  The connection between inner small planets and outer giant planets is crucial
to our understanding of planet formation across a wide range of orbital
separations. While Kepler provided a plethora of compact multi-planet systems
at short separations ($\lesssim 1$ AU), relatively little is known about the
occurrence of giant companions at larger separations and how they impact the
architectures of the inner systems. Here, we use the catalog of systems from
the Kepler Giant Planet Search (KGPS) to study how the architectures of the
inner transiting planets correlate with the presence of outer giant planets. We
find that for systems with at least three small transiting planets, the
distribution of inner-system gap complexity ($\mathcal{C}$), a measure of the
deviation from uniform spacings, appears to differ ($p \lesssim 0.02$) between
those with an outer giant planet ($50 M_\oplus \leq M_p\sin{i} \leq 13 M_{\rm
Jup}$) and those without any outer giants. All four inner systems (with 3+
transiting planets) with outer giant(s) have a higher gap complexity
($\mathcal{C} > 0.32$) than 79% (19/24) of the inner systems without any outer
giants (median $\mathcal{C} \simeq 0.06$). This suggests that one can predict
the occurrence of outer giant companions by selecting multi-transiting systems
with highly irregular spacings. We do not find any correlation between outer
giant occurrence and the size (similarity or ordering) patterns of the inner
planets. The larger gap complexities of inner systems with an outer giant hints
that massive external planets play an important role in the formation and/or
disruption of the inner systems.
