Transport-stable representation regularization

Add this loss to supervised classification or contrastive training. For every minibatch, generate a second nearby sample set using weak augmentation, small Gaussian perturbations, token dropout, or mild feature masking. Run both versions through the encoder to obtain embeddings Z and Z-prime and logits P and P-prime. Compute the cost matrix C_i_j=||stop-gradient(z_i)-stop-gradient(z-prime_j)||_2^2. Obtain a coupling with entropic Sinkhorn iterations: initialize u and v as positive vectors; set K_i_j=exp(-C_i_j/tau); repeatedly update u_i=(1/n)/(sum_j K_i_j v_j) and v_j=(1/n)/(sum_i K_i_j u_i). Form pi_i_j=u_i K_i_j v_j. Stop gradients through pi initially. Add lambda times sum over i,j of pi_i_j ||P_i-P-prime_j||_2^2 to the ordinary cross-entropy loss, ramping lambda from zero during the first 10 percent of training. The empirical-measure and vanishing-transport-displacement motivation comes from the paper; the entropic coupling and Sinkhorn solver are the implementation choices. Monitor the average transport cost sum_i,j pi_i_j C_i_j and disable the regularizer for unusually large costs, so unrelated examples are not forced together. First test on CIFAR-10 with a four-layer CNN or ViT-Tiny against standard consistency regularization using the same augmentations. Measure clean accuracy, corruption accuracy, calibration, prediction variance under resampling, and training overhead. Success is improved robustness or calibration at matched clean accuracy, with less than 20 percent additional training time.