Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to sca...Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.展开更多
当前基于神经网络的端到端SAT求解模型在各类SAT问题求解上展现了巨大潜力。然而SAT问题难以容忍误差存在,神经网络模型无法保证不产生预测误差。为利用SAT问题实例特性来减少模型预测误差,提出了错误偏好变量嵌入架构(architecture of ...当前基于神经网络的端到端SAT求解模型在各类SAT问题求解上展现了巨大潜力。然而SAT问题难以容忍误差存在,神经网络模型无法保证不产生预测误差。为利用SAT问题实例特性来减少模型预测误差,提出了错误偏好变量嵌入架构(architecture of embedding error-preference variables, AEEV)。该架构包含错误偏好变量嵌入调整算法和动态部分标签训练模式。首先,为利用参与越多未满足子句的变量越可能被错误分类这一特性,提出了错误偏好变量嵌入调整算法,在消息传递过程中根据变量参与的未满足子句个数来调整其嵌入。此外,提出了动态部分标签监督训练模式,该模式利用了SAT问题实例的变量赋值之间存在复杂依赖关系这一特性,避免为全部变量提供标签,仅为错误偏好变量提供一组来自真实解的标签,保持其他变量标签为预测值不变,以在训练过程管理一个更小的搜索空间。最后,在3-SAT、k-SAT、k-Coloring、3-Clique、SHA-1原像攻击以及收集的SAT竞赛数据集上进行了实验验证。结果表明,相较于目前较先进的基于神经网络的端到端求解模型QuerySAT,AEEV在包含600个变量的k-SAT数据集上准确率提升了45.81%。展开更多
空间耦合低密度奇偶校验(spatially coupled low density parity check,SC-LDPC)码在次最优迭代译码算法下能够达到最大后验概率(maximum a posterior,MAP)译码性能,但其优异的性能需要在码长很长迭代次数很多时才能实现。当采用传统迭...空间耦合低密度奇偶校验(spatially coupled low density parity check,SC-LDPC)码在次最优迭代译码算法下能够达到最大后验概率(maximum a posterior,MAP)译码性能,但其优异的性能需要在码长很长迭代次数很多时才能实现。当采用传统迭代译码算法时,实现的复杂度将以指数增加,无法应用。为有效降低译码复杂度,滑窗译码算法被应用于空间耦合LDPC码的译码,但由于引入窗口截断,会造成译码性能的损失。针对上述问题,结合深度学习技术提出了一种空间耦合LDPC码的深度迭代译码算法。通过在消息传递过程中引入权重系数并采用深度神经网络对其进行训练获取权重系数,以此优化消息的可靠性度量值,从而加快译码收敛速度,提升译码性能。仿真结果表明:当传输在加性高斯白噪声信道时,所提的深度迭代译码算法在相同迭代次数下的译码性能均优于传统迭代译码算法和滑窗译码算法。展开更多
基金supported by the National Natural Science Foundation of China-China State Railway Group Co.,Ltd.Railway Basic Research Joint Fund (Grant No.U2268217)the Scientific Funding for China Academy of Railway Sciences Corporation Limited (No.2021YJ183).
文摘Graph Convolutional Neural Networks(GCNs)have been widely used in various fields due to their powerful capabilities in processing graph-structured data.However,GCNs encounter significant challenges when applied to scale-free graphs with power-law distributions,resulting in substantial distortions.Moreover,most of the existing GCN models are shallow structures,which restricts their ability to capture dependencies among distant nodes and more refined high-order node features in scale-free graphs with hierarchical structures.To more broadly and precisely apply GCNs to real-world graphs exhibiting scale-free or hierarchical structures and utilize multi-level aggregation of GCNs for capturing high-level information in local representations,we propose the Hyperbolic Deep Graph Convolutional Neural Network(HDGCNN),an end-to-end deep graph representation learning framework that can map scale-free graphs from Euclidean space to hyperbolic space.In HDGCNN,we define the fundamental operations of deep graph convolutional neural networks in hyperbolic space.Additionally,we introduce a hyperbolic feature transformation method based on identity mapping and a dense connection scheme based on a novel non-local message passing framework.In addition,we present a neighborhood aggregation method that combines initial structural featureswith hyperbolic attention coefficients.Through the above methods,HDGCNN effectively leverages both the structural features and node features of graph data,enabling enhanced exploration of non-local structural features and more refined node features in scale-free or hierarchical graphs.Experimental results demonstrate that HDGCNN achieves remarkable performance improvements over state-ofthe-art GCNs in node classification and link prediction tasks,even when utilizing low-dimensional embedding representations.Furthermore,when compared to shallow hyperbolic graph convolutional neural network models,HDGCNN exhibits notable advantages and performance enhancements.
文摘空间耦合低密度奇偶校验(spatially coupled low density parity check,SC-LDPC)码在次最优迭代译码算法下能够达到最大后验概率(maximum a posterior,MAP)译码性能,但其优异的性能需要在码长很长迭代次数很多时才能实现。当采用传统迭代译码算法时,实现的复杂度将以指数增加,无法应用。为有效降低译码复杂度,滑窗译码算法被应用于空间耦合LDPC码的译码,但由于引入窗口截断,会造成译码性能的损失。针对上述问题,结合深度学习技术提出了一种空间耦合LDPC码的深度迭代译码算法。通过在消息传递过程中引入权重系数并采用深度神经网络对其进行训练获取权重系数,以此优化消息的可靠性度量值,从而加快译码收敛速度,提升译码性能。仿真结果表明:当传输在加性高斯白噪声信道时,所提的深度迭代译码算法在相同迭代次数下的译码性能均优于传统迭代译码算法和滑窗译码算法。
