To solve Math Word Problems, human students leverage diverse reasoning logic that reaches different possible equation solutions. However, the mainstream sequence-to-sequence approach of automatic solvers aims to decode a fixed solution equation supervised by human annotation. In this paper, we propose a controlled equation generation solver by leveraging a set of control codes to guide the model to consider certain reasoning logic and decode the corresponding equations expressions transformed from the human reference. The empirical results suggest that our method universally improves the performance on single-unknown (Math23K) and multiple-unknown (DRAW1K, HMWP) benchmarks, with substantial improvements up to 13.2% accuracy on the challenging multiple-unknown datasets.

Word alignment has proven to benefit many-to-many neural machine translation (NMT). However, high-quality ground-truth bilingual dictionaries were used for pre-editing in previous methods, which are unavailable for most language pairs. Meanwhile, the contrastive objective can implicitly utilize automatically learned word alignment, which has not been explored in many-to-many NMT. This work proposes a word-level contrastive objective to leverage word alignments for many-to-many NMT. Empirical results show that this leads to 0.8 BLEU gains for several language pairs. Analyses reveal that in many-to-many NMT, the encoder’s sentence retrieval performance highly correlates with the translation quality, which explains when the proposed method impacts translation. This motivates future exploration for many-to-many NMT to improve the encoder’s sentence retrieval performance.