自注意力驱动的张量表示用于高阶数据恢复
Self-Attention Driven Tensor Representation for High-Order Data Recovery
把自注意力引入低秩张量分解的因子空间，用动态全局映射替代 MLP/CNN 的固定局部映射，可直接迁移到多光谱图像、视频、彩色图像等张量形式数据的补全与去噪任务中。
原文依据 we construct a novel paradigm called Self-Attention Driven Tensor Representation (SADTR)
摘要译文
由模型翻译 · 术语统一 · 请对照原文核对关键结论低秩张量表示（LRTR）是紧凑建模高阶数据的有效工具。尽管非线性 LRTR 模型能够更好地刻画真实世界中的非线性依赖关系，但现有方法大多依赖多层感知机（MLP）或卷积神经网络（CNN）的固定局部映射，限制了其建模复杂全局依赖的能力。为克服这一局限，我们构建了一种新范式，称为自注意力驱动的张量表示（SADTR），这是首个从自注意力角度建模非线性的框架。具体而言，我们设计了因子自表示机制以建立动态全局映射，从而在因子空间中自适应地捕获局部与非局部非线性依赖关系。此外，我们引入隐式稀疏表示，在施加稀疏性约束的同时避免引入额外的优化问题。由此，所提出的 SADTR 能够获得更精确的低秩表示。在理论上，我们给出了详细分析以证明 SADTR 的可恢复性。为验证 SADTR 的有效性，我们将其应用于三项具有代表性的高阶数据恢复任务。实验结果表明，SADTR 持续优于现有的最优 LRTR 方法。
英文原文摘要 1301 字符
Low-rank tensor representation (LRTR) is an effective tool for compactly modeling high-order data. While nonlinear LRTR models can better capture real-world nonlinear dependencies, most existing methods rely on fixed local mappings of multilayer perceptrons (MLPs) or convolutional neural networks (CNNs), limiting their ability to model complex global dependencies. To overcome this limitation, we construct a novel paradigm called Self-Attention Driven Tensor Representation (SADTR), which is the first framework that models nonlinearity from the perspective of self-attention. Specifically, we design a factor self-representation mechanism to establish dynamic global mapping, thereby adaptively capturing both local and non-local nonlinear dependencies in the factor space. Moreover, we introduce an implicit sparse representation to impose sparsity constraint while avoiding additional optimization problems. As a result, the proposed SADTR can achieve a more accurate low-rank representation. In theory, we provide a detailed analysis to demonstrate the recoverability of SADTR. To validate the effectiveness of SADTR, we apply it to three representative high-order data recovery tasks. Experimental results demonstrate that SADTR consistently outperforms existing state-of-the-art LRTR methods.