# Geometric Regularization for Long-Tailed Semi-Supervised Learning via Gaussian Feature Bridges

arXiv: https://arxiv.org/abs/2608.20710 · HTML: https://mlsanity.com/paper/2608.20710/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 60 references that are in the map.
- First posted on arXiv 21 Aug 2026.

## Builds on (most cited first, 30 of 32)

- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Momentum Contrast for Unsupervised Visual Representation Learning](https://mlsanity.com/paper/1911.05722/) (2019)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Mamba: Linear-Time Sequence Modeling with Selective State Spaces](https://mlsanity.com/paper/2312.00752/) (2023)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [FixMatch: Simplifying Semi-Supervised Learning with Consistency and Confidence](https://mlsanity.com/paper/2001.07685/) (2020)
- [Improved Regularization of Convolutional Neural Networks with Cutout](https://mlsanity.com/paper/1708.04552/) (2017)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Unsupervised Data Augmentation for Consistency Training](https://mlsanity.com/paper/1904.12848/) (2019)
- [Vision Mamba: Efficient Visual Representation Learning with Bidirectional State Space Model](https://mlsanity.com/paper/2401.09417/) (2024)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning](https://mlsanity.com/paper/2205.07246/) (2022)
- [CReST: A Class-Rebalancing Self-Training Framework for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2102.09559/) (2021)
- [Distribution Aligning Refinery of Pseudo-label for Imbalanced Semi-supervised Learning](https://mlsanity.com/paper/2007.08844/) (2020)
- [Debiased Learning from Naturally Imbalanced Pseudo-Labels](https://mlsanity.com/paper/2201.01490/) (2022)
- [DASO: Distribution-Aware Semantics-Oriented Pseudo-label for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2106.05682/) (2021)
- [Semi-supervised Vision Transformers at Scale](https://mlsanity.com/paper/2208.05688/) (2022)
- [CoSSL: Co-Learning of Representation and Classifier for Imbalanced Semi-Supervised Learning](https://mlsanity.com/paper/2112.04564/) (2021)
- [Entropic Optimal Transport: Convergence of Potentials](https://mlsanity.com/paper/2104.11720/) (2021)
- [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)
- [BaCon: Boosting Imbalanced Semi-supervised Learning via Balanced Feature-Level Contrastive Learning](https://mlsanity.com/paper/2403.12986/) (2024)
- [A Square Peg in a Square Hole: Meta-Expert for Long-Tailed Semi-Supervised Learning](https://mlsanity.com/paper/2505.16341/) (2025)
- [TRiCo: Triadic Game-Theoretic Co-Training for Robust Semi-Supervised Learning](https://mlsanity.com/paper/2509.21526/) (2025)
- [Revisiting Chain-of-Thought Reasoning under Limited Supervision: Semi-supervised Chain-of-Thought Learning](https://mlsanity.com/paper/2607.01511/) (2026)

## Built on by (most cited first, 1 of 1)

- [ReCalMatch:Reliability-Calibrated Semantic Guidance for Semi-Supervised Fine-Grained Recognition](https://mlsanity.com/paper/2609.29678/) (2026)

## Abstract (arXiv)

Real-world semi-supervised learning (SSL) often encounters significant challenges with long-tailed label distributions and noisy pseudo-labels, which hinder generalization and amplify confirmation bias. In this work, we introduce a novel framework, Gaussian Bridge Consistency (GBC), to address these challenges by constructing semantic interpolation paths between unlabeled samples and high-quality class anchors. Our method maintains a dynamic Prototype Atlas that stores a diverse and evolving set of labeled and pseudo-labeled exemplars per class. For each unlabeled instance, GBC forms a class-conditional Gaussian Feature Bridge in the latent space, enabling the student model to traverse a smooth trajectory from uncertain predictions to reliable class prototypes. A bridge consistency loss is applied along this path to enforce alignment with a geometrically interpolated target distribution. Furthermore, we propose BridgeMix, a confidence-aware feature mixing strategy that interpolates both sample and anchor pairs to amplify cross-sample generalization. Extensive experiments on CIFAR10-LT and ImageNet-LT (USB benchmarks) validate the robustness and effectiveness of GBC under realistic long-tailed SSL settings, consistently improving long tail-class performance without sacrificing scalability.