Renyi Drift-Controlled Fine-Tuning

First, integrate the method into supervised fine-tuning, continual learning, or policy distillation. Freeze a reference network q, usually the pre-fine-tuning checkpoint or an exponential-moving-average teacher. For each minibatch, compute student logits, reference logits under no-gradient mode, and the task loss. Convert both logits to probabilities with a common temperature. Use log-space arithmetic: logp = log_softmax(student_logits divided by T), logq = log_softmax(reference_logits divided by T), logS = logsumexp(k times logp plus (1-k) times logq over classes), and renyi = mean(logS) divided by (k-1). For k close to 1, use KL divergence to avoid numerical cancellation. The update is task_loss plus lambda times renyi, followed by backpropagation through the student only. The paper supplies the divergence construction and the prediction that competing minima can exchange dominance as k changes; estimate basin structure, branch objective values, Hessian trace, gradient norms, and output drift empirically. The first cheap experiment should fine-tune a pretrained ResNet-18 on CIFAR-10 with 20 percent label corruption while retaining the original model behavior on a clean replay subset. Compare KL, k values 0.5, 2, 4, and 8, and no regularizer at matched lambda values over five seeds. Warm-start sweeps in both increasing and decreasing k directions. The quantitative prediction is a reproducible kink or hysteresis-like jump in clean-set KL and task accuracy near a critical k_c, especially when two lambda-dependent solutions coexist. Locate k_c from equal minimized objective values and require agreement within 20 percent across seeds. Increasing k should also disproportionately reduce the upper quantiles of log[p_theta divided by q], whereas k below 1 should reduce support-loss events where the student probability is near zero.