Pillar IV: Hessian & Loss Manifolds // Zoth Math Academy

Pillar IV: Hessian & Loss Manifolds Formal Systems

Curvature tensors, saddles, and second-order dynamics

• Condition number κ(H): 14.2 (bounded)
• Spectral radius λ_max: 4.82
• HVP compute cost: O(d) matrix-free

Closed-Form Mathematical Formulation

H = ∇²L(θ)

Advanced Tensor Equation

κ(H) = λ_max(H) / λ_min(H)