Armijo acceptance with decoupled LM damping

1. Integration point: modify the optimizer step after any subspace, diagonal, or Krylov LM direction has been computed. This can be used independently of the hybrid basis, but the intended integration is with the projected solve (U^THU+lambda I)z=-U^Tg. 2. Pseudocode: at iteration t, compute F(theta), g, and one damped direction p. Compute Pred=max(epsilon, -g dot p - 0.5 p dot H p), where Hp is obtained either from the already available projected curvature or one additional JVP/VJP. Set alpha=1. While F(theta+alpha*p)>F(theta)+c*alpha*(g dot p) and alpha>alpha_min, replace alpha by beta*alpha. If no acceptable alpha exists, skip the update and increase lambda. Otherwise set theta_new=theta+alpha*p, compute Act=F(theta)-F(theta_new), rho=Act/Pred, and update lambda using rho_low, rho_high, gamma_up, and gamma_down. Do not recompute p during backtracking. 3. Computed from the math: Armijo acceptance, the model-prediction term, and rho. Estimated empirically: F on each trial minibatch; to reduce noise, use the same minibatch for all trial evaluations or maintain an exponential moving average of Act and Pred. Use c=1e-4, beta=0.5, alpha_min=1/32, rho_low=0.25, rho_high=0.75, gamma_up=4, and gamma_down=2. 4. First cheap experiment: compare this policy against conventional LM that changes lambda and resolves the projected system after every rejected trial, using the same 2-layer MLP and regression dataset. Record wall-clock time, number of curvature products, rejected trials, accepted loss decrease, and final MSE. The expected signal is similar or better loss per accepted iteration with substantially fewer projected solves, especially when minibatch curvature makes full-step acceptance unreliable.