  Machine learning techniques are increasingly being applied toward data
analyses at the Large Hadron Collider, especially with applications for
discrimination of jets with different originating particles. Previous studies
of the power of machine learning to jet physics has typically employed image
recognition, natural language processing, or other algorithms that have been
extensively developed in computer science. While these studies have
demonstrated impressive discrimination power, often exceeding that of
widely-used observables, they have been formulated in a non-constructive manner
and it is not clear what additional information the machines are learning. In
this paper, we study machine learning for jet physics constructively,
expressing all of the information in a jet onto sets of observables that
completely and minimally span N-body phase space. For concreteness, we study
the application of machine learning for discrimination of boosted, hadronic
decays of Z bosons from jets initiated by QCD processes. Our results
demonstrate that the information in a jet that is useful for discrimination
power of QCD jets from Z bosons is saturated by only considering observables
that are sensitive to 4-body (8 dimensional) phase space.
