Although well-documented, the improved performance of deep learning methods in jet classification still needs a definitive understanding within perturbative QCD dynamics. In this talk, I'll discuss infra-red and collinear (IRC) safe deep learning algorithms as a first step to discussing the pQCD properties of deep learning on the measured jet constituents. The feature extraction has a natural connection with C-correlators--a complete basis of IRC-safe observables, which reveals that currently available algorithms fail to extract features from any N-point correlation that isn't a power of two. We introduce Hypergraph Energy-weighted Message Passing Networks (H-EMPNs) designed to efficiently capture any N-point correlation among particles to address this limitation. Using the case study of top vs. QCD jets, which holds significant information in its 3-point correlations, we demonstrate that H-EMPNs targeting up to N=3 correlations exhibit superior performance compared to EMPNs focusing on up to N=4 correlations within jet constituents.