发表机构
Northeastern University（东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出任务条件主动可观测性复杂度，通过任务预测等价性最小化商空间，并设计分阶段恢复的认证观测器，在保证零误接受的同时减少交互成本。
AI 中文摘要
在对不可观测的物理系统采取行动之前，自主智能体必须确定哪些潜在区分支配下游任务，需要多少次主动干预来认证这些区分，以及何时弃权（不执行）以防止灾难性错误。经典可观测性将状态重建视为无条件的二元谓词，当被动观测无法在没有扰动的情况下打破潜在简并时失败，完整的微观反演代价过高，而区分与任务无关的自由度浪费了交互预算。我们形式化了任务条件主动可观测性复杂度：在认证错误和安全弃权（不执行）保证下，识别任务相关状态所需的最小最坏情况期望交互成本。我们证明了任务预测等价性诱导出唯一的最小充分商空间 $\mathcal{H}/\\!\sim_\tau$，在消除多余区分的同时严格保持主动可观测性复杂度不变。在确定性情况下，该复杂度由最优自适应区分树和贝尔曼递归刻画；在噪声情况下，它服从停止转录相对熵下界和自适应鞅证书，这些证书无需独立性假设即可组合。我们实例化了一个具有分阶段恢复的前瞻性认证观测器：名义验证器推迟候选编译，仅在证据出现时触发主动探测，而历史可测量得分壳在不牺牲风险界限的情况下修剪假设。跨高维物理系统和数千次操作试验的压力审计证明了认证状态恢复具有零误接受率，并大幅减少了传感器读取和模型步骤。
英文摘要
Before acting upon an unobservable physical system, an autonomous agent must determine which latent distinctions govern downstream tasks, how many active interventions are necessary to certify them, and when to abstain to prevent catastrophic errors. Classical observability treats state reconstruction as an unconditioned binary predicate, failing when passive observations cannot break latent degeneracies without perturbation, full microscopic inversion is prohibitively costly, and distinguishing task-irrelevant degrees of freedom wastes interaction budgets. We formalize task-conditioned active observability complexity: the minimum worst-case expected interaction cost required to identify task-relevant states under certified error and safe abstention guarantees. We prove that task-predictive equivalence induces the unique minimal sufficient quotient $\mathcal{H}/\!\sim_τ$, leaving active observability complexity strictly invariant while eliminating superfluous distinctions. In deterministic regimes, this complexity is characterized by an optimal adaptive distinguishing tree and Bellman recursion; in noisy regimes, it obeys a stopped-transcript relative-entropy lower bound and adaptive martingale certificates that compose without independence assumptions. We instantiate a prospective certified observer with staged recovery: a nominal verifier defers candidate compilation, triggering active probing only upon evidence, while a history-measurable score shell prunes hypotheses without sacrificing risk bounds. Stress audits across high-dimensional physical systems and thousands of operational trials demonstrate certified state recovery with zero false acceptances and substantial reductions in sensor reads and model steps.
