Learning Dynamics over Formal Grammar-Structured Concept Spaces

Dynamical systems models have been widely employed to analyze how system states evolve over time, revealing structural patterns, attractors, and emergent behaviors. However, applying dynamical systems frameworks to learning processes involving abstract concepts remains fundamentally challenging. Abstract conceptual knowledge is typically not directly operable, lacks explicit structural formalization, and resists straightforward representation as state variables within a dynamical system. This work proposes a formal framework for modeling abstract conceptual learning as a dynamical process. We introduce a three-stage pipeline. First, abstract concepts are transformed into formalized representations that admit structural manipulation. Second, grammars governing concept generation are induced using generative language models, thereby constructing a grammar-structured conceptual space. Third, the induced formal grammar is translated into a dynamical systems formulation, enabling the study of learning as state evolution over structured concept spaces. Within this framework, learning is interpreted as dynamical evolution over grammar-induced conceptual structures. This formulation enables analysis of attractor formation, stability, phase transitions, and structural reorganization in conceptual development. By bridging formal language models and dynamical systems theory, the proposed approach offers a high-level, structurally interpretable alternative to low-level neural dynamical modeling. It provides a tractable and theoretically grounded foundation for analyzing how instructional interventions reshape the dynamics of conceptual learning.