arXiv:2606.16388cs.LG2026-06

改进神经Tucker分解,提升稀疏张量补全的稳定性与精度

Robust Neural Tucker Factorization with Bias Correction and Adaptive Initialization

论文配图:Robust Neural Tucker Factorization with Bias Correction and Adaptive Initialization
图 1 · 摘自论文原文
  • 采用Kaiming初始化和输出层偏置修正,解耦全局均值与局部结构
  • 在三个真实数据集上性能优于原始模型,且计算开销极小
  • 适合处理交通、气候等高维稀疏张量补全任务

高维不完整(HDI)张量广泛应用于交通与气候领域,但观测稀疏导致补全困难。跨多模态领域的非线性动态与非平稳变化严重制约传统线性重建框架的效果。神经Tucker分解通过将潜在结构特征参数化到连续隐空间,克服了经典代数方法的低秩刚性约束。然而其性能仍受实现层面选择影响,尤其是参数初始化和输出映射的偏置配置。次优初始化常引发立方扩展交互空间中的方差爆炸,使后续非线性激活边界进入严重梯度饱和区;忽略专用平移参数则迫使交互权重隐式吸收全局统计偏差。本文提出一种简单而有效的神经Tucker分解模型(KaBiN),结合Kaiming均匀初始化与输出映射偏置修正。通过优雅解耦全局均值偏移与局部结构表示,构建高度稳定且条件良好的优化景观。在三个真实世界HDI张量数据集上的实验表明,KaBiN性能优于原始NeuTucF,同时引入极小计算开销。

原文摘要 · Abstract (English)

High-dimensional incomplete (HDI) tensors are widely used in traffic and climate applications, but sparse observations make accurate completion difficult. The intrinsic non-linear dynamics and non-stationary variations across distinct multi-modal fields severely hinder the efficacy of conventional linear reconstruction frameworks. Neural Tucker factorization provides an effective framework for modeling high-order interactions among tensor modes. By parameterizing underlying structural characteristics into continuous latent spaces, neural representations circumvent the rigid low-rank constraints of classical algebra. However, its performance can still be affected by implementation-level choices, especially parameter initialization and the bias configuration of the final output mapping. Suboptimal initializations frequently lead to variance explosion across the cubically expanded interaction spaces, driving the subsequent non-linear activation boundaries into severe gradient saturation zones, while the omission of a dedicated translation parameter forces interaction weights to implicitly absorb global statistical deviations. This paper proposes a simple yet effective neural Tucker factorization model with Kaiming initialization and bias correction (KaBiN) for HDI tensor completion. The proposed model utilizes Kaiming uniform initialization for the embedding and Tucker linear parameters, and adopts a simple bias correction in output mapping. By elegantly decoupling global mean shifts from local structural representations, the framework provides a highly stable and well-conditioned optimization landscape. Experiments on three real-world HDI tensor datasets show that KaBiN achieves better performance than the original NeuTucF, while introducing minimal computational overhead.

张量补全神经网络深度学习稀疏数据

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