Low-Rank Adaptation (LoRA) has gained popularity for fine-tuning large foundation models, leveraging low-rank matrices \mathbf A and \mathbf B to represent weight changes (i.e., 𝛥 \mathbf W = \mathbf B \mathbf A). This method reduces trainable parameters and mitigates heavy memory consumption associated with full delta matrices by sequentially multiplying \mathbf A and \mathbf B with the activation. Despite its success, the intrinsic low-rank characteristic may limit its performance. Although several variants have been proposed to address this issue, they often overlook the crucial computational and memory efficiency brought by LoRA. In this paper, we propose Circular Convolution Adaptation (C³A), which not only achieves high-rank adaptation with enhanced performance but also excels in both computational power and memory utilization. Extensive experiments demonstrate that C³A consistently outperforms LoRA and its variants across various fine-tuning tasks.

Low-Rank Adaptation (LoRA) has emerged as a prominent technique for fine-tuning large foundation models. Despite its successes, the substantial parameter redundancy, which limits the capacity and efficiency of LoRA, has been recognized as a bottleneck. In this work, we systematically investigate the impact of redundancy in fine-tuning LoRA and reveal that reducing density redundancy does not degrade expressiveness. Based on this insight, we introduce Spectral-encoding Low-Rank Adaptation (SeLoRA), which harnesses the robust expressiveness of spectral bases to re-parameterize LoRA from a sparse spectral subspace. Designed with simplicity, SeLoRA enables seamless integration with various LoRA variants for performance boosting, serving as a scalable plug-and-play framework. Extensive experiments substantiate that SeLoRA achieves greater efficiency with fewer parameters, delivering superior performance enhancements over strong baselines on various downstream tasks, including commonsense reasoning, math reasoning, and code generation.