arXiv:2508.06784cs.LGcs.AI2025-08

新模型用非线性张量分解,高效压缩高阶数据。

Mode-Aware Non-Linear Tucker Autoencoder for Tensor-based Unsupervised Learning

  • 用递归展开-编码-折叠策略,灵活处理高阶张量每维特征。
  • 计算复杂度随张量阶数线性增长,远优于传统方法。
  • 适合处理高阶、高维数据的压缩与聚类任务,如图像/视频分析。

高维数据,尤其是高阶张量,在自监督学习中面临巨大挑战。尽管基于MLP的自编码器(AE)被广泛使用,但其依赖展平操作会加剧维度灾难,导致模型过大、计算开销高且难以优化深层特征。现有张量网络虽通过张量分解缓解计算负担,但大多难以捕捉非线性关系。为此,本文提出模式感知的非线性托克尔自编码器(MA-NTAE)。MA-NTAE将经典托克尔分解推广至非线性框架,并采用拾取-展开策略,通过递归的展开-编码-折叠操作,实现高阶张量各维度的灵活编码,有效融入张量结构先验。显著地,MA-NTAE的计算复杂度随张量阶数呈线性增长,随模式维度呈比例增长。大量实验表明,相较于标准自编码器和当前张量网络,MA-NTAE在压缩与聚类任务中表现更优,尤其在高阶、高维张量上优势愈发明显。

原文摘要 · Abstract (English)

High-dimensional data, particularly in the form of high-order tensors, presents a major challenge in self-supervised learning. While MLP-based autoencoders (AE) are commonly employed, their dependence on flattening operations exacerbates the curse of dimensionality, leading to excessively large model sizes, high computational overhead, and challenging optimization for deep structural feature capture. Although existing tensor networks alleviate computational burdens through tensor decomposition techniques, most exhibit limited capability in learning non-linear relationships. To overcome these limitations, we introduce the Mode-Aware Non-linear Tucker Autoencoder (MA-NTAE). MA-NTAE generalized classical Tucker decomposition to a non-linear framework and employs a Pick-and-Unfold strategy, facilitating flexible per-mode encoding of high-order tensors via recursive unfold-encode-fold operations, effectively integrating tensor structural priors. Notably, MA-NTAE exhibits linear growth in computational complexity with tensor order and proportional growth with mode dimensions. Extensive experiments demonstrate MA-NTAE's performance advantages over standard AE and current tensor networks in compression and clustering tasks, which become increasingly pronounced for higher-order, higher-dimensional tensors.

张量分解自编码器非线性建模高维数据

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