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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.