Recoverability Has a Law: The ERR Measure for Tool-Augmented Agents

• URL: http://arxiv.org/abs/2601.22352v1
• Date: Thu, 29 Jan 2026 21:55:50 GMT
• Title: Recoverability Has a Law: The ERR Measure for Tool-Augmented Agents
• Abstract summary: We show that recoverability follows a measurable law in language model agents.<n>We empirically validate the law across five tool-use benchmarks spanning controlled perturbations, diagnostic reasoning, and real-world APIs.<n>Our results reveal that recoverability is not an artifact of model scale or architecture, but a governed property of interaction dynamics.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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