Embedding knowledge graphs (KGs) for multi-hop logical reasoning is a challenging problem due to massive and complicated structures in many KGs. Recently, many promising works projected entities and queries into a geometric space to efficiently find answers. However, it remains challenging to model the negation and union operator. The negation operator has no strict boundaries, which generates overlapped embeddings and leads to obtaining ambiguous answers. An additional limitation is that the union operator is non-closure, which undermines the model to handle a series of union operators. To address these problems, we propose a novel probabilistic embedding model, namely Gamma Embeddings (GammaE), for encoding entities and queries to answer different types of FOL queries on KGs. We utilize the linear property and strong boundary support of the Gamma distribution to capture more features of entities and queries, which dramatically reduces model uncertainty. Furthermore, GammaE implements the Gamma mixture method to design the closed union operator. The performance of GammaE is validated on three large logical query datasets. Experimental results show that GammaE significantly outperforms state-of-the-art models on public benchmarks.

Manifold’s English-Chinese System at WMT22 is an ensemble of 4 models trained by different configurations with scheduled sampling-based fine-tuning. The four configurations are DeepBig (XenC), DeepLarger (XenC), DeepBig-TalkingHeads (XenC) and DeepBig (LaBSE). Concretely, DeepBig extends Transformer-Big to 24 encoder layers. DeepLarger has 20 encoder layers and its feed-forward network (FFN) dimension is 8192. TalkingHeads applies the talking-heads trick. For XenC configs, we selected monolingual and parallel data that is similar to the past newstest datasets using XenC, and for LaBSE, we cleaned the officially provided parallel data using LaBSE pretrained model. According to the officially released autonomic metrics leaderboard, our final constrained system ranked 1st among all others when evaluated by bleu-all, chrf-all and COMET-B, 2nd by COMET-A.