Fast Rates for Semi-Supervised Learning via Data-Augmentation Graph Regularization

arXiv:2607.07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation. We provide one. Data augmentation induces a similarity graph on the unlabeled data, so downstream learning on that graph is graph-Laplacian-regularized learning. We prove a fast transductive rate, O(1/n_L) in the number of labels, in place of the supervised O(1/sqrt{n_L}), by carrying the leave-one-out stability apparatus of Johnson and Zhang (JMLR 2007) over to the augmentation graph, and without the unrealistic assumptions of limit-based analyses (exact kernel, generalizing features). The bound makes augmentation quality explicit: the expected error is at most C/n_L + R_{DA}(y), where the data-augmentation alignment error R_{DA}(y) is the graph-cut mass of augmentations that cross a label boundary, so good augmentations let few labels suffice. The analysis uses a streamlined loss that drops the projector, negative-sample, and orthogonality overhead of standard objectives yet still recovers the top-K ideal features in the infinite-data limit, the augmentation-kernel eigenspace studied by Zhai et al. The result explains the observed accuracy-versus-label-count curve rather than only bounding a generalization gap.

Source: arXiv cs.LG | 2026-07-09