CoDe-LoRA: Mitigating the Orthogonality Dilemma in Continual Learning of LLMs via Knowledge Consolidation and Decoupling

Continual learning (CL) is essential for Large Language Models (LLMs) to sequentially adapt to evolving tasks. To mitigate catastrophic forgetting, recent advances implement low-rank adaptation with orthogonal projections (e.g., O-LoRA) to isolate task parameters. However, we reveal that such strict geometric constraints trigger an "Orthogonality Dilemma": rigid parameter isolation impedes the transfer and accumulation of shared representations across semantically related tasks. In this work, we propose a new replay-free method, called Consolidation and Decoupling LoRA (CoDe-LoRA), for CL of LLMs. CoDe-LoRA disentangles the learning process into Consolidating Universal Knowledge and Decoupling Task-Specific Knowledge. To achieve this, CoDe-LoRA leverages an adaptive null space projection mechanism and semantic routing to balance knowledge accumulation with task-specific adaptation. Experimental results across four backbones and three CL benchmarks show that CoDe-LoRA achieves the best average accuracy. Our code is available at https://github.com/Estrellajer/CoDe-LoRA.