Continual Learning (CL) for Large Language Models (LLMs) faces a fundamental Stability-Plasticity Dilemma: balancing the plasticity to acquire new capabilities with the stability to preserve prior knowledge. While Parameter-Efficient Fine-Tuning methods, such as LoRA, enable efficient adaptation, we identify a critical flaw in current approaches termed Rank-Blindness: the enforcement of a single rank constraint across diverse tasks, which entangles task-shared and task-specific knowledge, leading to catastrophic forgetting of earlier tasks and underfitting on complex new ones. To address this, we propose SpaRTA, a novel rehearsal-free framework guided by a rank-spectrum perspective that explicitly disentangles knowledge into two orthogonal subspaces. Specifically, SpaRTA employs a low-rank branch to capture task-shared representations and a high-rank branch to model task-specific features. To integrate these complementary representations, we introduce a context-aware dynamic router that adaptively fuses the two branches based on input semantics, while an explicit orthogonality constraint minimizes interference between shared and specific parameter subspaces. This design effectively isolates task-specific updates from shared knowledge, preventing the overwriting of prior capabilities while preserving strong adaptation capacity. Extensive experiments demonstrate that SpaRTA achieves a superior stability-plasticity balance compared to single-rank baselines. Notably, the proposed spectral disentanglement strategy substantially reduces inter-task interference and yields strong zero-shot generalization on unseen tasks. Our code will be available at https://github.com/Xnhyacinth/SpaRTA.

Enabling Large Language Models (LLMs) to evolve sustainably requires simultaneously preserving previously acquired knowledge (Past), effectively acquiring new task-specific skills (Present), and reserving sufficient parameter capacity for subsequent adaptation (Future). However, existing continual learning (CL) paradigms often prioritize immediate performance through dense updates, leading to catastrophic forgetting and rapid exhaustion of model capacity. To harmonize these conflicting demands, we draw inspiration from the brain’s functional partitioning and propose the Null-Space Constrained Parameter Region Specificity Method (PaRSP). PaRSP establishes a dynamic "Task-Region Mapping" that distinguishes between specialized neurons and generalist neurons. By precisely localizing a sparse "functional core" for each task, PaRSP restricts updates to specific regions via null-space orthogonality, preserving the vast majority of the network as an immutable "long-term memory bank." This induced sparsity not only enhances plasticity via targeted adaptation and minimizes interference to ensure stability, but also strategically reserves substantial capacity, securing sustainability for future evolution. Extensive experiments validate PaRSP’s state-of-the-art performance, particularly on Standard CL and Long Sequence benchmarks, effectively harmonizing the stability-plasticity-sustainability trade-off. Code is available at https://github.com/JinhuiBot/PaRSP