  Theories with large mass anomalous dimensions ($\gamma_m$) have been
extensively studied because of their deep consequences for models where the
scalar bosons are composite. Large $\gamma_m$ values may appear when a
non-Abelian gauge theory has a large number of fermions or is affected by
four-fermion interactions. In this note we provide a simple explanation how
$\gamma_m$ can be directly read out from the IR and UV boundary conditions
derived from the gap equation, and verify that moderate $\gamma_m$ values
appear when the theory possess a large number of fermions, but large $\gamma_m$
values are obtained only when four-fermion interactions are added to the
theory. We also verify how the critical line separating the different chiral
phases emerge from these conditions.
