  We introduce and analytically illustrate that hitherto unexplored imaginary
components of out-of-time correlators can provide unprecedented insight into
the information scrambling capacity of a graph neural network. Furthermore, we
demonstrate that it can be related to conventional measures of correlation like
quantum mutual information and rigorously establish the inherent mathematical
bounds (both upper and lower bound) jointly shared by such seemingly disparate
quantities. To consolidate the geometrical ramifications of such bounds during
the dynamical evolution of training we thereafter construct an emergent convex
space. This newly designed space offers much surprising information including
the saturation of lower bound by the trained network even for physical systems
of large sizes, transference, and quantitative mirroring of spin correlation
from the simulated physical system across phase boundaries as desirable
features within the latent sub-units of the network (even though the latent
units are directly oblivious to the simulated physical system) and the ability
of the network to distinguish exotic spin connectivity(volume-law vs area law).
Such an analysis demystifies the training of quantum machine learning models by
unraveling how quantum information is scrambled through such a network
introducing correlation surreptitiously among its constituent sub-systems and
open a window into the underlying physical mechanism behind the emulative
ability of the model.
