  We introduce the notion of dR-absolutely special subvarieties in motivic
variations of Hodge structure as special subvarieties cut out by (de
Rham-)absolute Hodge cycles and conjecture that all special subvarieties are
dR-absolutely special. This is implied by Deligne's conjecture that all Hodge
cycles are absolute Hodge cycles, but is a much weaker conjecture. We prove our
conjecture for subvarieties satisfying a simple monodromy condition introduced
by Klingler-Otwinowska-Urbanik. We study applications to typical respectively
atypical intersections and $\bar{\mathbb{Q}}$-bialgebraic subvarieties.
Finally, we show that Deligne's conjecture as well as ours can be reduced to
the case of special points in motivic variations.
