AI 中文总结
研究一群廉价不可靠智能体如何通过少数强大昂贵的预言机达成正确共识，探讨花费及放置位置。通过建模将群体视为图上共识，利用相干性衡量质量，得出相关结论，包括次模性、预算 - 正确性边界等，还分析了成本 - 质量定律的曲率。
AI 中文摘要
一群廉价但不可靠的智能体可以通过少数强大且昂贵的“预言机”校正器被引导至正确的共识。我们研究需要花费多少以及预言机应放置在哪里。我们将群体建模为图上的共识，每个预言机以成本耦合的凹强度将一个节点固定到真相，并通过相干性H(R)=tr M(R)^{-1}来衡量质量。首先，即使预言机强度不同，H仍保持次模性，所以成本效益贪婪算法在任何预算下都能达到最优放置的1 - 1/e以内。通过反转预算可得到预算 - 正确性边界B*(eps)，即保证eps - 正确共识的最小花费：在完全图上有闭式解；当预言机成本相同时，可得到最小预言机数量k*。预算购买少数强大预言机还是许多中等强度预言机取决于成本 - 质量定律的曲率：收益递减有利于分散放置。在Qwen3阶梯上测量（0.6 - 32B），该定律在数学验证方面是凹的，在紧急代码追踪方面是凸的。
英文摘要
A cheap swarm of unreliable agents can be steered to a correct consensus by a few strong, expensive "oracle" correctors. We ask how much one must spend, and where to place the oracles. We model the swarm as a consensus on a graph in which each oracle pins one node toward the truth at a cost-coupled, concave strength, and measure quality by the coherence H(R)=tr M(R)^{-1}. Our first result is that H stays submodular (each added oracle helps less than the last) even when the oracles differ in strength, so a cost-benefit greedy comes within 1-1/e of the best placement at any budget. Inverting the budget gives the budget-correctness frontier B*(eps), the least spend that guarantees an eps-correct consensus: closed-form on the complete graph, and a minimal oracle count k* when oracles cost the same. Whether a budget then buys a few strong oracles or many medium onese curvature of the cost-quality law: diminishing returns favour spreadsharply increasion. Measured onthe Qwen3 ladder (0.6-32B), the law is concave for math verificatio convex foremergent code tracing, so the verdict is genuinely task-dependent.https://github.com/YehudaItkin/budgeted-oracle-placemen
Comments30 pages, 9 figures, 1 table.. Code and data: https://github.com/YehudaItkin/budgeted-oracle-placement
