A buddy had the same issue, where I worked, and I benefited from learning from it. Corporations, which includes schools and large companies, somehow think it's moral and productive to claim to own the ideas of someone who develops them while working in their midst. I call bullshit.*
However, they have attorneys they already waste money on. I think the best policy is not to say anything. If you develop a really good idea, separate from them and claim they had nothing to do with it. Do what you can to hide any implication that there's a connection. The worst thing you can do is "discuss" it with anyone in the corporation.
*Obviously, there are times when they would seem to own (under current law) what you "think up." This would be when it applies directly to the subject matter you're working on, solving the same problems, for the same purposes, etc. You probably can't win in this situation.