Multi-view cycle-consistent matching layer

Integrate this at the point where a network has produced K representations of the same unordered set, such as K augmentations of an image patch set, K views of a point cloud, or K modalities containing the same entities. Let H[v] have shape [B,K,n,d]. First L2-normalize the d-dimensional rows. For every ordered pair (u,v), construct the cost matrix C_uv[i,j] = (1 - cosine(H[u,i], H[v,j]))/tau. Add a small diagonal or positional prior only when the application has a meaningful approximate ordering; otherwise use no prior. Compute P_uv as a differentiable Sinkhorn normalization of exp(-C_uv), with 5-20 iterations and log-domain stabilization. During training, use the alignment loss sum_uv <P_uv,C_uv> plus lambda_cycle times the average Frobenius cycle error ||P_uv P_vw - P_uw||_F^2/n. To prevent collapse, either stop gradients through one view in the pairwise cost or add an entropy or feature-variance term ensuring that all rows do not become identical. For inference, discretize a reference-to-view matrix with Hungarian matching, or compose P_0v through a reference view before rounding. The paper contributes the multi-view threshold intuition and the requirement for independent view redundancy; the Sinkhorn relaxation and cycle loss are the neural implementation. Estimate empirical benefit by measuring the fraction of correct assignments when synthetic Gaussian embeddings use sigma^2=d/(b log n), sweeping b around 2 and K=2,3,4. The first cheap experiment should use n=64 tokens, d=128, a six-layer Transformer, and three independently augmented CIFAR-100 or ModelNet views. Compare independent Sinkhorn matching against pairwise-plus-cycle matching at equal FLOPs. Success is higher exact-match accuracy and lower variance across seeds, especially in the regime where pairwise matching is near chance but K=3 achieves stable alignment.