  In this study, we critically evaluate the approximation capabilities of
existing infra-red and collinear (IRC) safe feature extraction algorithms,
namely Energy Flow Networks (EFNs) and Energy-weighted Message Passing Networks
(EMPNs). Our analysis reveals that these algorithms fall short in extracting
features from any $N$-point correlation that isn't a power of two, based on the
complete basis of IRC safe observables, specifically C-correlators. To address
this limitation, we introduce the Hypergraph Energy-weighted Message Passing
Networks (H-EMPNs), designed to capture any $N$-point correlation among
particles efficiently. 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.
