A Formal Descriptive Language for Learning Dynamics: A Five-Layer Structural Coordinate System

TL;DR

This paper addresses the challenge of describing learning dynamics without committing to predictive models by introducing a five-layer descriptive language. It formalizes the description with state variables $x(t)=(p(t), f(t))$, a family of load-generation mappings $\{\Phi^{(c)}\}$, and a dynamical rule $\frac{dx}{dt} = G(x, \ell_x, \ell_n)$, together with observation $y = Q(x)$ and regulation $r = R(\frac{dx}{dt}, E)$. Key contributions include explicit separation of descriptive responsibilities across layers, enabling existing theories to be expressed as constrained instances within a common substrate, and preserving extensibility for future empirical work. The framework supports analysis of human and AI learning by providing a non-normative, structurally transparent language to compare theories and interventions across contexts.

Abstract

Understanding learning as a dynamic process is challenging due to the interaction of multiple factors, including cognitive load, internal state change, and subjective evaluation. Existing approaches often address these elements in isolation, limiting the ability to describe learning phenomena within a unified and structurally explicit framework. This paper proposes a multi-layer formal descriptive framework for learning dynamics. Rather than offering a predictive or prescriptive model, the framework introduces a symbolic language composed of state variables, mappings, and layer-specific responsibilities, enabling consistent description of learning processes without commitment to specific functional forms or optimization objectives. This descriptive framework is intended to serve as a structural substrate for analyzing learning processes in human learners, and by extension, in adaptive and Al-assisted learning systems. A central design principle is the explicit separation of descriptive responsibilities across layers, distinguishing load generation, internal understanding transformation, observation, and evaluation. Within this structure, cognitive load is treated as a relational quantity arising from interactions between external input and internal organization, while subjective evaluation is modeled as a minimal regulatory interface responding to learning dynamics and environmental conditions. By emphasizing descriptive clarity and extensibility, the framework provides a common language for organizing existing theories and supporting future empirical and theoretical work.

Figures (1)

• Figure 1: Five-layer descriptive framework for learning dynamics, illustrating the separation of descriptive responsibilities across external input, load generation, internal state transformation, observation, and subjective evaluation.