# Geometric Gradient Rectification for Safe Open-Set Semi-Supervised Learning

arXiv: https://arxiv.org/abs/2606.26973 · HTML: https://mlsanity.com/paper/2606.26973/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 35 references that are in the map.
- First posted on arXiv 25 Jun 2026.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [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)
- [MixMatch: A Holistic Approach to Semi-Supervised Learning](https://mlsanity.com/paper/1905.02249/) (2019)
- [Gradient Surgery for Multi-Task Learning](https://mlsanity.com/paper/2001.06782/) (2020)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Virtual Adversarial Training: A Regularization Method for Supervised and Semi-Supervised Learning](https://mlsanity.com/paper/1704.03976/) (2017)
- [FlexMatch: Boosting Semi-Supervised Learning with Curriculum Pseudo Labeling](https://mlsanity.com/paper/2110.08263/) (2021)
- [ReMixMatch: Semi-Supervised Learning with Distribution Alignment and Augmentation Anchoring](https://mlsanity.com/paper/1911.09785/) (2019)
- [A Survey on Deep Semi-supervised Learning](https://mlsanity.com/paper/2103.00550/) (2021)
- [Learning with Pseudo-Ensembles](https://mlsanity.com/paper/1412.4864/) (2014)
- [FreeMatch: Self-adaptive Thresholding for Semi-supervised Learning](https://mlsanity.com/paper/2205.07246/) (2022)
- [CoMatch: Semi-supervised Learning with Contrastive Graph Regularization](https://mlsanity.com/paper/2011.11183/) (2020)
- [SoftMatch: Addressing the Quantity-Quality Trade-off in Semi-supervised Learning](https://mlsanity.com/paper/2301.10921/) (2023)
- [SimMatch: Semi-supervised Learning with Similarity Matching](https://mlsanity.com/paper/2203.06915/) (2022)
- [USB: A Unified Semi-supervised Learning Benchmark for Classification](https://mlsanity.com/paper/2208.07204/) (2022)
- [Multi-Task Curriculum Framework for Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2007.11330/) (2020)
- [OpenMatch: Open-set Consistency Regularization for Semi-supervised Learning with Outliers](https://mlsanity.com/paper/2105.14148/) (2021)
- [Trash to Treasure: Harvesting OOD Data with Cross-Modal Matching for Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2108.05617/) (2021)
- [IOMatch: Simplifying Open-Set Semi-Supervised Learning with Joint Inliers and Outliers Utilization](https://mlsanity.com/paper/2308.13168/) (2023)
- [Robust Semi-supervised Learning by Wisely Leveraging Open-set Data](https://mlsanity.com/paper/2405.06979/) (2024)
- [S2OSC: A Holistic Semi-Supervised Approach for Open Set Classification](https://mlsanity.com/paper/2008.04662/) (2020)
- [SSB: Simple but Strong Baseline for Boosting Performance of Open-Set Semi-Supervised Learning](https://mlsanity.com/paper/2311.10572/) (2023)
- [ProSub: Probabilistic Open-Set Semi-Supervised Learning with Subspace-Based Out-of-Distribution Detection](https://mlsanity.com/paper/2407.11735/) (2024)
- [Diversify and Conquer: Open-set Disagreement for Robust Semi-supervised Learning with Outliers](https://mlsanity.com/paper/2505.24443/) (2025)

## Abstract (arXiv)

Open-set semi-supervised learning aims to leverage unlabeled data that may contain out-of-distribution outliers while maintaining performance on in-distribution classes. Existing methods mainly follow two paradigms: filtering suspicious samples or incorporating unlabeled objectives with soft weighting. We argue that both face a common trade-off: aggressive filtering can discard informative but hard ID samples, whereas utilization can introduce auxiliary gradients that conflict with supervised learning when pseudo labels are wrong. We therefore shift the focus from sample selection to gradient-level control. We propose textitGeometric Gradient Rectification (GGR), a plug-in framework that uses the supervised gradient as an anchor and projects conflicting auxiliary gradients onto an admissible region in gradient space. This makes the applied auxiliary update first-order non-opposing within the rectified coordinate block while preserving orthogonal components that may still carry useful representation signals. We further extend GGR with subspace-aware rectification to stabilize the anchor under noisy mini-batch gradients. Experiments on CIFAR and ImageNet benchmarks show that GGR improves representative OSSL baselines in most settings and yields gains in both closed-set generalization and open-set robustness. Code will be available at https://github.com/JiaheChen2002/GGR.