Orthogonal Low-rank Adaptation in Lie Groups for Continual Learning of Large Language Models

Kefan Cao; Shuaicheng Wu

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arXiv · 2509.06100

Orthogonal Low-rank Adaptation in Lie Groups for Continual Learning of Large Language Models

Kefan Cao·Shuaicheng Wu

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Abstract

Large language models (LLMs) suffer from catastrophic forgetting in sequential multi-task learning. Existing parameter regularization methods (e.g., O-LoRA, N-LoRA) mitigate interference via low-rank subspace orthogonality, but additive updates distort the intrinsic geometry of model parameters. We propose \textbf{OLieRA}, a Lie group based fine-tuning framework that preserves parameter geometry through multiplicative updates while enforcing orthogonality across task subspaces. OLieRA achieves state-of-the-art performance on the Standard CL benchmark and remains highly competitive under large task sequences. It further inherits the replay-free and task-ID free inference properties of O-LoRA, establishing a principled paradigm for continual learning in LLMs.

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Kefan Cao, Shuaicheng Wu. 2025-09-07. Orthogonal Low-rank Adaptation in Lie Groups for Continual Learning of Large Language Models. https://arxiv.org/abs/2509.06100

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