  We study the effectiveness of theoretically-motivated high-level jet
observables in the extreme context of jets with a large number of hard sub-jets
(up to $N=8$). Previous studies indicate that high-level observables are
powerful, interpretable tools to probe jet substructure for $N\le 3$ hard
sub-jets, but that deep neural networks trained on low-level jet constituents
match or slightly exceed their performance. We extend this work for up to $N=8$
hard sub-jets, using deep particle-flow networks (PFNs) and Transformer based
networks to estimate a loose upper bound on the classification performance. A
fully-connected neural network operating on a standard set of high-level jet
observables, 135 $\textrm{N}$-subjetiness observables and jet mass, reach
classification accuracy of 86.90\%, but fall short of the PFN and Transformer
models, which reach classification accuracies of 89.19\% and 91.27\%
respectively, suggesting that the constituent networks utilize information not
captured by the set of high-level observables. We then identify additional
high-level observables which are able to narrow this gap, and utilize LASSO
regularization for feature selection to identify and rank the most relevant
observables and provide further insights into the learning strategies used by
the constituent-based neural networks. The final model contains only 31
high-level observables and is able to match the performance of the PFN and
approximate the performance of the Transformer model to within 2\%.
