A Unified Advanced Framework for Sparse Data Modeling in Quantum-Enhanced Artificial Intelligence - Pasupuleti, Murali Krishna (International Journal of Academic and Industrial Research Innovations(IJAIRI), 2025)
Sparse and high-dimensional data present persistent challenges in artificial intelligence (AI), particularly in maintaining generalizability, interpretability, and computational efficiency. This study proposes a unified advanced framework that integrates tensor algebra, number theory, topology, and analytic geometry to address the limitations of traditional machine learning models when handling sparse data. The methodology leverages high-order tensor representations for compact and expressive encoding of multi-dimensional information, modular arithmetic for robust and secure feature embedding, and persistent homology to capture topological invariants within data distributions. Additionally, geometric learning principles based on Riemannian manifolds are incorporated to guide optimization processes through curvature-aware gradient flows. The proposed framework is further enhanced by quantum computational principles, where tensor networks and entangled state representations are simulated for efficient processing. Experimental evaluation on classical and quantum datasets demonstrates superior performance in terms of accuracy, F1 score, and convergence rate when compared to baseline and modular AI architectures. The results validate that the integration of mathematical rigor and quantum principles can offer scalable, interpretable, and resilient solutions for sparse data modeling. This framework not only contributes to the theoretical foundation of AI and quantum learning but also provides practical implications for applications in cryptography, biomedical analysis, and high-dimensional signal processing. Keywords Sparse data modeling, tensor algebra, quantum machine learning, topological data analysis, modular arithmetic, Riemannian geometry, tensor networks, persistent homology, quantum-enhanced AI, high-dimensional data