RepG: New semi-supervised generative model beats curse of dimensionality

A new paper on arXiv (2607.16725) introduces RepG, a semi-supervised conditional generative learning framework that tackles the challenge of scarce labeled data. Authors Liu, Jiao, and Huang combine conditional stochastic interpolation with low-dimensional latent representations to effectively leverage abundant unlabeled samples. RepG works in two stages: first, it samples a latent variable conditioned on labels in a low-dimensional space; second, it reconstructs the high-dimensional output using only unlabeled data. This decomposition isolates the supervised learning burden to a compact latent space, dramatically reducing the number of labels required. The team provides rigorous theoretical guarantees, deriving non-asymptotic convergence rates showing RepG achieves strictly faster convergence than ambient-space methods, effectively mitigating the curse of dimensionality.

RepG's error decomposition reveals that the Kullback-Leibler divergence consists of stage-wise estimation errors plus a structural bias measured by conditional mutual information. For deep neural network estimators, the sample complexity improves significantly because the supervised estimation is confined to the intrinsic dimension of the latent representation. A minimax lower bound confirms that this approach is near-optimal. While the paper is purely theoretical, the implications are clear: generative AI models that need far fewer labeled examples, relying on cheap unlabeled data for high-quality reconstruction. This could lower the barrier for applications in domains like medical imaging, where labels are expensive, or any field requiring conditional generation with limited supervision.