I’m not sure if I’d say it’s “faster than usual” since I don’t have data on what usual looks like, but I’ve been applying techniques to my violin practice that have been very helpful: interleaved practice (contextual interference) + variability of practice.
Interleaved practice means only doing a few minutes of practice on something at a time, then switching to another task. So instead of the traditional way of practicing for maybe 30-60 minutes straight on one piece (“block” or “batch” practice), I might practice just line 1 of a piece for 3 minutes, then switch to another piece for 3 mins, then practice a scale for 3 mins, then go back to the first piece.
Contextual interference Variability of practice involves adding variations to the task you’re practicing, so rather than trying to play the same piece the exact same way every time, I might play it normally, then play it again but with an altered rhythm (dotted instead of straight, etc), then play it again but alternating between loud and quiet notes, or staccato / legato etc.
Much of the research comes from sports, where they’d do stuff in baseball training like “hit every 3rd ball as far left out of bounds as possible”.
There’s some controversy in psychology/education research over how helpful these techniques are, with conflicting results in some of the studies. But I’ve found it helpful in the learning/practice tasks I’ve used it on (violin, piano and snooker), and perhaps more importantly it makes practice more fun so I’m more likely to actually put quality time into it. Plus it keeps me slightly more focused and engaged, rather than just mindlessly playing the same way over and over on autopilot.
[edit]
Oh, regarding the learning without actually doing the task thing: there has also been some research on visualisation as a substitute or booster for real practice. From what I heard, it’s (much) better than nothing, but not better than real practice, so you should try to really do the task.
But if it’s not always practical to really do the task (e.g. you can only access your piano on weekends), then visualisation practice can be helpful. It seems that it’s most effective when you do it for short bursts (maybe 10 seconds imagining yourself playing one small section, repeatedly), and without trying to imagine too much visual detail (which might place too much load on your working memory and detract from the practice). You should also actually move your hands along, although it doesn’t have to be the full range of motion.
[edit 2]
Note: I mixed up “contextual interference” and “variability of practice”. Contextual interference is basically the theory that led to interleaved practice as potentially more valuable than blocked practice. Variability of practice is about adding variations so you’re not doing exactly the same thing over and over.