The H-Bar Model of Knowledge Development: A Formal Curriculum Framework for Schema Coherence and Compositional Generalization in AI Agents
In ProgressBasyirin Amsyar · 2026 · Journal of Artificial Intelligence Research
Current AI agent training pipelines optimize for parametric depth without a formal account of schema coherence — the structured, compositionally valid representation of domain knowledge. We argue this structural omission explains systematic failures in compositional generalization and out-of-distribution robustness that depth-only models cannot account for. We introduce the H-Bar Model, a formal framework that distinguishes parametric depth (δ) from schema coherence (σ) as independently necessary and non-substitutable dimensions of agent capability, and provides a phase-structured developmental account of how both variables evolve during training. The framework introduces the delegation gradient (𝒟*), intersection activation (Ψ), and a two-mechanism decay decomposition separating cognitive decay (λ_c) from frontier obsolescence (λ_f). We apply the framework to physics-informed residual learning as a motivating case study, derive six falsifiable predictions, and provide curriculum design prescriptions derived directly from the phase structure. … show more Current AI agent training pipelines optimize for parametric depth without a formal account of schema coherence — the structured, compositionally valid representation of domain knowledge. We argue this structural omission explains systematic failures in compositional generalization and out-of-distribution robustness that depth-only models cannot account for. We introduce the H-Bar Model, a formal framework that distinguishes parametric depth (δ) from schema coherence (σ) as independently necessary and non-substitutable dimensions of agent capability, and provides a phase-structured developmental account of how both variables evolve during training. The framework introduces the delegation gradient (𝒟*), intersection activation (Ψ), and a two-mechanism decay decomposition separating cognitive decay (λ_c) from frontier obsolescence (λ_f). We apply the framework to physics-informed residual learning as a motivating case study, derive six falsifiable predictions, and provide curriculum design prescriptions derived directly from the phase structure. show less
BibTeX
@unpublished{amsyar2026hbar,
author = {Basyirin Amsyar},
title = {The {H-Bar} Model of Knowledge Development: A Formal Curriculum Framework for Schema Coherence and Compositional Generalization in {AI} Agents},
year = {2026},
note = {In preparation. Target venue: Journal of Artificial Intelligence Research}
}
H-Bar ModelSchema CoherenceCompositional GeneralizationAI TrainingCurriculum LearningPIRLFormal Methods