An example of an inverse sugar, simple syrup, can be made at home by bringing one cup of water and two cups of granulated sugar to a boil, then reducing the heat and simmering for 5-7 minutes until the mixture is clear. The simple sugar solution can be stored for up to six months.
According to Wikipedia, the term "inverse sugar" refers to the way planes of light rotate within the solution. Normal sugars rotate left to right, while invert sugars rotate right to left. Since physics was never my forté, if someone can explain that better, please feel free.
Another example of invert sugar would be honey. Making a jam, with the interaction of the sugar and acid from the fruit, would make a kind of invert sugar. Since they're liquid, yes, you could theoretically reduce the sugar, but you would also have to find somewhere to reduce the total liquid as well.