Who knows? I found a few articles with quotes like this:
“It will also be fitted with a mechanical supercharger, to pack more air into the cylinders, boosting power 10 to 30 percent over the current generation of SkyActiv engines now used across Mazda’s lineup.”
This one’s pretty specific:
"Unlike most diesel engines which are equipped with turbochargers, the Skyactiv-X HCCI engine will be supercharged which will give is a 10-30 percent torque boost over the current Skyactiv-G engine. Mazda is claiming fuel efficiency will be 20-30 percent better than the gas engine it’s replacing and a whopping 35-45 percent more efficient than a Mazda engine the same size from 2008. Mazda currently makes a Skyactiv-D diesel engine and the company said the Skyactiv-X will be as efficient or more efficient than their own diesel."