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SMGI: A Structural Theory of General Artificial Intelligence

Aomar Osmani

TL;DR

A strict structural inclusion theorem is established 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

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 $θ= (r,\mathcal H,Π,\mathcal L,\mathcal E,\mathcal M)$ 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 ($θ$) and its induced behavioral semantics ($T_θ$), we define general artificial intelligence as a class of admissible coupled dynamics $(θ, T_θ)$ 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.

SMGI: A Structural Theory of General Artificial Intelligence

TL;DR

A strict structural inclusion theorem is established 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

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 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 () and its induced behavioral semantics (), we define general artificial intelligence as a class of admissible coupled dynamics 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.
Paper Structure (223 sections, 25 theorems, 109 equations, 1 figure, 3 tables)

This paper contains 223 sections, 25 theorems, 109 equations, 1 figure, 3 tables.

Table of Contents

  1. Introduction
  2. Diagnosis: Local guarantees versus structural transformations.
  3. The fragmentation of current solutions: partial internal fixes and external wrappers.
  4. Why safety and security force a structural theory.
  5. Why agentic evaluation makes internalization unavoidable.
  6. Thesis: structural generalization and control-by-structure.
  7. Epistemological necessity: from external metrics to structural objects.
  8. The structural meta-model and the coupled view $(\theta,T_\theta)$.
  9. Structural definition of AGI: admissibility obligations.
  10. What is (and is not) claimed here.
  11. Minimal checkability (pointer).
  12. Why scale is not sufficient (as an instance).
  13. Contributions.
  14. Organization.
  15. Philosophical and Scientific Foundations
  16. ...and 208 more sections

Key Result

Lemma 3.1

In the meta-structure $\theta=(r,\mathcal{H}(\theta),\Pi,\mathcal{L},\mathcal{E}(\theta),\mathcal{M}(\theta))$, the components $r$ and $\mathcal{E}(\theta)$ are not interchangeable: (i) removing $\mathcal{E}(\theta)$ eliminates a well-typed notion of admissible task transformations $\tau:\mathcal{E}

Figures (1)

  • Figure 1: Formal architecture of the SMGI meta-model.

Theorems & Definitions (47)

  • Lemma 3.1: Non-reducibility of $r$ and $\mathcal{E}(\theta)$ (structural roles)
  • Definition 4.1: Topologically admissible task transformations
  • Definition 4.2: Structural Model of General Intelligence (SMGI)
  • Theorem 4.3: Minimality of the SMGI conditions
  • proof
  • Theorem 4.4: Structural generalization bound for SMGI
  • proof
  • Definition 4.5: Unified admissibility bundle
  • Theorem 4.6: Unified structural guarantee under admissible transformations
  • proof
  • ...and 37 more