  We address the scaling behaviour of contour-shape-dependent ultra-violet
singularities of the light-like cusped Wilson loops in Yang-Mills and ${\cal N}
= 4$ super-Yang-Mills theories in the higher orders of the perturbative
expansion. We give the simple arguments to support the idea that identifying of
a special type of non-local infinitesimal shape variations of the light-like
Wilson polygons with the Fr\'echet differentials results in the combined
geometric and renormalization-group evolution equation, which is applicable
beyond the leading order exponentiated Wilson loops.
