Cekirge Perturbation Report v4

This report introduces a deterministic σ-regularized framework for transformer-style models that computes attention and decoding in closed form without iterative gradient descent. By constructing nonsingular query (Q), key (K), value (V), and output (W) matrices, the method ensures invertibility, numerical stability, and reproducibility. Stability is probed by uniform matrix perturbations of amplitude ε, and the resulting change in loss ΔL = L(ε) − L(0) is recorded. Empirically, ΔL increases nearly linearly with a gently decreasing slope (≈1.84 → ≈1.70 for ε = 0.01 → 0.10), confirming energy-bounded forward determinism. This linear ε–ΔL dependence distinguishes the Çekirge method from stochastic training, revealing a predictable, non-chaotic energy profile. The deterministic σ-regularized formulation provides a foundation for algebraic pretraining, analytical model verification, and thermodynamically aligned, energy-efficient artificial intelligence.