Human-LLM Deliberation as Interactive Proof: Conditions for Verifiability Without Transparency

Baotong Zhang, Dean Foster, João Sedoc

When an LLM supplies an argument a user could not produce, how can the user decide whether to accept its claim? Inspired by interactive proofs, we pair a computationally unbounded LLM prover with a resource-bounded human verifier. The verifier checks requested details without seeing the LLM's internals; passed checks accumulate evidence toward an acceptance threshold. Given task-supplied bounds on false passes and human checking errors, we prove anytime-valid soundness against adaptive provers: the probability of ever accepting a false claim is at most a chosen error level. For a true claim, acceptance within the budget has probability at least the product of per-round probabilities that the LLM responds adequately and the human checks correctly, provided the threshold is reachable in time. Each additional check guards against false claims but gives a true claim another chance to fail. Which review lengths meet both error targets depends on the verifier's effort, cognitive load, expertise, and fatigue. With equal resources, we identify conditions under which the bounds certify a review by local checks but not a one-shot check. In LLM-only simulations on GPQA Diamond and…