  In a joint work [9] with Kazuya Kato and Chikara Nakayama, log higher
Albanese manifolds was constructed as an application of log mixed Hodge theory
with group action. In this framework, we describe a work of Deligne in [3] on
some nilpotent quotients of the fundamental group of the projective line minus
three points, where polylogarithms appear. As a result, we have $q$-expansions
of higher Albanese maps at boundary points, i.e., log higher Albanese maps over
the boundary.
