Beyond Distribution Estimation: Simplex Anchored Structural Inference Towards Universal Semi-Supervised Learning

TL;DR

This paper introduces SAGE, a novel structural inference method for universal semi-supervised learning that leverages inter-sample relations and simplex-based representation separation to improve accuracy in scarce label scenarios.

Contribution

The paper proposes SAGE, a representation-level structural inference approach that bypasses distribution estimation and enhances semi-supervised learning under unknown data distributions.

Findings

SAGE outperforms state-of-the-art methods on five benchmarks.

Achieves an average accuracy gain of 8.52%.

Utilizes simplex equiangular tight frames for class separation.

Abstract

Semi-supervised learning faces significant challenges in realistic scenarios where labeled data is scarce and unlabeled data follows unknown, arbitrary distributions. We formalize this critical yet under-explored paradigm as Universal Semi-supervised Learning (UniSSL). Existing methods typically leverage unlabeled data via pseudo-labeling. However, they often rely on the idealized assumption of a uniform unlabeled data distribution or require sufficient labeled data to estimate it. In the UniSSL setting, such dependencies lead to numerous erroneous pseudo-labels, thereby triggering representation confusion. Fortunately, we observe that inter-sample relations captured by representations are more reliable than pseudo-labels. Leveraging this insight, we shift our focus to representation-level structural inference to bypass distribution estimation. Accordingly, we propose Simplex Anchored Graph-state Equipartition (SAGE), which captures high-order inter-sample dependencies to establish structural consensus for guiding representation learning. Meanwhile, to mitigate representation confusion, we employ vectors that satisfy a simplex equiangular tight frame to serve as a coordinate frame for guiding inter-class representation separation. Finally, we introduce a weighting strategy based on distribution-agnostic metrics to prioritize reliable pseudo-labels and an auxiliary branch to isolate potentially erroneous pseudo-labels. Evaluations on five standard benchmarks show that SAGE consistently outperforms state-of-the-art methods, with an average accuracy gain of $\textbf{8.52%}$.