AI 中文总结
该研究对比智能体AI的多种改进机制，通过带隐藏终端随机性的有界验证分析其语言类的性质，证明多数放大保留语言、存在性接受可能出错，还探讨递归自我改进的边界及相关审计要求。
AI 中文摘要
智能体AI系统可通过更长时间搜索、获得额外支持或修改输出的提出与验证方式实现改进，而性能评分无法区分这些机制。我们通过带隐藏终端随机性的有界验证来对比这些变化：一个阶段指定可接受的记录、多项式界、交替验证协议和终端检查器，其原生可达性使用默认支持，闭包前沿则允许接口已接纳的所有支持。在均匀逐点概率间隙和任务相对可靠性下，这些是良定义的语言。我们证明独立多数放大可保留两种语言，而对随机磁带的存在性接受可能接纳错误输出；精确验证是零随机性情形，有位置和完备性结果。随机验证器类满足Σₖ^P⊆Σₖ^RV⊆Σₖ₊₁^P，严格扩大和深度分离需显式复杂性假设，而BPP=P会产生具有相同前沿的精确对应物。表示分析将不变接受与可在重构时改变的核心-支持标签区分开。对于递归自我改进，在通用可靠解释器和固定验证协议下的均匀有界自修改仍处于同一验证类中；单独的条件误差预算控制自适应选择候选者间的错误选择，配额约束的异或合成族将搜索成功的无界比例与已接纳语言的变化区分开，精确和概率审计检查由此产生的证据要求。该框架将自我改进主张与正确性、可接纳证据、验证资源及选择误差的义务关联起来。
英文摘要
Agentic AI systems can improve by searching longer, receiving additional support, or modifying how they propose and verify outputs. A performance score does not distinguish these mechanisms. We compare these changes through bounded verification with hidden terminal randomness. A stage specifies admissible transcripts, polynomial bounds, an alternating verification protocol, and a terminal checker. Its native reach uses default support; its closure frontier permits all support already admitted by the interface. Under a uniform pointwise probability gap and task-relative soundness, these are well-defined languages. We prove that independent majority amplification preserves both languages, whereas existential acceptance over random tapes can admit incorrect outputs. Exact verification is the zero-randomness case, with placement and completeness results. The randomized-verifier classes satisfy $Σ_k^{\mathrm{P}}\subseteqΣ_k^{\mathrm{RV}}\subseteqΣ_{k+1}^{\mathrm{P}}$; strict enlargement and depth separation require explicit complexity assumptions, while $\mathrm{BPP}=\mathrm{P}$ yields exact companions with the same frontiers. Representation analysis separates invariant acceptance from core-versus-support labels that can change under refactoring. For recursive self-improvement, uniformly bounded self-modification under a common sound interpreter and fixed verification protocol remains within the same verification class. A separate conditional-error budget controls false selection across adaptively chosen candidates. A quota-enforced XOR-synthesis family separates unbounded ratios of search success from changes in the accepted languages; exact and probabilistic audits check the resulting evidence requirements. The framework ties self-improvement claims to obligations on correctness, admissible evidence, verification resources, and selection error.
Comments26 pages, 5 figures. Includes proofs and reproducibility artifacts
