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| Main Authors: | , , , , , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.08630 |
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| _version_ | 1866910016589529088 |
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| author | Brown-Cohen, Jonah Irving, Geoffrey Marshall, Simon C. Newman, Ilan Piliouras, Georgios Szegedy, Mario |
| author_facet | Brown-Cohen, Jonah Irving, Geoffrey Marshall, Simon C. Newman, Ilan Piliouras, Georgios Szegedy, Mario |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_08630 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Debate is efficient with your time Brown-Cohen, Jonah Irving, Geoffrey Marshall, Simon C. Newman, Ilan Piliouras, Georgios Szegedy, Mario Artificial Intelligence Computational Complexity 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. |
| title | Debate is efficient with your time |
| topic | Artificial Intelligence Computational Complexity |
| url | https://arxiv.org/abs/2602.08630 |