Loaded question for sure. Let's think about this one out loud.
You're hiring for what you want in your culture. You say you have a culture of innovation and thus, want to hire someone with the ability to innovate. You could make the mistake a lot of people make and do the following:
-Ask them to tell you about a time they innovated to solve a business problem, or
-Think that only certain types of people have the ability to innovate, that it takes high energy to innovate, etc.
Don't get me wrong - I'm a behavioral interviewer, so the fact you're asking for examples is good. The problem is that most of us won't dig deep enough on those behavioral questions. We'll accept answers that sound great without really digging in. Were they really in charge of the innovation? Were they just part of a team? What happened after they innovated? Did it work? Is it innovation if nothing really changed as a result?
Interviewing is hard and false positives are everywhere - especially when it comes to factors like innovation.
For me, you really need help to figure out if someone has the ability to innovate. Start with how they view the world.
How do you do that? I've used an assessment that talks about "Rules Orientation". People who are high rules actively look for the operations manual on the shelf when they're dealing with issues. Doesn't matter what they're annual salary is, high rules people want to be told what to do. As you might expect, you really can't expect a high rules person to have a jones for innovation. They're looking for the Ops Manual, people...
Low Rules people, on the other hand, cringe at the thought of having to comply with a ops manual. Low Rules people love the chaos, and they want to be the one to figure out what to do given a specific set of circumstances. They'll help you build the ops manual, but you better have another challenge for them once it's built, because they'll refuse to be managed by that manual, or have a job that could be handled by that low level of protocol.
In addition to Rules Orientation, add a couple of other factors - cognitive processing speed and assertiveness - and I think you've got a pretty good platform for having directional information on whether someone has the capacity to innovate.
And no, someone simply using a Mac rather than a PC doesn't mean they're an innovator. Trendy? Yes. Jeans over khakis means little as well.
You laugh, but you'd be surprised the factors people include in their head to measure the ability to innovate.