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Many real-world data can be modeled as 3D graphs, but learningrepresentations that incorporates 3D information completely and efficiently ischallenging. Existing methods either use partial 3D information, or suffer fromexcessive computational cost. To incorporate 3D information completely andefficiently, we propose a novel message passing scheme that operates within1-hop neighborhood. Our method guarantees full completeness of 3D informationon 3D graphs by achieving global and local completeness. Notably, we proposethe important rotation angles to fulfill global completeness. Additionally, weshow that our method is orders of magnitude faster than prior methods. Weprovide rigorous proof of completeness and analysis of time complexity for ourmethods. As molecules are in essence quantum systems, we build the\underline{com}plete and \underline{e}fficient graph neural network (ComENet)by combing quantum inspired basis functions and the proposed message passingscheme. Experimental results demonstrate the capability and efficiency ofComENet, especially on real-world datasets that are large in both numbers andsizes of graphs. Our code is publicly available as part of the DIG library(\url{https://github.com/divelab/DIG}).

ComENet: Towards Complete and Efficient Message Passing for 3D Molecular Graphs