A Theoretical Framework for Developmental AI Alignment: Formal Foundations of Staged Safety Training

Abstract

We present a formal theoretical framework for training aligned language models through developmental staging. Our framework, INFANT (Incremental Nurturing Framework for Aligned Neural Training), provides provable safety guarantees by combining constrained behavioral cloning, adversarial robustness optimization, and runtime safety verification. We establish three main theoretical results: (1) a PAC-style safety bound showing violation probability scales as $O(\epsilon_M + \epsilon_\Pi + (1-\gamma)\cdot p_{\text{unsafe}})$ where $\epsilon_M$ is world-model error, $\epsilon_\Pi$ is projection error, and $\gamma$ is safety coverage; (2) convergence guarantees for our min-max adversarial training procedure at rate $O(1/\sqrt{T})$ to an $\epsilon$-Nash equilibrium; and (3) monotonic safety improvement under staged maturation with bounded perturbation impact. We characterize the capability-safety Pareto frontier and prove its traversability through hyperparameter variation. This work provides mathematical foundations for principled AI safety training.

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