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

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 8.52\%.

In many real world situations, we have very few labeled examples to train a machine learning model, but plenty of unlabeled data that can take almost any form. Most existing methods try to guess labels for the unlabeled data, but they assume the unlabeled data follows a predictable pattern or that enough labeled data exists to understand that pattern. When these assumptions fail, the guessing leads to many mistakes, which confuses the model. Our work, called SAGE, takes a different approach. Instead of relying on guessed labels, we focus on the natural relationships between data points themselves, how similar or different they are. By analyzing these connections, SAGE creates a kind of “coordinate system” that helps keep different classes of data well separated. It also carefully weighs which guessed labels to trust and isolates the unreliable ones. Tested on five standard datasets, SAGE consistently beats existing methods, improving accuracy by 8.5\% on average. This makes it a more robust solution for learning from limited labels in messy real world data.