SMGI: A Structural Theory of General Artificial Intelligence

TL;DR

This paper introduces SMGI, a formal structural theory of general AI that unifies various learning paradigms through a typed meta-model and provides theoretical bounds on capacity and stability.

Contribution

It formalizes a comprehensive structural framework for general AI, linking existing learning models under a unified theory with new capacity and stability guarantees.

Findings

Proves a structural generalization bound connecting PAC-Bayes and Lyapunov stability.

Demonstrates classical and modern AI models as instances of SMGI.

Establishes conditions for capacity control and bounded drift in AI systems.

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.