Large language models (LLMs) often leverage adapters, such as low-rank-based adapters, to achieve strong performance on downstream tasks. However, storing a separate adapter for each task significantly increases memory requirements, posing a challenge for resource-constrained environ ments such as mobile devices. Although model merging techniques can reduce storage costs, they typically result in substantial performance degradation. In this work, we introduce HydraOpt, a new model merging technique that capitalizes on the inherent similarities between the matrices of low-rank adapters. Unlike existing methods that produce a fixed trade-off between storage size and performance, HydraOpt allows us to navigate this spectrum of efficiency and performance. Our experiments show that HydraOpt significantly reduces storage size (48% reduction) compared to storing all adapters, while achieving competitive performance (0.2-1.8% drop). Furthermore, it outperforms existing merging techniques in terms of performance at the same or slightly worse storage efficiency.

The growing size of large language models (LLMs) requires parameter-efficient fine-tuning (PEFT) methods for their adaptation to new tasks. Existing methods, such as Low-Rank Adaptation (LoRA), typically involve model adaptation by training the PEFT parameters. One open problem required to be solved to effectively employ these methods is the identification of PEFT parameters. More precisely, related works identify PEFT parameters by projecting high dimensional parameters of LLMs onto low dimensional parameter manifolds with predefined projections, or identifying PEFT parameters as projections themselves. To study this problem, we propose a new approach called Learning to Efficiently Fine-tune (LEFT) where we aim to learn spaces of PEFT parameters from data. In order to learn how to generate the PEFT parameters on a learned parameter space while fine-tuning the LLMs, we propose the Parameter Generation (PG) method. In the experimental analyses, we examine the effectiveness of our solutions exploring accuracy of fine-tuned LLMs and characteristics of PEFT parameters on benchmark GLUE tasks.