Abstract: Graph matching aims to establishing node-wise correspondence between two graphs, which is a classic combinatorial problem and in general NP-complete. Until very recently, deep graph matching methods start to resort to deep networks to achieve unprecedented matching accuracy. Along this direction, this paper makes two complementary contributions which can also be reused as plugin in existing works: i) a novel node and edge embedding strategy which stimulates the multi-head strategy in attention models and allows the information in each channel to be merged independently. In contrast, only node embedding is accounted in previous works; ii) a general masking mechanism over the loss function is devised to improve the smoothness of objective learning for graph matching. Using Hungarian algorithm, it dynamically constructs a structured and sparsely connected layer, taking into account the most contributing matching pairs as hard attention. Our approach performs competitively, and can also improve state-of-the-art methods as plugin, regarding with matching accuracy on three public benchmarks.