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Jet substructure observable basis is a systematic and powerful tool foranalyzing the internal energy distribution of constituent particles within ajet. In this work, we propose a novel method to insert neural networks into jetsubstructure basis as a simple yet efficient interpretable IRC-safe deeplearning framework to discover discriminative jet observables. The Energy FlowPolynomial (EFP) could be computed with a certain summation order, resulting ina reorganized form which exhibits hierarchical IRC-safety. Thus insertingnon-linear functions after the separate summation could significantly extendthe scope of IRC-safe jet substructure observables, where neural networks cancome into play as an important role. Based on the structure of the simplestclass of EFPs which corresponds to path graphs, we propose the HierarchicalEnergy Flow Networks and the Local Hierarchical Energy Flow Networks. These twoarchitectures exhibit remarkable discrimination performance on the top taggingdataset and quark-gluon dataset compared to other benchmark algorithms evenonly utilizing the kinematic information of constituent particles.

Hierarchical High-Point Energy Flow Network for Jet Tagging