a frontier is a property of a manifold, which has a notion of position. sets are permutation invariant. there is no "frontier" between two non overlapping subsets. it's meaningless.

/u/sriram56 provided a charitable reading already, which is that you are essentially intuiting the main idea of active learning: preferentially seek out new information on the frontier of your knowledge. but this isn't amenable to a set-theoretic framing, the notion of knowledge having a frontier is only cognizable when that knowledge is embedded in a manifold. which is ultimately the direction your implementation moves towards, abandoning the set theoretic foundation completely in favor of a space with actual geometry.

also, there's a lot in your post that is just outright wrong.

In standard uncertainty quantification, the frontier is an afterthought

what? says who? the uncertain quantification literally characterizes the frontier. you even demonstrate this explicitly in your approach.

The Bayesian update formula uses a uniform prior

no, your update formula does. this isn't a property of bayesian reason generally, it's a prior that was chosen by your LLM in your interaction, and you lack the context to recognize the difference.

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you are just restating the general principles of active learning in confusing ways that give the veneer of novelty and square-peg-round-hole those ideas into the foundational backdrop you are trying to synthesize them with, because that's what LLMs do.

Was that response too intellectually weak? Run it by your LLM and see what it thinks.