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

2026-06-25

AI Summary

This work addresses the challenge of gradient conflicts in open-set semi-supervised learning (OSSL), where unlabeled data contain out-of-distribution outliers and erroneous pseudo-labels that mislead model training. To mitigate this issue, the authors propose a Geometric Gradient Rectification (GGR) framework that shifts the paradigm from sample-level filtering to gradient-level control. GGR treats supervised gradients as anchors and rectifies conflicting auxiliary gradients by projecting them geometrically onto a feasible region within the gradient space. This projection, informed by subspace-aware correction, preserves beneficial update directions while discarding those inconsistent with the supervised objective. Extensive experiments demonstrate that GGR significantly enhances both closed-set generalization and open-set robustness of existing OSSL methods on CIFAR and ImageNet benchmarks.

Abstract

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 \textit{Geometric 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.

Problem

• open-set semi-supervised learning
• out-of-distribution outliers
• gradient conflict
• pseudo-labeling
• robustness

Innovation

• Geometric Gradient Rectification
• Open-Set Semi-Supervised Learning
• Gradient Projection
• Out-of-Distribution Robustness
• Plug-in Framework