Structural Variable Relationship Modeling in Cutting-Edge AI: A Framework Based on Spectra, Topology, and Entropy

This study aims to overcome the structural and interpretative limitations encountered in artificial intelligence causal modelling and explainable AI (XAI) when employing advanced topic modelling techniques (LDA/HDP) alongside traditional grounded theory (GT). It proposes a novel structural variable-relationship modelling framework tailored for complex systems. Employing the Structured Variable-Relationship Modelling (SVRM) methodology, this work integrates the Semantic-Structural Variable Modelling with Policy and Power Analysis (SSVM-PPA) framework. It further incorporates cutting-edge mathematical tools including spectral graph theory, topological data analysis, and information entropy analysis. This comprehensive approach enables an end-to-end modelling system spanning semantic text extraction, causal path modelling, AI graph structure construction, and simulation prediction. Systematic evaluation across 30 texts demonstrates SVRM's superiority over LDA and GT in key metrics: average variable extraction (31.07), structural relationship count (40.13), path significance (0.9), and consistency (0.93), showcasing efficiency, stability, and structural completeness. The research concludes that SVRM not only effectively constructs multi-layered, causally directed variable systems but also broadly adapts to Graph Neural Networks (GNN), Bayesian Networks (BN), and Transformer architectures. This enables embeddable, inferable, and interpretable AI modelling pathways, representing a structural and algorithmic breakthrough in post-empiricism knowledge construction. It provides robust support for strategic simulation, policy intervention, and cognitive modelling.