  Jet substructure observable basis is a systematic and powerful tool for
analyzing the internal energy distribution of constituent particles within a
jet. In this work, we propose a novel method to insert neural networks into jet
substructure basis as a simple yet efficient interpretable IRC-safe deep
learning framework to discover discriminative jet observables. The Energy Flow
Polynomial (EFP) could be computed with a certain summation order, resulting in
a reorganized form which exhibits hierarchical IRC-safety. Thus inserting
non-linear functions after the separate summation could significantly extend
the scope of IRC-safe jet substructure observables, where neural networks can
come into play as an important role. Based on the structure of the simplest
class of EFPs which corresponds to path graphs, we propose the Hierarchical
Energy Flow Networks and the Local Hierarchical Energy Flow Networks. These two
architectures exhibit remarkable discrimination performance on the top tagging
dataset and quark-gluon dataset compared to other benchmark algorithms even
only utilizing the kinematic information of constituent particles.
