Spectra-Guided Neural Tucker Factorization

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.

Tensor factorization (TF) has been widely adopted for high-dimensional sparse data completion tasks. Despite significant progress, neural TF methods often struggle to capture complex cross-mode interactions and remain vulnerable to (extreme) data sparsity. To address these challenges, we propose a novel neural tensor factorization approach, termed Dual-Attention Convolution Expert Networks with Group-Level Contrastive Learning (DCGC). For the first problem, DCGC generates diverse non-linear alignment patterns of latent factors via a multi-channel convolution network, and leverages the gated dual-attention mechanism to drive the model to focus on more important output channels (i.e., convolution experts) and the aligned features. Furthermore, DCGC introduces a group-level contrastive learning strategy that aggregates positive samples with identical feedback levels while separating negative samples across different levels. This strategy injects high-quality self-supervised signals to mitigate data sparsity. Extensive experiments conducted on five datasets demonstrate that our DCGC outperforms the state-of-the-art methods in sparse tensor completion for traffic and recommendation applications. Code to reproduce the experimental results in the paper is available at https://github.com/ku1z/DCGC.

Many biomedical challenges can be posed as tensor completion problems where the observed entries of a multidimensional array (a tensor) are used to impute the missing values. In such settings, incorporating side information about the modes of the tensor, such as gene-gene similarity, can significantly enhance the solutions of the completion problem. Most existing tensor completion methods can only incorporate side information in the form of matrices. In this study, we introduce a novel framework to incorporate side information in the form of tensors. Our new approach, called Coupled Tensor-Tensor Completion (CTTC), leverages the hidden connections among multimodal tensors to improve tensor completion performance. In addition to practical utility, CTTC has theoretical foundations in distance metric learning and group theory. We derive an alternating algorithm to solve the CTTC optimization problem and establish its convergence to a stationary point. Finally, we show that CTTC outperforms state-of-the-art tensor completion methods at predicting drug effects. Results: Compared with other tensor completion methods, including HaLRTC, CTRC, Cell, and NTDDR, CTTC demonstrates superior run-time and RSE tensor completion accuracy on two benchmark datasets, DTD and LINCS.