Mental Speed
Mental Speed is how quickly your brain can interpret what you have perceived and send a message to your body to react. 
Increasing mental speed is sometimes more difficult than any of the others, as well as being the most useful.  The ability to process the action in your head faster than your opponent is priceless.  This gives you the chance to control the action instead of simply reacting to it. 
Building mental speed requires exercise of the muscles just as with any other activity.  The difference is that the muscle involved is your brain.  Your brain is no different from your bi-ceps or abs, in that the more you work it, the stronger it gets.  The best advice I could give is that knowledge is power.  In your off time, read, write, and learn as much as you can.  Even if it is not martial arts related, any learning or brain stimulating activity will in turn help mental speed.  In your mind-expanding drills, you can read about and anywise the strategies of other methods of fighting.  This is not to borrow from them or to look for better ideas.  Rather, use this information to formulate a strategy for each of the different types of fighters you may encounter. 
Physical training that will help mental speed should consist of drills that require choices and decisions.  The idea is to exercise the brain's ability to send messages to your body.  You could have a partner put on a pair of focus mitts and move around, holding them up for you to strike.  The best training is if they hold them up randomly, at different angles, heights etc.  The more choices they give you, the harder you will have to work mentally.  As you become more advanced, have them throw attacks at you as well as holding the mitts up to be hit.  This will give you both defensive and offensive choices.  Obviously, the variables possible with this drill are endless. 
The last thing to consider in improving mental speed is in the formation of your overall strategy.  Since mental speed is impacted so greatly by the number of choice reactions you have, it makes sense to cut down from the beginning.  Anyone with more than six months of experience in the martial arts knows that there is more than one way to skin a cat.  You could spend a lifetime discussing how many ways there are to counter a jab.  It is ridiculous to attempt to practice them all.  Find a couple that are simple, direct, and work well for you then practice them to death.  Every technique in your arsenal should be selected for its simplicity and effectiveness.  Do not overload yourself with flowery garbage that can only be used against a drunk, overweight, seventy year old with a wooden leg.  Chances are, he will not show up for a sparring session anytime soon.
Initiation Speed
After you have perceived the need to act and have mentally sent the signals to the proper muscles, it then comes down to how quickly you can physically initiate the motion. 
Improvement requires a concentrated effort on a very small amount of physical motion.  Supplemental training, such as weights or calisthenics are great to strengthen the major muscle groups involved in the initiation.  When doing so, it is important to note that you should be working fast twitch fibers of the muscles rather than the slow.  You need quick, explosive power as opposed to raw strength.  This is acquired using fast explosive repetitions with light weights.  Another type of supplemental exercise that can be of benefit is isometrics.  More and more studies are showing that both fast and slow twitch muscle fibers are worked in an isometric contraction.
Other than supplemental exercises, the initiation itself should be isolated and practiced by itself.  There are a couple of ways to do this: First is to practice the initiation from a dead still position, concentrating on beginning in your stance with no pre-empting movement, then bursting into the technique.  Starting from a still position is more difficult than when the body is already in motion.  Therefore, it will add the ultimate resistance, working the muscles harder, as well as teaching the body to be non-telegraphic.  Finally, you should work the initiation while in motion.  Most of the time, when the technique will be utilized, you will already be moving.  You will need to practice it until it is possible to initiate with immaculate balance, free of excess energy.  Continued……..