Natural Language Premise Selection (NLPS) is a mathematical Natural Language Processing (NLP) task that retrieves a set of applicable relevant premises to support the end-user finding the proof for a particular statement. In this research, we evaluate the impact of Transformer-based contextual information and different fundamental similarity scores toward NLPS. The results demonstrate that the contextual representation is better at capturing meaningful information despite not being pretrained in the mathematical background compared to the statistical approach (e.g., the TF-IDF) with a boost of around 3.00% MAP@500.

The reverse dictionary task is a sequence-to-vector task in which a gloss is provided as input, and the output must be a semantically matching word vector. The reverse dictionary is useful in practical applications such as solving the tip-of-the-tongue problem, helping new language learners, etc. In this paper, we evaluate the effect of a Transformer-based model with cross-lingual zero-shot learning to improve the reverse dictionary performance. Our experiments are conducted in five languages in the CODWOE dataset, including English, French, Italian, Spanish, and Russian. Even if we did not achieve a good ranking in the CODWOE competition, we show that our work partially improves the current baseline from the organizers with a hypothesis on the impact of LSTM in monolingual, multilingual, and zero-shot learning. All the codes are available at https://github.com/honghanhh/codwoe2021.