Active Graph Learning Meets Low-Rank Feature Fusion: Cross-Discipline Mathematics Course Matching

The formalization of structural alignment in high-dimensional cross-discipline mathematical mappings has historically been constrained by unimodal heuristic assumptions, failing to model the essential topological congruence between active master statesałgraph neural representationsałand low-rank constraintsałmanifold prerequisites. We hypothesize that superior matching fidelity emerges from a Graph-Low-rank Symbiosis, where latent cognitive trajectories are stochastically independent of yet structurally governed by the non-stationary curricular topology. To compute this, we propose AGL-LowRank, an Active Graph Learning architecture Meeting Low-rank Feature Fusion designed to optimize structural course alignment through this bifocal lens. Our system utilizes a dual-pathway latent encoder: the Active Graph stream distills multi-scale mastery primitives from concept embeddings and mastery manifolds, while the Low-rank stream characterizes the pedagogical domain as a spectral interaction graph to resolve global dependencies and latent structural gaps. We deploy a Duality-Aware Low-rank Fusion module that arbitrates asynchronous information gradients, allowing the network to synchronize graph-based master signatures with cross-discipline objective functions. Additionally, a Temporal Low-rank Gate is implemented to identify the singular epochs where cognitive mastery and structural prerequisites intersect to optimize alignment stability. Experimental validation on cross-discipline corpora indicates that AGL-LowRank defines a new state-of-the-art benchmark, transitioning the domain from frequentist modeling to diagnostic academic intelligence. By engineering an interpretable synthesis of active graphs and low-rank manifolds, AGL-LowRank provides a rigorous framework for interdisciplinary learner path optimization.