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

arXiv: https://arxiv.org/abs/2605.07557 · HTML: https://mlsanity.com/paper/2605.07557/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 47 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 26 of 26)

- [SGDR: Stochastic Gradient Descent with Warm Restarts](https://mlsanity.com/paper/1608.03983/) (2016)
- [Wide Residual Networks](https://mlsanity.com/paper/1605.07146/) (2016)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Prevalence of Neural Collapse during the terminal phase of deep learning training](https://mlsanity.com/paper/2008.08186/) (2020)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning](https://mlsanity.com/paper/2205.07246/) (2022)
- [SoftMatch: Addressing the Quantity-Quality Trade-off in Semi-supervised Learning](https://mlsanity.com/paper/2301.10921/) (2023)
- [Targeted Supervised Contrastive Learning for Long-Tailed Recognition](https://mlsanity.com/paper/2111.13998/) (2021)
- [Dual Student: Breaking the Limits of the Teacher in Semi-supervised Learning](https://mlsanity.com/paper/1909.01804/) (2019)
- [ABC: Auxiliary Balanced Classifier for Class-imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2110.10368/) (2021)
- [CoSSL: Co-Learning of Representation and Classifier for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2112.04564/) (2021)
- [Detecting Out-of-Distribution Through the Lens of Neural Collapse](https://mlsanity.com/paper/2311.01479/) (2023)
- [Policy Filtration for RLHF to Mitigate Noise in Reward Models](https://mlsanity.com/paper/2409.06957/) (2024)
- [Adapt in Contexts: Retrieval-Augmented Domain Adaptation via In-Context Learning](https://mlsanity.com/paper/2311.11551/) (2023)
- [SemiReward: A General Reward Model for Semi-supervised Learning](https://mlsanity.com/paper/2310.03013/) (2023)
- [SimPro: A Simple Probabilistic Framework Towards Realistic Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2402.13505/) (2024)
- [Three Heads Are Better Than One: Complementary Experts for Long-Tailed Semi-supervised Learning](https://mlsanity.com/paper/2312.15702/) (2023)
- [CGMatch: A Different Perspective of Semi-supervised Learning](https://mlsanity.com/paper/2503.02231/) (2025)
- [CDMAD: Class-Distribution-Mismatch-Aware Debiasing for Class-Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2403.10391/) (2024)
- [SSB: Simple but Strong Baseline for Boosting Performance of Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2311.10572/) (2023)
- [Semi-supervised Fine-tuning for Large Language Models](https://mlsanity.com/paper/2410.14745/) (2024)
- [A Square Peg in a Square Hole: Meta-Expert for Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2505.16341/) (2025)
- [TraPO: A Semi-Supervised Reinforcement Learning Framework for Boosting LLM Reasoning](https://mlsanity.com/paper/2512.13106/) (2025)
- [Text-driven Multiplanar Visual Interaction for Semi-supervised Medical Image Segmentation](https://mlsanity.com/paper/2507.12382/) (2025)
- [Keep It on a Leash: Controllable Pseudo-label Generation Towards Realistic Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2510.03993/) (2025)

## Abstract (arXiv)

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%.