Cekirge’s σ-Based ANN Model for Deterministic, Energy-Efficient, Scalable AI with Large-Matrix Capability
Huseyin Murat Cekirge · American Journal of Artificial Intelligence · 2025
Experimental evaluations of the strongly Cekirge-developed algebraic method were conducted across multiple input dimensions (3, 4, 10, 20, and 50) and σ values (0.01 to 0.05, to assess the robustness, scalability, and sensitivity of the approach. A 3-input sample matrix is presented to illustrate the computational procedure, demonstrating how the method directly computes weights by solving a system of algebraic linear equations with σ-based perturbations. This perturbation ensures a nonsingular coefficient matrix, thereby guaranteeing a unique, deterministic, and reproducible solution. The results indicate that the Cekirge algebraic method consistently achieves accuracy comparable to or exceeding that of conventional Gradient Descent algorithms, while significantly reducing computational resources. Specifically, the method requires fewer iterations, lowers computation time, and reduces energy consumption—a crucial advantage for large-scale or resource-constrained applications. Detailed tables are provided, comparing computed weights, error metrics, timing ratios, and estimated energy savings, highlighting the method’s efficiency and consistency across varying input sizes. Beyond performance metrics, the method offers several practical advantages. Its deterministic nature eliminates variability due to random initialization or iterative convergence issues commonly encountered in Gradient Descent. The straightforward implementation and scalability make it applicable to regression tasks, generalized function approximation, and potentially more complex single-layer ANN configurations. By lowering both computational and energy requirements, the Cekirge method advances the goal of environmentally sustainable AI, promoting the development of energy-conscious and broadly deployable AI systems, particularly in settings where computational resources are limited. These findings collectively underscore the method’s potential to enable efficient, green, and responsible AI development, establishing the strongly Cekirge approach as a foundational contribution to neural network research. Its scalability allows efficient handling of increasing input dimensions and larger datasets, making it suitable for resource-constrained environments and edge AI applications. The combination of deterministic solutions, rapid computation, and environmental sustainability positions this methodology as a promising avenue for future AI innovations, fostering broader adoption and supporting the responsible deployment of AI technologies worldwide. The extension of the Cekirge model to large-matrix AI applications is also introduced.