Low-Rank Adaptation (LoRA) has achieved remarkable progress in improving the fine-tuning efficiency and downstream performance of large language models (LLMs). Although prior work has recognized that different weight update matrices 𝛥 𝐖 exhibit varying importance and therefore should be allocated different ranks, parameters within the same update matrix are still typically constrained to a uniform rank configuration, neglecting fine-grained parameter-level heterogeneity. To address this limitation, we propose G-LoRA (Global-Local Decoupled LoRA), which decomposes each update matrix into global and local adapters. The key idea is to reorganize the rows and columns of the update matrix using a first-order Taylor approximation of parameter importance, such that highly influential parameters are clustered into a local sub-block of 𝛥 𝐖. During training, the local adapter then focuses on this high-importance sub-region and is allocated a higher rank, whereas the global adapter captures the residual updates for the entire update matrix with relatively lower rank. By allocating higher representational capacity to more critical parameters, G-LoRA enables more efficient utilization of model resources. Extensive evaluations on benchmarks spanning commonsense reasoning, mathematical reasoning, and code generation demonstrate that G-LoRA achieves up to 2.7% absolute accuracy improvement over LoRA and its variants, validating its effectiveness for LLM fine-tuning.

Low-Rank Adaptation (LoRA) for large language models (LLMs) has achieved significant success in various domains. So far, most algorithms in the LoRA-family rely on global low-rank factors spanning the entire update weight matrix (𝛥 𝐖). Through careful analysis, however, we observe that the 𝛥 𝐖 during fine-tuning typically exhibit heterogeneous subspace clusters, each corresponding to specific sub-sets of rows and columns. This structural heterogeneity suggests that global low-rank factors may not optimally capture the local variations needed for effective model adaptation. To address this limitation, we propose LoRA within Clustered Parameter Subspaces, or CPS-LoRA, which performs independent low-rank updates within clustered blocks of parameter matrices. The key idea is to group the rows/columns of the update matrix into locally coherent, and maximally uncorrelated subspaces, perform low-rank adaptations in each subspace, and iteratively update the partition and local adaptations. This allows adapting to local structures more precisely while preserving high efficiency. Theoretical analysis reveals that in case 𝛥 𝐖 can be partitioned into subspace blocks with non-overlapping basis, CPS-LoRA have superior parameter efficiency than global adaptations. Empirical evaluations further demonstrate better rank utilization of CPS-LoRA and its consistent improvements against LoRA (and variants) by up to 3.0% in absolute accuracy in various benchmarks.