  An affine connection is said to be flat if its curvature tensor vanishes
identically. Koszul-Vinberg (KV for abbreviation) cohomology has been invoked
to study the deformation theory of flat and torsion-free affine connections on
tangent bundle. In this Note, we compute explicitly the differentials of
various specific KV cochains, and study their relation to classical objects in
information geometry, including deformations associated with projective and
dual-projective transformations of a flat and torsion-free affine connection.
As an application, we also give a simple yet non-trivial example of a KV
algebra of which second cohomology group does not vanish.
