling models based on Transformer encoders like BERT, which involve token-level label space and therefore a large pre-defined vocabulary dictionary. In this paper we present a Hierarchical Character Tagger model, or HCTagger, for short text spelling error correction. We use a pre-trained language model at the character level as a text encoder, and then predict character-level edits to transform the original text into its error-free form with a much smaller label space. For decoding, we propose a hierarchical multi-task approach to alleviate the issue of long-tail label distribution without introducing extra model parameters. Experiments on two public misspelling correction datasets demonstrate that HCTagger is an accurate and much faster approach than many existing models.

Link prediction is critical for the application of incomplete knowledge graph (KG) in the downstream tasks. As a family of effective approaches for link predictions, embedding methods try to learn low-rank representations for both entities and relations such that the bilinear form defined therein is a well-behaved scoring function. Despite of their successful performances, existing bilinear forms overlook the modeling of relation compositions, resulting in lacks of interpretability for reasoning on KG. To fulfill this gap, we propose a new model called DihEdral, named after dihedral symmetry group. This new model learns knowledge graph embeddings that can capture relation compositions by nature. Furthermore, our approach models the relation embeddings parametrized by discrete values, thereby decrease the solution space drastically. Our experiments show that DihEdral is able to capture all desired properties such as (skew-) symmetry, inversion and (non-) Abelian composition, and outperforms existing bilinear form based approach and is comparable to or better than deep learning models such as ConvE.