The \({\cal G}\)-SGD algorithm significantly outperforms the conventional SGD algorithm in ReLU neural networks by adopting the basis path set. However, how the inner mechanism of basis paths works remains mysterious, and the \({\cal G}\)-SGD algorithm that helps to find a basis path set is heuristic. This paper employs graph theory to investigate structure properties of basis paths in a more general and complicated neural network with unbalanced layers and edge-skipping. The hierarchical Algorithm HBPS is proposed to find a basis path set, by decomposing the complicated network into several independent and parallel substructures. The paper theoretically extends the study of basis paths and provides one methodology to find the basis path set in a more general neural network.

的\（{\ CAL绿} \） -SGD算法显著性能优于通过采用依据路径集RELU神经网络的常规SGD算法。但是，基本路径的内部机制如何工作仍然是个谜，而有助于找到基本路径集的\（{\ cal G} \）- SGD算法是启发式的。本文利用图论研究了具有不平衡层和边缘跳跃的更通用，更复杂的神经网络中基本路径的结构特性。提出了一种分层算法HBPS，通过将复杂的网络分解为几个独立的并行子结构来找到基本路径集。本文从理论上扩展了对基础路径的研究，并提供了一种在更通用的神经网络中找到基础路径集的方法。