Low-Rank Adaptation (LoRA) is widely used for parameter-efficient fine-tuning, yet merging multiple task-specific LoRA updates without additional training remains challenging. Most existing LoRA merging methods rely on SVD-based alignment, which emphasizes globally shared structure across tasks. In this work, we show that LoRA merging performance can be further improved by combining SVD with CUR decomposition. Through a representation-level analysis, we find that SVD-based decompositions primarily model shared components across tasks, while CUR-based decompositions better preserve task-specific and localized updates. These two perspectives are geometrically misaligned and exhibit complementary advantages, revealing an inherent trade-off between capturing shared structure and preserving task-specific information in LoRA model merging. Guided by this analysis, we propose a training-free merging procedure that explicitly combines the shared structure captured by SVD with the task-specific components preserved by CUR. Experiments on both vision and language benchmarks demonstrate consistent improvements over existing gradient-free LoRA merging methods.

In this work, we propose FoRA-UA, a novel method that, using only 1–5% of the standard LoRA’s parameters, achieves state-of-the-art performance across a wide range of tasks. Specifically, we explore scenarios with extremely limited parameter budgets and derive two key insights: (1) fix-sized sparse frequency representations approximate small matrices more accurately; and (2) with a fixed number of trainable parameters, introducing a smaller intermediate representation to approximate larger matrices results in lower construction error. These findings form the foundation of our FoRA-UA method. By inserting a small intermediate parameter set, we achieve greater model compression without sacrificing performance. We evaluate FoRA-UA across diverse tasks, including natural language understanding (NLU), natural language generation (NLG), instruction tuning, and image classification, demonstrating strong generalisation and robustness under extreme compression.