标题： tCURLoRA：基于张量CUR分解的低秩参数自适应及其在医学图像分割中的应用 显示英文标题

标题： tCURLoRA: Tensor CUR Decomposition Based Low-Rank Parameter Adaptation and Its Application in Medical Image Segmentation

摘要： 迁移学习通过利用预训练模型的知识，显著提升了目标任务的性能。 然而，随着深度神经网络的规模扩大，完整的微调在资源受限的环境中引入了大量的计算和存储挑战，限制了其广泛应用。 为了解决这个问题，参数高效的微调（PEFT）方法被开发出来，通过减少更新参数的数量来降低计算复杂度和存储需求。 尽管基于矩阵分解的PEFT方法，如LoRA，显示出潜力，但它们难以完全捕捉模型权重的高维结构特征。 相比之下，高维张量为神经网络权重提供了更自然的表示，能够更全面地捕捉高阶特征和多维交互。 在本文中，我们提出了tCURLoRA，一种基于张量CUR分解的新型微调方法。 通过将预训练的权重矩阵连接成一个三维张量并应用张量CUR分解，在微调过程中仅更新低阶张量组件，从而有效降低计算和存储开销。 实验结果表明，tCURLoRA在医学图像分割任务中优于现有的PEFT方法。 显示英文摘要

摘要： Transfer learning, by leveraging knowledge from pre-trained models, has significantly enhanced the performance of target tasks. However, as deep neural networks scale up, full fine-tuning introduces substantial computational and storage challenges in resource-constrained environments, limiting its widespread adoption. To address this, parameter-efficient fine-tuning (PEFT) methods have been developed to reduce computational complexity and storage requirements by minimizing the number of updated parameters. While matrix decomposition-based PEFT methods, such as LoRA, show promise, they struggle to fully capture the high-dimensional structural characteristics of model weights. In contrast, high-dimensional tensors offer a more natural representation of neural network weights, allowing for a more comprehensive capture of higher-order features and multi-dimensional interactions. In this paper, we propose tCURLoRA, a novel fine-tuning method based on tensor CUR decomposition. By concatenating pre-trained weight matrices into a three-dimensional tensor and applying tensor CUR decomposition, we update only the lower-order tensor components during fine-tuning, effectively reducing computational and storage overhead. Experimental results demonstrate that tCURLoRA outperforms existing PEFT methods in medical image segmentation tasks.