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

Open-set semi-supervised learning aims to leverage unlabeleddata that may contain out-of-distribution outliers while maintainingperformance on in-distribution classes. Existing methods mainly followtwo paradigms: filtering suspicious samples or incorporating unlabeledobjectives 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 withsupervised learning when pseudo labels are wrong. We therefore shiftthe focus from sample selection to gradient-level control. We proposeGeometric Gradient Rectification (GGR), a plug-in framework that usesthe supervised gradient as an anchor and projects conflicting auxiliarygradients onto an admissible region in gradient space. This makes theapplied auxiliary update first-order non-opposing within the rectifiedcoordinate block while preserving orthogonal components that may stillcarry 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 GGRimproves representative OSSL baselines in most settings and yields gainsin both closed-set generalization and open-set robustness. Code will beavailable at https://github.com/JiaheChen2002/GGR.