REKHA: Relational Encoding of Knowledge in Hyperbolic Architecture

REKHA (Relational Encoding of Knowledge in Hyperbolic Architecture) is a research paper exploring novel approaches to knowledge representation using hyperbolic geometric spaces. This work investigates how hyperbolic neural architectures can more effectively capture hierarchical and relational structures in knowledge graphs compared to traditional Euclidean approaches. Hyperbolic spaces naturally model tree-like and hierarchical data structures with lower distortion than Euclidean spaces. This property makes them particularly suited for encoding knowledge graphs where entities are organized in taxonomic or part-whole hierarchies. The REKHA framework proposes a unified architecture that combines: 1. Hyperbolic embeddings for entity representation, preserving hierarchical distances 2. Relational operators defined in hyperbolic space for link prediction 3. A novel training procedure that leverages the geometric properties of the Poincare ball model 4. Scalable inference mechanisms for large-scale knowledge bases This research contributes to the growing body of work at the intersection of geometric deep learning and knowledge representation, with potential applications in: - Natural language understanding and reasoning - Drug discovery and biomedical knowledge graphs - Recommendation systems with hierarchical item taxonomies - Defence and intelligence analysis with structured entity relationships The paper demonstrates state-of-the-art results on standard knowledge graph completion benchmarks while using significantly fewer parameters than competing Euclidean models. Published by Chakra Dialogues Foundation Think Tank as part of its research initiative on emerging technologies and their applications for strengthening India's Comprehensive National Power.