  We present the generating function approach to the perturbative
exponentiation of correlators of a product of Wilson lines and loops. The
exponentiated expression is presented in closed form as an algebraic function
of correlators of known operators, which can be seen as a generating function
for web diagrams. The expression is naturally split onto two parts: the
exponentiation kernel, which accumulates all non-trivial information about web
diagrams, and the defect of exponentiation, which reconstructs the matrix
exponent and is a function of the exponentiation kernel. The detailed
comparison of the presented approach with existing approaches to exponentiation
is presented as well. We also give examples of calculations within the
generating function exponentiation, namely, we consider different
configurations of light-like Wilson lines in the multi-gluon-exchange-webs
(MGEW) approximation. Within this approximation the corresponding correlators
can be calculated exactly at any order of perturbative expansion by only
algebraic manipulations. The MGEW approximation shows violation of the dipole
formula for infrared singularities at three-loop order.
