Guanglai Gao’s research while affiliated with Inner Mongolia University and other places

The great challenge of handwritten mathematical expression recognition (HMER) is the complex structures of the expressions, which are directly related to the symbol spatial positions. Existing HMER methods typically employ attention mechanisms in the decoder of their models to implicitly perceive the symbol positions, or employ symbol counting and tree-based strategies to model the symbol spatial relation. However, these methods still cannot effectively capture the structural information of formulas, thus negatively impacting the symbol decoding in HMER. To deal with this problem and enhance the HMER performance, this paper proposes a novel auxiliary task, namely predicting the symbol spatial distribution map of handwritten expression images. On such basis, this paper designs a symbol spatial-aware network (SSAN) for this task, which is jointly optimized with the HMER model. Specifically, considering the similarity of the symbol spatial positions between the handwritten mathematical expression images and their corresponding printed templates, we obtain the symbol spatial distribution map by first generating printed templates from LaTeX ground-truth for handwritten formula images and then replacing the connected components of printed templates with 2D Gaussian distribution maps of the same size. Meanwhile, due to the loose alignment of the symbol spatial positions between handwritten and printed formula images, and misclassification of similar symbols, we further propose a coarse-to-fine alignment strategy and an attention-guided symbol masking strategy in SSAN to tackle these issues. Extensive experiments demonstrate that SSAN significantly improves the recognition performance of the HMER models, and the proposed auxiliary tasks are more effective in enhancing HMER performance than existing auxiliary tasks.

Entity alignment aims to match identical entities across different knowledge graphs (KGs). Graph neural network-based entity alignment methods have achieved promising results in Euclidean space. However, KGs often contain complex structures, including both local and hierarchical ones, which make it challenging to efficiently represent them within a single space. In this paper, we proposed a novel method UniEA, which unifies dual-space embedding to preserve the intrinsic structure of KGs. Specifically, we learn graph structure embedding in both Euclidean and hyperbolic spaces simultaneously to maximize the consistency between the embedding in both spaces. Moreover, we employ contrastive learning to mitigate the misalignment issues caused by similar entities, where embedding of similar neighboring entities within the KG become too close in distance. Extensive experiments on benchmark datasets demonstrate that our method achieves state-of-the-art performance in structure-based EA. Our code is available at https://github.com/wonderCS1213/UniEA.

Quaternion contains one real part and three imaginary parts, which provided a more expressive hypercomplex space for learning knowledge graph. Existing quaternion embedding models measure the plausibility of a triplet either through semantic matching or geometric distance scoring functions. However, it appears that semantic matching diminishes the separability of entities, while the distance scoring function weakens the semantics of entities. To address this issue, we propose a novel quaternion knowledge graph embedding model. Our model combines semantic matching with entity's geometric distance to better measure the plausibility of triplets. Specifically, in the quaternion space, we perform a right rotation on head entity and a reverse rotation on tail entity to learn rich semantic features. Then, we utilize distance adaptive translations to learn geometric distance between entities. Furthermore, we provide mathematical proofs to demonstrate our model can handle complex logical relationships. Extensive experimental results and analyses show our model significantly outperforms previous models on well-known knowledge graph completion benchmark datasets. Our code is available at https://github.com/llqy123/DaBR.