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Geo-LoRA: Geometry-Aware Subspace Evolution for Low-Rank Adaptation in Continual Learning

arXiv · AI, language, vision and robotics · article · Aug 27, 2026 · UTC

Rehearsal-free class-incremental learning (CIL) with LoRA adapters remains challenging because the low-rank subspaces updated across tasks evolve without geometric control, causing unstable shared representations and repetitive collapse of task-specific updates into previously occupied directions. We introduce Geo-LoRA, a geometry-aware framework that explicitly regulates how low-rank subspaces, both shared and task-specific, evolve during continual learning. For the shared branch, Subspace Projection Preservation (SPP) constrains consecutive updates to follow smooth trajectories on the Grassm

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