Semi-Supervised Conditional Generative Learning through Stochastic Interpolation and Sufficient Representations

2026-07-18

AI Summary

This work addresses the challenge of leveraging unlabeled data effectively in semi-supervised conditional generative modeling under label scarcity. The authors propose RepG, a framework that decouples the generation process into two stages: supervised sampling in a low-dimensional latent space and unsupervised reconstruction in the high-dimensional data space. By restricting conditional modeling to the low-dimensional space, RepG substantially reduces sample complexity and mitigates the curse of dimensionality. Theoretical analysis reveals that RepG achieves a faster non-asymptotic convergence rate through an error decomposition driven by conditional mutual information, and its optimality is confirmed by matching the minimax lower bound. Empirical results demonstrate the superior performance of RepG in semi-supervised conditional generation tasks.

Abstract

Conditional generative modeling remains a challenging problem in semi-supervised settings where labeled data is scarce but unlabeled samples are abundant. To effectively leverage structural information embedded within the unlabeled dataset and compensate for sparse conditioning signals, we propose a semi-supervised framework combining conditional stochastic interpolation with low-dimensional latent representations. RepG decomposes generation into two stages: label-dependent latent sampling and high-dimensional reconstruction. This isolates the supervised learning of conditional dependencies to a low-dimensional space, requiring few labels while utilizing the abundant unlabeled data purely for reconstruction. Theoretically, we establish an error decomposition showing that the Kullback-Leibler divergence of RepG comprises stage-wise estimation errors and a structural bias quantified by conditional mutual information. For deep neural network estimators, we derive non-asymptotic convergence rates proving that RepG significantly improves sample complexity. By confining the supervised estimation burden to the low intrinsic dimension of the latent representation, RepG achieves a strictly faster convergence rate. Complemented by a minimax lower bound, our theoretical results demonstrate that this method effectively mitigates the curse of dimensionality inherent in direct ambient-space generative modeling.

Problem

• semi-supervised learning
• conditional generative modeling
• label scarcity
• high-dimensional generation
• curse of dimensionality

Innovation

• semi-supervised generative modeling
• stochastic interpolation
• low-dimensional latent representation
• conditional mutual information
• non-asymptotic convergence