一种针对三维图分类问题的量子群等变图神经网络  

A quantum group equivariant graph neural network for 3D graph classification

作　　者：刘文杰[1,2,3] 朱奕帆 吴青山 LIU Wenjie;ZHU Yifan;WU Qingshan(The School of Software,Nanjing University of Information Science and Technology,Nanjing 210044,China;Jiangsu Collaborative Innovation Center of Atmospheric Environment and Equipment Technology,Nanjing University of Information Science and Technology,Nanjing 210044,China;Jiangsu Province Engineering Research Center of Advanced Computing and Intelligent Services,Nanjing University of Information Science and Technology,Nanjing 210044,China)

机构地区：[1]南京信息工程大学软件学院,南京210044 [2]南京信息工程大学江苏省大气环境与装备技术协同创新中心,南京210044 [3]南京信息工程大学江苏省先进计算与智能服务工程研究中心,南京210044

出　　处：《中国科学:物理学、力学、天文学》2025年第4期108-115,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(编号:62071240);科技创新2030—“量子通信与量子计算机”重大项目(编号:2021ZD0302901);江苏省自然科学基金(编号:BK20231142)资助项目。

摘　　要：作为三维图数据的重要特征,等变性近年来一直受到研究者们的密切关注.研究者们通过设计针对不同等变性的量子门集来构建等变量子图神经网络,显著提升了图学习模型的性能.然而,三维图数据包含多种等变性,如旋转等变性、平移等变性、反射等变性和排列等变性等,使研究者们难以构建满足所有等变性的量子等变图神经网络.为了解决上述问题,本文设计了一种三维图节点相对坐标计算方法,并提出了一种新型的量子群等变图神经网络.在该网络中,我们构建了一个群等变编码模块以编码相对坐标,并用一个排列等变卷积模块来学习编码的几何信息,最后采用一个纠缠模块来聚合全局特征.ModelNet40数据集和ShapeNet数据集上的分类实验表明,所提模型表现优于QGCNN,sQCNN-3D和PI-QSVM,同时在训练参数更少的情况下,准确度接近Q3DGL.Equivariance is a crucial property of 3D graph data that has gathered significant attention from researchers in recent years.By designing quantum gate sets tailored to specific types of equivariance,researchers have successfully developed equivariant quantum graph neural networks,significantly improving the performance of graph learning models.However,3D graph data exhibit various types of equivariances,such as rotation,translation,reflection,and permutation equivariances,which complicates the construction of a quantum graph neural network that can accommodate all these equivariances To overcome this challenge,this study introduces a method for calculating relative coordinates of 3D graph nodes and proposes a novel quantum group-equivariant graph neural network.This network incorporates a group-equivariant encoding module to encode relative coordinates,a permutation-equivariant convolution module to extract geometric information,and an entanglement module to aggregate global features.Classification experiments conducted on the ModelNet40 and ShapeNet datasets reveal that the proposed model outperforms existing approaches,including QGCNN,sQCNN-3D,and PI-QSVM.Furthermore,it achieves accuracy comparable to Q3DGL while requiring fewer training parameters.

关 键 词：等变图神经网络 三维图数据 E(3)等变群 排列等变 点云分类 三维模型分类 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]