  The way the basis path set works in neural network remains mysterious, and
the generalization of newly appeared G-SGD algorithm to more practical network
is hindered. The Basis Path Set Searching problem is formulated from the
perspective of graph theory, to find the basis path set in a regular
complicated neural network. Our paper aims to discover the underlying cause of
path dependency between two independent substructures. Algorithm DEAH is
designed to solve the Basis Path Set Searching problem by eliminating such path
dependency. The path subdivision chain is proposed to effectively eliminate the
path dependency inside the chain and between chains. The theoretical proofs and
analysis of polynomial time complexity are presented. The paper therefore
provides one methodology to find the basis path set in a more general neural
network, which offers theoretical and algorithmic support for the application
of G-SGD algorithm in more practical scenarios.
