SMGI: A Structural Theory of General Artificial Intelligence

Aomar Osmani

cs.AIMar 9, 2026

SMGI: A Structural Theory of General Artificial Intelligence

Authors: Aomar Osmani

Organizations: INSA-Rouen, France

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.

Figures & tables

Framework	Core Structural Assumption	Strengths	Structural Limitations (relative to unified AGI meta-model)
Statistical Learning Theory (PAC / VC / Rademacher) ( Vapnik, 1998a ; Bousquet and Elisseeff, 2002 )	Fixed hypothesis class under i.i.d. sampling	Finite-sample guarantees; capacity control; generalization theory	Not first-class objects in the canonical i.i.d. SLT core: sequential composition of tasks/regimes, persistent memory dynamics, and explicit invariance obligations across typed transformations (these require an extension of the formal object beyond a fixed $(\mathcal{H},\ell)$ under i.i.d. sampling).
Solomonoff Induction / AIXI ( Solomonoff, 1964 ; Hutter, 2005 )	Universal Bayesian mixture over programs	Asymptotic optimality under computability assumptions; universal prediction framework	Non-computable in its standard form; treats memory implicitly as part of the program/state without an explicit write/consolidate/forget operator interface; does not provide operator-level stability/admissibility obligations for certified structural evolution.
Reinforcement Learning ( Sutton and Barto, 2018 )	Markov decision processes with reward maximization	Sequential decision guarantees; regret bounds; convergence in stationary environments	Canonical RL formalizes sequential decision-making given fixed state/action semantics and a reward functional; even when enriched with partial observability (POMDPs/belief-state planning) and temporal abstraction (options/hierarchical RL), the core object typically keeps the interface and evaluative regime fixed, so cross-task/interface transformations, persistent multi-system memory operators (write/consolidate/forget), and invariance/certification obligations must be introduced explicitly beyond the base MDP/POMDP formalism.
(standard) Meta-learning (Learning-to-Learn) ( Finn et al., 2017 ; Nichol and Schulman, 2018 )	Task-distribution adaptation through shared meta-parameters	Rapid adaptation across related tasks; few-shot generalization	Typically optimizes shared meta-parameters over a task distribution; persistent memory decomposition (with explicit write/consolidate/forget operators) and invariance obligations under heterogeneous typed transformations are not part of the canonical meta-learning object unless added explicitly.
Transformer-based Architectures ( Vaswani, 2017 )	Fixed parametric attention-based function class	High expressive capacity; contextual reasoning; scalable sequence modeling	Standard transformer models fix a parametric sequence-to-sequence class; explicit persistent memory operators and certified stability/invariance under continual cross-task adaptation are external to the core architecture unless specified as part of the training/evaluation/control interface.
Retrieval-Augmented Systems (RAG) ( Lewis et al., 2020 )	Parametric model coupled with external retrieval mechanism	Improved factual recall; scalable knowledge access; modular memory augmentation	Adds retrieval as an external interface; the write/consolidate/forget semantics of long-term memory and the stability/invariance of behavior under retrieval-policy drift are typically not formalized as certified obligations in the standard RAG formulation.

Table 1: Comparative structural positioning of major theoretical frameworks relevant to AGI. Each framework formalizes a principled axis of learning or intelligence, but typically leaves implicit the joint structural constraints required for a persistent, transformable learning system.

Structural Concept	Engineering Principle	AGI Meta-Model Analogue
Inheritance / refinement	Structural inclusion	Submodel / restriction theorems
Interface contracts	Invariant constraints	Normative/evaluative invariant core
Meta-model	Defines admissible models	$\theta=(r,\mathcal{H},\Pi,\mathcal{L},\mathcal{E},\mathcal{M})$
Model conformance	Well-formedness predicate	Semantic admissibility: $(\theta,T)\in\mathrm{Graph}(\mathsf{Sem})$
Model transformation	Closure under refinement	Task/environment transformation operators
Well-formedness rules	Constraint enforcement	Stability and capacity admissibility constraints

Table 2: Methodological precedent from engineering meta-models: explicit admissibility, transformation, and invariants.

Program class	(i) Closure	(ii) Stability	(iii) Capacity	(iv) Eval. inv.	Canonical structural emphasis
World Models / latent simulators ( Ha and Schmidhuber, 2018 ; Hafner and others, 2023 )	$\circ$	$\circ$	$\circ$	$\times$	Latent predictive dynamics $m_{t+1}=F(m_{t},a_{t})$ supporting planning
JEPA / World-Model Hypothesis ( LeCun, 2022 )	$\circ$	$\circ$	$\circ$	$\times$	Predictive latent representations and invariances for autonomy
System-2 / Consciousness prior ( Bengio, 2017 ; Bengio, 2019 )	$\circ$	$\times$	$\circ$	$\circ$	Sparse causal abstractions; deliberative control and constraint-like structure
Gödel machines / self-improving systems ( Schmidhuber, 2006 ; Schmidhuber, 2010 )	$\circ$	$\circ$	$\times$	$\circ$	Self-modification under proof-based improvement criteria
Generalist agents (Transformer agents) ( Reed and others, 2022 ; Silver, 2021 )	$\circ$	$\times$	$\circ$	$\times$	Unified sequence modeling across modalities and action spaces
Causal modeling / Ladder of Causation ( Pearl, 2009 )	$\circ$	$\times$	$\circ$	$\circ$	Interventions/counterfactual structure constraining representation and evaluation

Table 3: Program classes as structural emphases relative to the SMGI requirements. Symbols indicate whether a requirement is made explicit within the program’s formal structure. This does not constitute a claim that any concrete system satisfies SMGI.

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

Artificial General Intelligence

Artificial General Intelligence studies AI systems that can learn, reason, and act across diverse tasks and environments.

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Conventional uniform convergence bounds and empirical risk minimization break down in massive over-parameterized models, such as large language transformers and biological sequence networks. With near-infinite unconstrained internal degrees of freedom, their optimization landscapes develop flat vertical gauge valleys, rendering classical generalization metrics vacuous and inducing severe pathologies, specifically generative hallucination and catastrophic forgetting. We introduce the Statistically Meaningful Geometry (SMG) framework, an information-geometric paradigm lifting deterministic parametric models into infinite-dimensional non-parametric Orlicz statistical manifolds. Modeling the total state space as a differential fiber bundle (

\mathcal{M}, \mathcal{B}, π, \mathcal{V}, \mathcal{H}, ω

), we establish a Two-Fold Inference Paradigm. We formalize an Ehresmann connection 1-form

ω

as a dynamic geometric filter that strips away vertical gauge noise (Structural Internal Directions, or SID) and isolates learning trajectories along the strictly non-degenerate horizontal distribution (Statistical Variational Directions, or SVD

χ

). We prove that under connection-filtered pre-training, out-of-distribution predictive variance is strictly upper-bounded by the finite diameter of the identifiable quotient base manifold

\mathcal{B}

, establishing a hard geometric containment of generative hallucinations. By projecting downstream updates onto the orthogonal complement of the historical horizontal carriage, we formalize the SMG Sequential Adaptation Flow, proving the total non-asymptotic elimination of catastrophic forgetting. SMG replaces empirical fine-tuning heuristics with coordinate-free topological constraints, bridging advanced differential geometry with structural reliability in AI.

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