  One of the major sources of perturbation in the solar cycle amplitude is
believed to be the emergence of anomalous active regions which do not obey
Hale's polarity law and Joy's law of tilt angles. Anomalous regions containing
high magnetic flux that disproportionately impact the polar field are sometimes
referred to as ``rogue regions". In this study -- utilizing a surface flux
transport model -- we analyze the large-scale dipole moment build-up due to the
emergence of anomalous active regions on the solar surface. Although these
active regions comprise a small fraction of the total sunspot number, they can
substantially influence the magnetic dipole moment build-up and subsequent
solar cycle amplitude. Our numerical simulations demonstrate that the impact of
``Anti-Joy'' regions on the solar cycle is similar to those of ``Anti-Hale''
regions. We also find that the emergence time, emergence latitude, relative
number and flux distribution of anomalous regions influence the large-scale
magnetic field dynamics in diverse ways. We establish that the results of our
numerical study are consistent with the algebraic (analytic) approach to
explaining the Sun's dipole moment evolution. Our results are relevant for
understanding how anomalous active regions modulate the Sun's large-scale
dipole moment build-up and its reversal timing within the framework of the
Babcock-Leighton dynamo mechanism -- now believed to be the primary source of
solar cycle variations.
