Abstract
We introduce SMGI, a structural theory of general artificial intelligence, and recast the foundational problem of learning from the optimization of hypotheses within fixed environments to the controlled evolution of the learning interface itself. We formalize the Structural Model of General Intelligence (SMGI) via a typed meta-model $\theta = (r,\mathcal H,\Pi,\mathcal L,\mathcal E,\mathcal M)$ that treats representational maps, hypothesis spaces, structural priors, multi-regime evaluators, and memory operators as explicitly typed, dynamic components. By enforcing a strict mathematical separation between this structural ontology ($\theta$) and its induced behavioral semantics ($T_\theta$), we define general artificial intelligence as a class of admissible coupled dynamics $(\theta, T_\theta)$ satisfying four obligations: structural closure under typed transformations, dynamical stability under certified evolution, bounded statistical capacity, and evaluative invariance across regime shifts. We prove a structural generalization bound that links sequential PAC-Bayes analysis and Lyapunov stability, providing sufficient conditions for capacity control and bounded drift under admissible task transformations. Furthermore, we establish a strict structural inclusion theorem demonstrating that classical empirical risk minimization, reinforcement learning, program-prior models (Solomonoff-style), and modern frontier agentic pipelines operate as structurally restricted instances of SMGI.
Abstract (translated)
我们介绍了SMGI，即通用人工智能的结构理论，并将从固定环境中优化假设的基础学习问题转化为自身学习界面的可控进化。通过一个类型化元模型 $\theta = (r, \mathcal{H}, \Pi, \mathcal{L}, \mathcal{E}, \mathcal{M})$，我们形式化了结构智能模型（Structural Model of General Intelligence，SMGI），该模型将表示映射、假设空间、结构性先验、多制式评估器和记忆操作符视为显式的类型化动态组件。通过在这一结构本体论（$\theta$）与其诱导的行为语义（$T_\theta$）之间强制执行严格的数学分离，我们将通用人工智能定义为一类可接受的耦合动力学（$\theta, T_\theta$），这些动力学满足四个义务：类型变换下的结构性闭包、认证演化下的动态稳定性、统计容量有限以及制式转换下的评估不变性。我们证明了一个结构泛化界限，该界限将序列PAC-Bayes分析和李雅普诺夫稳定性联系起来，为在可接受的任务转换下控制容量并限制漂移提供了充分条件。此外，我们建立了一个严格的结构包含定理，表明传统的经验风险最小化、强化学习、程序先验模型（如Solomonoff风格）以及现代前沿代理管道都是SMGI的结构受限实例。
URL
https://arxiv.org/abs/2603.07896
