Augmentation-Graph Label Propagation Head

(1) Integration point: modify the classifier loss during semi-supervised fine-tuning. Use an encoder h_phi and classifier g_theta. For every indexed example x_i in a minibatch, compute an embedding h_i and prediction p_i = softmax(g_theta(x_i)/tau). Initially freeze h_phi or update it only with the ordinary supervised loss; construct the graph from detached embeddings so the graph cannot be manipulated by the encoder to remove the penalty. (2) Pseudocode: generate two stochastic augmented views for each example; compute detached view embeddings; form a sparse k-nearest-neighbor matrix W using W_ij = exp(-||h_i-h_j||^2/(2 rho^2)) when j is among i's neighbors and zero otherwise; symmetrize W with (W+W^T)/2; calculate d_i = sum_j W_ij and L = diag(d)-W; compute predictions P; calculate R_graph = tr(P^T L P)/m^2, equivalently R_graph = (1/(2m^2)) sum_ij W_ij ||p_i-p_j||^2; minimize L_sup + lambda R_graph, where L_sup is cross-entropy or another convex supervised loss over labeled nodes. Rebuild the graph every epoch or every few hundred steps. (3) The Laplacian identity and the C/n_L + R_DA(y) rate are taken from the paper. The neighbor count k, bandwidth rho, temperature tau, regularization coefficient lambda, and stability constant C are empirical; do not assume C is known. Estimate the alignment proxy using ground-truth labels when both endpoints are labeled and pseudo-labels only when prediction confidence exceeds gamma. (4) First experiment: use CIFAR-10 with 1%, 2%, 5%, and 10% labels, a frozen pretrained ResNet-18 or ViT-small, and compare ordinary linear probing against the same head with graph regularization. Measure test accuracy, transductive accuracy on the unlabeled pool, training loss at equal FLOPs, graph-cut proxy, and n_L times the residual error after subtracting the cut proxy. Success is improved accuracy at low label counts and a substantially smaller gap between transductive and test performance without increasing encoder compute excessively.