  Gradient Flow Exact Renormalization Group (GFERG) is a framework to define
the Wilson action via a gradient flow equation. We study the fixed point
structure of the GFERG equation associated with a general gradient flow
equation for scalar field theories and show that it is the same as that of the
conventional Wilson-Polchinski (WP) equation in general. Furthermore, we
discuss that the GFERG equation has a similar RG flow structure around a fixed
point to the WP equation. We illustrate these results with the $O(N)$
non-linear sigma model in $4-\epsilon$ dimensions and the Wilson-Fisher fixed
point.
