Differential rank preservation manifold learning

arXiv:2610.41107v1 Announce Type: new Abstract: Manifold learning methods like t-SNE and UMAP preserve local neighborhoods, but they do not preserve the ranking of the neighbors inside them. Two embeddings can return the same neighbor set while disagreeing on which point is closest. This loss of order degrades downstream applications that value the order in the embedding. We propose Smooth Rank t-SNE (SR-tSNE), which adds a differentiable rank term to the standard t-SNE loss. To enable efficient training, this term uses a sigmoid rank approximation to explicitly force a point's true high-dimensional neighbors to outrank unrelated intruders and retain their original order.