My guess would be self-replicating biological organisms capable of significant rates of mutation.
But then my preferred solution to the paradox as a whole is basically the "nobody tries" idea.
I don't think there's tremendous reason to try to make ones-self detectable at long distances. It's an expenditure of non-trivial resources for an uncertain result. Since there isn't really any robustly sound logic for making the attempt outside of dramatized sci fi stories, I imagine a vanishingly small percentage of occurrences of intelligent life would make a serious, high-powered attempt at any point.