If you are going to be faster, which to me means hitting someone quicker, or maybe more times within a given time frame (i.e. 5 times in 1 sec vs. 3 times in 1 sec.), the way I see it, you can do two possible things:
1. Keep the same amount of movement, but train the muscles to respond faster.
2. Accomplish the same amount but move less.
For #1, you can only get so fast -- eventually you reach the limits of what your brain can process, and that's it. You may also get sloppy if you are going faster than you should. #2 should be easier, and all it really is is economy of motion. Think about two scenarios, both in which someone is trying to hit someone with their hands a few consecutive times and then toss them to the ground, and the stylists and opponents in question are of equal skill:
1. Stylist A: Has hands in typical "boxing" stance. Launches and connects with left jab, retracts hand back to starting position, relaunches left hand out to grab opponent's wrist, controls wrist, strikes opponent on side of the head with their right hand, retracts right hand, throws out right hand again and hooks back of opponent's head and neck, pushes left hand and pulls with right, dumping them onto the ground.
2. Stylist B: Hands in same stance. Launches left jab, slides left hand down to wrist, controls the wrist, launches right to side of head, leaves hand there and hooks, pushes and pulls, and then dumps.
Which stylist do you think was faster? I would think stylist B - the one who used less wasted movement. While both technically hit their opponent the same number of times, B didn't have to move so much, because he omitted the returns of his hands to starting position.
