I'm going to hold to the traditional line - there already is training going on, you just don't really see it reflected in mechanics until the moment of leveling. The stepwise nature of learning is an artifact of the system, but it really isn't too hard to gloss over, such that it looks like a smooth continuum.
For example, I'm playing in a Star Wars Saga Edition game right now, and my Scout is about to pick up a level of Jedi, along with several other characters in the party. Technically speaking, he's going to pick up a Force-related talent and three powers overnight - we all are, and if you take that too literally, it'll be kind of weird. In-game, though, the characters have been training for this for two levels, and we're not having them all step up and announce all of his abilities to the rest of the party at once. For myself, I'm treating it more like an emerging process - he finally "gets it", and comes into some of his powers over the course of the next couple of sessions, as situations in which his powers are useful arise.
Voilà! The gain in power now looks like the result of a longer learning process, without ugly discontinuity.
For example, I'm playing in a Star Wars Saga Edition game right now, and my Scout is about to pick up a level of Jedi, along with several other characters in the party. Technically speaking, he's going to pick up a Force-related talent and three powers overnight - we all are, and if you take that too literally, it'll be kind of weird. In-game, though, the characters have been training for this for two levels, and we're not having them all step up and announce all of his abilities to the rest of the party at once. For myself, I'm treating it more like an emerging process - he finally "gets it", and comes into some of his powers over the course of the next couple of sessions, as situations in which his powers are useful arise.
Voilà! The gain in power now looks like the result of a longer learning process, without ugly discontinuity.