MAGNET-KG: Maximum-Entropy Geometric Networks for Temporal Knowledge Graphs: Theoretical Foundations and Mathematical Framework

Abstract

We present a unified theoretical framework for temporal knowledge graphs grounded in maximum-entropy principles, differential geometry, and information theory. We prove a unique characterization of scoring functions via the maximum-entropy principle and establish necessity theorems for specific geometric choices. We further provide rigorous derivations of generalization bounds with explicit constants and outline conditions under which consistency guarantees hold under temporal dependence. The framework establishes principled foundations for temporal knowledge graph modeling with formal connections to differential geometric methods.