Without my books, I cannot remember what if any are the rules for abilities with accelerated advancement? Which abilities are these and how does such advancement work?
Accelerated abilites are generally those whose effects are generally weighed against a Creature's Might score (Hermetic Sahir, for example). The mechanic involved is that the ability advancement is done as with Arts rather than abilities (e.g. lvl1xp rather than lvl5xp).