Deterministic σ-Regularized Benchmarking of the Cekirge Model Against GPT-Transformer Baselines

The Cekirge Method introduces a deterministic, algebraic paradigm for artificial intelligence—one that replaces iterative optimization with direct analytical resolution. Instead of adjusting parameters through stochastic gradient descent, the method determines the optimal mapping between inputs and targets in a single closed-form computation. Every training run yields identical outcomes, free from the randomness, noise, and instability inherent to conventional neural networks. By enforcing σ-regularization, the system guarantees numerical stability, bounded spectral energy, and reproducible behavior across platforms and hardware. This deterministic approach transforms learning from a process of random search into a solvable physical equation. It behaves like a stable mechanical system—elastic, self-damping, and energy-conserving—rather than a stochastic process prone to divergence. Small perturbations in the internal matrices produce proportionally small and predictable variations in loss, confirming that learning unfolds within a confined, thermodynamically bounded energy basin. The Cekirge framework therefore unites computational mathematics with physical law, showing that intelligence can be achieved through equilibrium rather than iteration. Its advantages are multifold: training completes in a single analytical step, energy consumption drops by orders of magnitude, and reproducibility becomes absolute. All internal matrices remain invertible and transparent, making the system fully auditable and interpretable. Because the σ-regularization principle scales naturally to multi-head attention and large-matrix architectures, the method extends beyond toy models to industrial-scale applications. It offers a foundation for deterministic, energy-efficient, and ecologically responsible AI, where computation aligns with the fundamental symmetry and conservation principles of physics.