Freeze-Out-Aware Noise Annealing

1. Integration point: apply the method to stochastic gradient Langevin dynamics, SGD with explicit Gaussian perturbations, or noisy Adam. Let theta be the parameter vector, L(theta) the loss, eta_k the step size, and T_k the noise temperature. Estimate an effective dimension N_eff as the number of parameters or principal gradient-variance modes whose running variance exceeds a threshold; initially compare this with the total parameter count. 2. Pseudocode: initialize T at T0, calibrate C, and maintain an exponential moving average theta_bar. At each step compute a normalized residual energy E_k = norm(theta_k - theta_bar_k)^2 divided by 2 tau^2. Set xi_k to the minimum of the requested cooling rate and (E_target/C)^(3/2)/N_eff. Apply theta <- theta - eta times noisy_gradient + sqrt(2 eta T) times Gaussian_noise, then set T <- max(T_min, T - eta xi_k). 3. The 2/3 exponent and xi N dependence come from the paper; C, N_eff, tau, and the mapping from parameter variance to energy must be estimated. 4. First cheap experiment: train an MLP and ResNet-18 on CIFAR-10 using constant-noise, linearly cooled, and constrained schedules, with five cooling rates and three widths. Measure terminal parameter variance after reaching T_min. The prediction is a fitted exponent near 2/3 and collapse versus xi N_eff; the adaptive schedule should keep residual energy near E_target. An exponent outside approximately 0.45 to 0.9 falsifies the direct transfer.