Low Rank Adaptation (LoRA) is a popular Parameter Efficient Fine Tuning (PEFT) method that effectively adapts large pre-trained models for downstream tasks. LoRA parameterizes model updates using low-rank matrices at each layer, significantly reducing the number of trainable parameters and, consequently, resource requirements during fine-tuning. However, the lower bound on the number of trainable parameters remains high due to the use of the low-rank matrix model. In this paper, we address this limitation by proposing a novel approach that employs a low rank tensor parametrization for model updates. The proposed low rank tensor model can significantly reduce the number of trainable parameters, while also allowing for finer-grained control over adapter size. Our experiments on Natural Language Understanding, Instruction Tuning, Preference Optimization and Protein Folding benchmarks demonstrate that our method is both efficient and effective for fine-tuning large language models, achieving a substantial reduction in the number of parameters while maintaining comparable performance.

Low-rank adaptation (LoRA) and its variants are widely employed in fine-tuning large models, including large language models for natural language processing and diffusion models for computer vision. This paper proposes a generalized framework called SuperLoRA that unifies and extends different LoRA variants, which can be realized under different hyper-parameter settings. Introducing grouping, folding, shuffling, projecting, and tensor factoring, SuperLoRA offers high flexibility compared with other LoRA variants and demonstrates superior performance for transfer learning tasks especially in the extremely few-parameter regimes.