提出可量化恢复能力的理论，揭示语言模型在工具使用中的容错规律。
Recoverability Has a Law: The ERR Measure for Tool-Augmented Agents
- 用期望恢复遗憾（ERR）度量恢复策略与最优策略的偏差
- 发现ERR与效率得分（ES）存在可验证的一阶定量关系
- 适用于不同规模模型和真实API场景，为智能体鲁棒性提供理论支撑
语言模型智能体在工具调用失败后常表现出自我恢复能力，但缺乏正式解释。本文提出一种预测性理论，证明恢复能力遵循可测量的规律。通过定义期望恢复遗憾（ERR），量化恢复策略在随机执行噪声下的偏离程度，并推导出ERR与可观测指标效率得分（ES）之间的一阶关系，形成可证伪的恢复动态定量定律。我们在五个工具使用基准上进行验证，涵盖受控扰动、诊断推理和真实API场景。在不同模型规模、扰动类型和恢复时间窗下，基于ERR-ES定律预测的后悔值与蒙特卡洛回溯实测值差距不超过0.05。结果表明，恢复能力并非模型规模或架构的副产物，而是交互动态的内在属性，为语言智能体的执行级鲁棒性提供了理论基础。
原文摘要 · Abstract (English)
Language model agents often appear capable of self-recovery after failing tool call executions, yet this behavior lacks a formal explanation. We present a predictive theory that resolves this gap by showing that recoverability follows a measurable law. To elaborate, we formalize recoverability through Expected Recovery Regret (ERR), which quantifies the deviation of a recovery policy from the optimal one under stochastic execution noise, and derive a first-order relationship between ERR and an empirical observable quantity, the Efficiency Score (ES). This yields a falsifiable first-order quantitative law of recovery dynamics in tool-using agents. We empirically validate the law across five tool-use benchmarks spanning controlled perturbations, diagnostic reasoning, and real-world APIs. Across model scales, perturbation regimes, and recovery horizons, predicted regret under the ERR-ES law closely matched observed post-failure regret measured from Monte Carlo rollouts, within delta less than or equal to 0.05. Our results reveal that recoverability is not an artifact of model scale or architecture, but a governed property of interaction dynamics, providing a theoretical foundation for execution-level robustness in language agents.
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