We propose Tied-LoRA , a simple paradigm utilizes weight tying and selective training to further increase parameter efficiency of the Low-rank adaptation (LoRA)  method.
Our investigations include all feasible combinations parameter training/freezing in conjunction with weight tying to identify the optimal balance between performance and the number of trainable parameters. Through experiments covering a variety of tasks and two base language models, we provide analysis revealing trade-offs between efficiency and performance. Our experiments uncovered a particular Tied-LoRA configuration that stands out by demonstrating comparable performance across several tasks while employing only 13 % percent of parameters utilized by the standard LoRA method.