Debate is efficient with your time

2026-02-09

AI Summary

This work investigates how to quantify and reduce the query burden on human supervisors when verifying complex computational tasks within AI debate frameworks. It introduces Debate Query Complexity (DQC) as a formal measure of the minimal information a human must inspect to make correct judgments, and for the first time systematically connects supervision costs in AI debates to computational complexity theory. The main contributions include proving that problems in PSPACE/poly correspond precisely to those with DQC O(log n), establishing a tight relationship between DQC and circuit complexity by showing DQC ≤ log(s) + 3 where s is the circuit size, and demonstrating that improving DQC lower bounds would yield new circuit complexity lower bounds—thereby revealing a profound link between AI safety and fundamental limits in computational complexity.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Humans and AI: Other Foundations of Human Computation & AI

Application Category

• Economics, Online Markets and Human Computation: Data quality aspects of human-annotated datasets
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

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.

Problem

• AI safety
• debate
• query complexity
• human oversight
• verifier

Innovation

• Debate Query Complexity
• AI safety via debate
• PSPACE/poly
• query efficiency
• circuit lower bounds