English

Debate is efficient with your time

Artificial Intelligence 2026-02-10 v1 Computational Complexity

Abstract

AI safety via debate uses two competing models to help a human judge verify complex computational tasks. Previous work has established what problems debate can solve in principle, but has not analysed the practical cost of human oversight: how many queries must the judge make to the debate transcript? We introduce Debate Query Complexity}(DQC), the minimum number of bits a verifier must inspect to correctly decide a debate. Surprisingly, we find that PSPACE/poly (the class of problems which debate can efficiently decide) is precisely the class of functions decidable with O(log n) queries. This characterisation shows that debate is remarkably query-efficient: even for highly complex problems, logarithmic oversight suffices. We also establish that functions depending on all their input bits require Omega(log n) queries, and that any function computable by a circuit of size s satisfies DQC(f) <= log(s) + 3. Interestingly, this last result implies that proving DQC lower bounds of log(n) + 6 for languages in P would yield new circuit lower bounds, connecting debate query complexity to central questions in circuit complexity.

Cite

@article{arxiv.2602.08630,
  title  = {Debate is efficient with your time},
  author = {Jonah Brown-Cohen and Geoffrey Irving and Simon C. Marshall and Ilan Newman and Georgios Piliouras and Mario Szegedy},
  journal= {arXiv preprint arXiv:2602.08630},
  year   = {2026}
}

Comments

11 Pages, 0 figures

R2 v1 2026-07-01T10:27:52.694Z