The Transformer architecture has become a dominant choice in many domains, such as natural language processing and computer vision. Yet, it has not achieved competitive performance on popular leaderboards of graph-level prediction compared to mainstream GNN variants. Therefore, it remains a mystery how Transformers could perform well for graph representation learning. In this paper, we solve this mystery by presenting Graphormer, which is built upon the standard Transformer architecture, and could attain excellent results on a broad range of graph representation learning tasks, especially on the recent OGB Large-Scale Challenge. Our key insight to utilizing Transformer in the graph is the necessity of effectively encoding the structural information of a graph into the model. To this end, we propose several simple yet effective structural encoding methods to help Graphormer better model graph-structured data. Besides, we mathematically characterize the expressive power of Graphormer and exhibit that with our ways of encoding the structural information of graphs, many popular GNN variants could be covered as the special cases of Graphormer. The code and models of Graphormer will be made publicly available at https://github.com/Microsoft/Graphormer.

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Transforming an organic/inorganic hybrid material into a pure inorganic material without losing its original structure is of interest for a range of applications. In this work, a simple and effective vapor phase hydrothermal method was developed to transform a 3D honeycomb structured PS/TTIP hybrid film into a photoactive TiO2 film without dismantling the originally templated 3D structure. The method utilizes the vapor phase hydrothermal process to create titania network/clusters with sufficient mechanical strength via the formation of Ti-oxo bridges. The organic components of the sample can be removed by means of pyrolysis while perfectly maintaining the original 3D honeycomb structure. The resultant film can be directly used for photocatalysis applications and could be further modified for other applications. In principle, this method can be used to preserve 3D structures of other organic/inorganic hybrid films during their conversion to pure inorganic films via a pyrolysis process, if mechanically strong networks can be formed as a result of hydrolysis reactions. The ability to preserve the preferred 3D structure during the subsequent conversion processes enables realization of the full benefit of unique architectures created by a templating method.