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Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…

This paper presents the Tensor Product Network (TPNet), a novel neural architecture for efficient and accurate function approximation and PDE solving. The core of the proposal involves constructing the solution explicitly as a linear…

This paper studies the traffic state estimation (TSE) problem using sparse observations from mobile sensors. Most existing TSE methods either rely on well-defined physical traffic flow models or require large amounts of simulation data as…

The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…

We introduce and detail an atypical neural network architecture, called time elastic neural network (teNN), for multivariate time series classification. The novelty compared to classical neural network architecture is that it explicitly…

In this paper, we investigate a new variant of neural architecture search (NAS) paradigm -- searching with random labels (RLNAS). The task sounds counter-intuitive for most existing NAS algorithms since random label provides few information…

Tensor-valued data arise frequently from a wide variety of scientific applications, and many among them can be translated into an alteration detection problem of tensor dependence structures. In this article, we formulate the problem under…

In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…

The low-tubal-rank tensor model has been recently proposed for real-world multidimensional data. In this paper, we study the low-tubal-rank tensor completion problem, i.e., to recover a third-order tensor by observing a subset of its…

Structural equation modeling (SEM) and path analysis have long been central tools for studying complex causal relationships in the social and behavioral sciences, yet their reliance on parametric assumptions can lead to biased inference…

The accuracy and complexity of machine learning algorithms based on kernel optimization are limited by the set of kernels over which they are able to optimize. An ideal set of kernels should: admit a linear parameterization (for…

We propose a loop optimization algorithm based on nuclear norm regularization for tensor network. The key ingredient of this scheme is to introduce a rank penalty term proposed in the context of data processing. Compared to standard…

In deep neural networks, better results can often be obtained by increasing the complexity of previously developed basic models. However, it is unclear whether there is a way to boost performance by decreasing the complexity of such models.…

Over the past few years, various word-level textual attack approaches have been proposed to reveal the vulnerability of deep neural networks used in natural language processing. Typically, these approaches involve an important optimization…

The key challenge in neural architecture search (NAS) is designing how to explore wisely in the huge search space. We propose a new NAS method called TNAS (NAS with trees), which improves search efficiency by exploring only a small number…

Despite their simple intuition, convolutions are more tedious to analyze than dense layers, which complicates the transfer of theoretical and algorithmic ideas to convolutions. We simplify convolutions by viewing them as tensor networks…

In remote sensing, most segmentation networks adopt the UNet architecture, often incorporating modules such as Transformers or Mamba to enhance global-local feature interactions within decoder stages. However, these enhancements typically…

The demands for higher performance and accuracy in neural networks (NNs) never end. Existing tensor compilation and Neural Architecture Search (NAS) techniques orthogonally optimize the two goals but actually share many similarities in…

We provide a new interpretation of Hessian locally linear embedding (HLLE), revealing that it is essentially a variant way to implement the same idea of locally linear embedding (LLE). Based on the new interpretation, a substantial…

Efficient and interpretable spatial analysis is crucial in many fields such as geology, sports, and climate science. Tensor latent factor models can describe higher-order correlations for spatial data. However, they are computationally…