  We construct small-x evolution equations which can be used to calculate quark
and anti-quark helicity TMDs and PDFs, along with the $g_1$ structure function.
These evolution equations resum powers of $\alpha_s \, \ln^2 (1/x)$ in the
polarization-dependent evolution along with the powers of $\alpha_s \, \ln
(1/x)$ in the unpolarized evolution which includes saturation effects. The
equations are written in an operator form in terms of polarization-dependent
Wilson line-like operators. While the equations do not close in general, they
become closed and self-contained systems of non-linear equations in the
large-$N_c$ and large-$N_c \, \& \, N_f$ limits. As a cross-check, in the
ladder approximation, our equations map onto the same ladder limit of the
infrared evolution equations for $g_1$ structure function derived previously by
Bartels, Ermolaev and Ryskin.
