Defensive Sufficiency in a Stackelberg Model of AI Security

arXiv:2610.09892v1 Announce Type: cross Abstract: Feedback from automated testing, human red teaming, and incident response can strengthen an AI system's defenses when discovered failures lead to effective repairs. We study when this feedback process provides sufficient protection and when investing in it is economically worthwhile. We begin by showing that an attack surface composed of finite number of inputs is defended with probability 1 if every unresolved attack has a persistent chance of discovery, repairs are effective, and subsequent updates preserve earlier protection. We derive completion-time bounds and extend the analysis to growing attack surfaces, repairs that generalize across related attacks, and multiple discovery mechanisms. These results distinguish eventual protection against each fixed attack from complete protection at a single time. We then formulate a defender-led Stackelberg game in which the defender invests in proactive discovery and reactive repair, anticipating the attacker's choice of search effort. We characterize the least-cost allocation that deters attack and the equilibrium regimes in which the defender funds neither capability, one capability, or both. Numerical experiments illustrate these regimes and show how faster repair can reduce compromise duration without reducing compromise probability.unified theory of performance limits in generative language models.

Abstract:Feedback from automated testing, human red teaming, and incident response can strengthen an AI system's defenses when discovered failures lead to effective repairs. We study when this feedback process provides sufficient protection and when investing in it is economically worthwhile. We begin by showing that an attack surface composed of finite number of inputs is defended with probability 1 if every unresolved attack has a persistent chance of discovery, repairs are effective, and subsequent updates preserve earlier protection. We derive completion-time bounds and extend the analysis to growing attack surfaces, repairs that generalize across related attacks, and multiple discovery mechanisms. These results distinguish eventual protection against each fixed attack from complete protection at a single time. We then formulate a defender-led Stackelberg game in which the defender invests in proactive discovery and reactive repair, anticipating the attacker's choice of search effort. We characterize the least-cost allocation that deters attack and the equilibrium regimes in which the defender funds neither capability, one capability, or both. Numerical experiments illustrate these regimes and show how faster repair can reduce compromise duration without reducing compromise this http URL theory of performance limits in generative language models.

Cryptography and Security (cs.CR); Artificial Intelligence (cs.AI)

arXiv:2610.09892 [cs.CR]

(or arXiv:2610.09892v1 [cs.CR] for this version)

https://doi.org/10.48550/arXiv.2610.09892 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

aiqbench analysis

Defensive Sufficiency in a Stackelberg Model of AI Security

Related coverage